pid2
and pidstd2
Model Objects: Represent, analyze, and use 2-DOF PID controllers for control
designThe new numeric LTI models pid2
and pidstd2
are specialized for modeling
two-degree-of-freedom (2-DOF) PID controllers. These are analogous
to the 1-DOF PID models pid
and pidstd
.
Use pid2
and pidstd2
to
represent a 2-DOF PID controller directly with the PID parameters,
expressed in parallel (pid2
) or standard (pidstd2
)
form. For example, C2 = pid2(Kp,Ki,Kd,Tf,b,c)
creates
a 2-DOF PID controller in parallel form with proportional, integral,
and derivative gains Kp
, Ki
,
and Kd
, derivative filter time constant Tf
,
and setpoint weights b
and c
.
In previous releases, to model a 2-DOF PID controller, you had to
derive the controller's equivalent transfer function (or other model),
and could not directly store the 2-DOF PID parameters.
The pid2
and pidstd2
commands
can also convert to PID form any type of LTI object that represents
a 2-DOF PID controller.
This release also includes new functions to help you work with 2-DOF PID controllers. These functions include:
getComponents
—
Extract two SISO control components from a 2-DOF pid2
or pidstd2
controller.
make1DOF
and make2DOF
— Convert 1-DOF pid
and pidstd
controllers
to 2-DOF pid2
and pidstd2
controllers,
and vice versa.
piddata2
and pidstddata2
— Access parameters
of 2-DOF PID controllers.
For more information about working with 2-DOF PID controller objects, see:
pidtune
commandYou can now use pidtune
and PID Tuner to
tune all parameters of a two-degree-of-freedom (2–DOF) PID
controller, including the setpoint weights b and c.
When you call pidtune
or open the PID Tuner app
with a plant, the software automatically tunes all parameters of the
block to achieve a balance between performance and robustness. When
you use the Response Time and Transient Behavior sliders to adjust
that balance, PID Tuner adjusts all parameters, including b and c if
necessary.
PID Tuner and pidtune
also include options
for tuning 2-DOF PID controllers with fixed setpoint weights, such
as I-PD (b = 0, c = 0) and P-ID
(b = 1, c = 0).
For more information, see:
In PID Tuner, you can now make the current controller design the baseline controller at any time. This feature allows to you compare the performance of a PID Tuner controller design to the performance of controllers obtained by further adjustment of the design.
To make the current PID Tuner design the baseline controller,
by click the Export arrow
and select Save
as Baseline
.
When you do so, the current Tuned response becomes the Baseline response. Further adjustment of the current design creates a new Tuned response line.
Previously, you could only designate a baseline controller when
you opened the PID Tuner using the syntax pidTuner(sys,C0)
.
For more information about analyzing controller performance in PID Tuner, see Analyze Design in PID Tuner.
The default value is now false
for Input
delay, Output delay, and Internal
delay, in the Fixed Entries tab of LPV
System Block Parameters dialog box. A false
value
means that model delays are treated as free during simulation.
For information about changing the default values, see the LPV System block reference page.
By default, response plots that show phase response, such as Bode and Nichols plots, display the exact phase. You can make these plots wrap the phase into the interval [0º,360º) by unchecking Unwrap Phase in the plot Property Editor. Previously, unchecking this option caused the plots to wrap the phase into [–180º,180º). The change makes it easier to visualize 180º phase crossings on analysis plots.
The default plot behavior (exact or unwrapped phase) is unchanged.
The behavior of commands that return numerical phase response data,
such as bode
, is also unchanged. These commands
always return the unwrapped phase.
Controller tuning with the PID Tuner app or the pidtune
command now
yields better disturbance rejection by default. For a given target
phase margin, the tuning algorithm selects PID coefficients that achieve
a balance between reference tracking and input disturbance rejection.
If you require more disturbance rejection or better reference tracking
than the default algorithm provides, PID Tuner and pidtune
have a
new Design Focus option. Use this option to alter the balance that
the tuning algorithm sets between reference tracking and input disturbance
rejection. For instance, setting the design focus to reference tracking
improves the reference tracking performance of the tuned controller,
with some cost to disturbance rejection. Similarly, setting the design
focus to input disturbance rejection improves rejection with some
cost to reference tracking. Changing design focus is most effective
when tuning PID and PIDF controllers,
rather than controllers with fewer free parameters, such as PI.
To use the Design Focus option in PID Tuner, click Options and select a design focus from the Focus menu.
You can still use the Response Time and Transient Behavior sliders to further adjust the balance between reference tracking and input disturbance rejection.
To specify a design focus for command-line
tuning with pidtune
, use pidtuneOptions
to
set the DesignFocus
option. For example, the following
commands design a PIDF controller for the plant G
with
a crossover frequency of 10 rad/s, specifying reference tracking as
the design focus.
opt = pidtuneOptions('DesignFocus','reference-tracking'); C = pidtune(G,'pidf',10,opt);
For more information about using the design focus option, see:
For more information about using PID Tuner, see Designing PID Controllers with the PID Tuner. For more information about command-line PID tuning, see PID Controller Design at the Command Line.
You can now specify code generation settings in the LPV System block. You specify these settings in the Code Generation tab of the block parameters dialog box.
For more information on Linear Parameter-Varying models, see Linear Parameter-Varying Models.
connect
command syntax for specifying analysis point locationsWhen you interconnect dynamic system models using the connect
command,
you can now specify analysis point locations as an input argument
to the command. The following syntax creates a dynamic system model
with analysis points by interconnecting multiple models sys1,sys2,...,sysN
:
sys = connect(sys1,sys2,...,sysN,inputs,outputs,APs);
inputs
and outputs
are
string vectors that specify the names of the inputs and outputs of
the interconnected model. APs
is a string vector
that lists the signal locations at which to insert analysis points.
The software automatically inserts an AnalysisPoint
block
with channels corresponding to these locations. Previously, you had
to create AnalysisPoint
blocks separately and
include them in the list of models to connect.
For example, consider the following control system.
Use connect
to build this system with an
analysis point at the plant input, u.
C.InputName = 'e'; C.OutputName = 'u'; G.InputName = 'u'; G.OutputName = 'y'; Sum = sumblk('e = r-y'); T = connect(G,C,Sum,'r','y','u');
These commands return a generalized state-space (genss
)
model with one AnalysisPoint
block. You can use
the analysis point, for example, to extract the open-loop response
of the system at u:
L = getLoopTransfer(T,'u',-1);
For a more detailed example, see Mark
Analysis Points in Closed-Loop Models. For more information
about using analysis points in dynamic system models, see the AnalysisPoint
reference
page.
The LTI Viewer app is now called Linear System Analyzer. The functionality of the app is unchanged.
You can access Linear System Analyzer in two ways:
From the MATLAB^{®} desktop, in the Apps tab, in the Control System Design and Analysis section, click Linear System Analyzer.
From the MATLAB command line, use the linearSystemAnalyzer
function.
Previously, this function was called ltiview
.
Using ltiview
to open Linear System Analyzer
does not generate an error in this release, but the function might
be removed in a future release.
If you have scripts or functions that use ltiview
,
consider replacing those calls with linearSystemAnalyzer
.
sisotool
function renamed to controlSystemDesigner
The sisotool
function is now called controlSystemDesigner
.
The controlSystemDesigner
opens the SISO Design
Tool. You can also access SISO Design Tool from MATLAB desktop.
In the Apps tab, in the Control System
Design and Analysis section, click Control System
Designer.
Using sisotool
to open SISO Design Tool
does not generate an error in this release, but the function might
be removed in a future release.
If you have scripts or functions that use sisotool
,
consider replacing those calls with controlSystemDesigner
.
getBlockValue
returns all block values in structure A new syntax of the getBlockValue
command
now returns the current values of all Control Design Blocks of a generalized
model (genss
) in a structure. The following syntax
returns a structure, S
, whose field names are
the names of the blocks in the genss
model M
.
The values of the fields are numerical LTI models or numerical values
equal to the current values of the corresponding Control Design Blocks.
S = getBlockValue(M)
This syntax lets you transfer the block values from one generalized model to another model that uses the same Control Design Blocks, as follows:
S = getBlockValue(M1); setBlockValue(M2,S);
For more information, see the getBlockValue
reference
page.
Previously, the syntax getBlockValue(M)
returned
the current values of the blocks of M
as a vector
list:
[Val1,Val2,...,ValN] = getBlockValue(M)
Now, using this syntax causes an error. You can still obtain block values in a list by specifying the block names as input arguments, as follows.
[Val1,Val2,...,ValN] = getBlockValue(M,Blkname1,Blkname2,...,BlknameN)
Functionality | What Happens When You Use This Functionality? | Use This Instead | Compatibility Considerations |
---|---|---|---|
[Val1,Val2,...] = getBlockValue(M) | Error | S = getBlockValue(M) | getBlockValue(M) now returns a structure
containing current values of all blocks. Update scripts and functions
that use getBlockValue(M) to use output structure. |
ltiview function | Still works | linearSystemAnalyzer | Consider replacing ltiview with linearSystemAnalyzer in
scripts and functions. |
sisotool function | Still works | controlSystemDesigner | Consider replacing sisotool with controlSystemDesigner |
This release introduces the LPV System block. You use this block to represent Linear Parameter Varying (LPV) systems in Simulink^{®}.
An LPV system is a linear state-space system whose dynamics vary as a function of certain time-varying parameters called the scheduling parameters. Mathematically, an LPV system is represented as:
$\begin{array}{l}dx\left(t\right)=A\left(p\right)x\left(t\right)+B\left(p\right)u\left(t\right)\\ y\left(t\right)=C\left(p\right)x\left(t\right)+D\left(p\right)u\left(t\right)\\ x\left(0\right)={x}_{0}\end{array}$
where
u(t)
are the inputs
y(t)
the outputs
x(t)
are the model states with
initial value x0
$dx\left(t\right)$ is the state derivative vector $\dot{x}$ for continuous-time systems and the state update vector $x\left(t+\Delta T\right)$ for discrete-time systems. ΔT is the sample time.
A(p)
, B(p)
, C(p)
and D(p)
are
the state-space matrices parameterized by the scheduling parameter
vector p
.
The parameters p = p(t)
are measurable
functions of the inputs and the states of the model. They can be a
scalar quantity or a vector of several parameters. The set of scheduling
parameters define the scheduling space over which
the LPV model is defined.
The linear system can be extended to contain offsets in the system's states, input, and output signals. Mathematically, the LPV system is represented by the following equations:
$\begin{array}{l}dx\left(t\right)=A\left(p\right)x\left(t\right)+B\left(p\right)u\left(t\right)+\left(\overline{dx}\left(p\right)-A\left(p\right)\overline{x}\left(p\right)-B(p)\overline{u}(p)\right)\\ y\left(t\right)=C\left(p\right)x\left(t\right)+D\left(p\right)u\left(t\right)+\left(\overline{y}\left(p\right)-C\left(p\right)\overline{x}\left(p\right)-D(p)\overline{u}(p)\right)\\ x\left(0\right)={x}_{0}\end{array}$
$\overline{dx}\left(p\right),\text{}\overline{x}\left(p\right),\text{}\overline{u}\left(p\right),\text{}\overline{y}\left(p\right)$ are
the offsets in the values of dx(t)
, x(t)
, u(t)
and y(t)
at
a given parameter value p = p(t)
.
LPV system can be thought of as a first-order approximation of a nonlinear system over a grid of scheduling parameter values. For example, you can linearize a Simulink model between a given input and output ports over a grid of equilibrium operating conditions. The values of the model inputs, outputs and state values at each operating point define the offsets, while the linear state-space models obtained by linearization define the state-space data. The LPV system thus generated can work as a proxy for the original model for facilitating faster simulations and control system design. For more information, see Linear Parameter-Varying Models.
The LPV System block accepts the state-space
matrices and offsets over a grid of scheduling parameter values. The
state-space matrices must be specified as an array of
model objects. The SamplingGrid
property
of the array defines the scheduling parameters for the LPV system.
For examples of using this block, see:
Use the Kalman Filter block to estimate the states of linear time-invariant and linear time-varying systems online. The states are estimated as new data becomes available during the operation of the system. The system can be continuous-time or discrete-time. You can generate code for this block using code generation products such as Simulink Coder™.
You can access this block from the Control System Toolbox library. For an example of using this block, see State Estimation Using Time-Varying Kalman Filter.
The new AnalysisPoint
block is a unit-gain
Control Design Block that you can insert anywhere in a control system
model to mark points of interest for linear analysis and tuning. Incorporate AnalysisPoint
blocks
into generalized state-space (genss
) control
system models by interconnecting them with numeric LTI models and
other Control Design Blocks. When you mark a location in a control
system model with an AnalysisPoint
block, you
can use that location for linear analysis tasks, such as extracting
responses using getIOTransfer
or getLoopTransfer
.
You can also use such locations to specify design requirements for
control system tuning using systune
or Control
System Tuner (requires Robust Control Toolbox™ software).
For more information about using AnalysisPoint
blocks,
see:
AnalysisPoint
replaces the loopswitch
Control
Design Block.
Models that contain loopswitch
blocks continue
to work, for backward compatibility. However, it is recommended that
you use AnalysisPoint
blocks in new models. If
you have scripts or functions that use loopswitch
blocks,
consider updating them to use AnalysisPoint
instead.
For documentation of loopswitch
, see loopswitch
in
the R2014a documentation.
The pidtool
function is now called pidTuner
.
To open PID Tuner, use the pidTuner
command or,
in the MATLAB desktop Apps tab, click PID
Tuner.
Using pidtool
does not generate an error
in this release, but the function may be removed in a future release.
If you have scripts that use pidtool
, consider
replacing those calls with pidTuner
.
The getSwitches
function is now called getPoints
to
match the renaming of loopswitch
to AnalysisPoint
.
Using getSwitches
does not generate an error
in this release, but the function may be removed in a future release.
If you have scripts or functions that use getSwitches
,
consider replacing those calls with getPoints
.
Functionality | What Happens When You Use This Functionality? | Use This Instead | Compatibility Considerations |
---|---|---|---|
loopswitch Control Design Block | Still works | AnalysisPoint | Consider replacing loopswitch with AnalysisPoint in
scripts and functions. |
getSwitches function | Returns loopswitch and AnalysisPoint blocks
in model | getPoints | Consider replacing getSwitches with getPoints in
scripts and functions. |
pidtool function | Still works | pidTuner | Consider replacing pidtool with pidTuner in
scripts. |
The redesigned PID Tuner streamlines workflows for interactively tuning PID controllers for reference tracking and disturbance rejection.
To access the PID Tuner, use the pidtool
command.
For example, to tune a PI controller for an LTI model, G
:
pidtool(G,'PI')
For more information about the PID Tuner, see Designing PID Controllers with the PID Tuner.
If you have System Identification Toolbox™ software, you can use PID Tuner to fit a linear model to the measured SISO response data from your system and tune a PID controller for the resulting model. For example, if you want to design a PID controller for a manufacturing process, you can start with response data from a bump test on your system.
PID Tuner uses system identification to estimate an LTI model from the response data. You can interactively adjust the identified parameters to obtain an LTI model with a response that fits your response data. PID Tuner automatically tunes a PID controller for the estimated model. You can then interactively adjust the performance of the tuned control system, and save the estimated plant and tuned controller.
For an example, see Interactively Estimate Plant Parameters from Response Data.
freqsep
function for decomposing a linear system into fast dynamics and slow dynamicsUse the new freqsep
command for separating
numeric LTI models into fast and slow components. freqsep
allows
you to specify the cutoff frequency about which the model is decomposed.
The slow component contains poles with natural frequency below the
cutoff frequency. The fast component contains poles at or above the
cutoff.
For more information, see the freqsep
reference
page.
damp
command display includes time constant information When you call the damp
command with no
output arguments, the display now includes the time constant for each
pole. The time constant is calculated as follows:
$$\tau =\frac{1}{{\omega}_{n}\zeta}.$$
ω_{n} is the natural frequency of the pole, and ζ is its damping ratio.
For a discrete-time system with unspecified sample time (Ts
= -1
), damp
now calculates the natural
frequency and damping ratio by assuming Ts = 1
.
Previously, the software returned []
for the natural
frequency and damping ratio of such systems.
damp
returns outputs in order of increasing
natural frequency. Therefore, this change can result in reordered
poles for systems with unspecified sample times.
For more information on the outputs, see the damp
reference
page.
SamplingGrid
property for tracking dependence of array of sampled models on variable valuesIn Control System Toolbox™, you can derive arrays of numeric
or generalized LTI models by sampling one or more independent variables.
The new SamplingGrid
property of LTI models tracks
the variable values associated with each model in such an array.
Set this property to a structure whose fields are the names of the sampling variables and contain the sampled variable values associated with each model. All sampling variables should be numeric and scalar valued, and all arrays of sampled values should match the dimensions of the model array.
For example, suppose you create a 11-by-1 array of linear models, sysarr
,
by taking snapshots of a linear time-varying system at times t
= 0:10
. The following code stores the time samples with
the linear models.
sys.SamplingGrid = struct('time',0:10)
For an additional examples, see:
connect
commandBy default, the connect
command discards
states that do not contribute to the dynamics in the path between
the inputs and outputs of the interconnected system. You can now optionally
retain such unconnected states. This option can be useful, for example,
when you want to compute the interconnected system response from known
initial state values of the components.
To instruct connect
to retain unconnected
states, use the new connectOptions
command with
the existing connect
command.
For more information, see the connectOptions
reference
page.
connect
command always returns state-space or frequency response data model The connect
command now always returns
a state-space model, such as an ss
, genss
,
or uss
model, unless one or more of the input
models is a frequency response data model. In that case, connect
returns
a frequency response data model, such as an frd
or genfrd
model.
For more information, see the connect
reference
page.
In previous releases, connect
returned
a tf
or zpk
model when all
input models were tf
or zpk
models.
Therefore, connect
might now return state-space
models in cases where it previously returned tf
or zpk
models.
updateSystem
command for updating dynamic system data in a response plotThe new updateSystem
command replaces the
system data used to compute a response plot with data derived from
a different dynamic system, and updates the plot. updateSystem
is
useful, for example, to cause a plot in a GUI to update in response
to interactive input.
For more information, see:
updateSystem
reference
page
getLoopID
renamed to getSwitches
The getLoopID
function is now called getSwitches
to
more clearly reflect the purpose of the function. Using getLoopID
does
not generate an error in this release, but the function may be removed
in a future release.
If you have scripts or functions that use getLoopID
,
consider replacing those calls with getSwitches
.
LoopID
property of loopswitch
renamed to Location
The LoopID
property of the loopswitch
model
component is now called Location
to more clearly
reflect the purpose of the property. Using LoopID
does
not generate an error in this release, but the name may be removed
in a future release.
If you have scripts or functions that use the LoopID
property,
consider updating your code to use Location
instead.
The PID Tuner now has a Transient behavior slider
for emphasizing either reference tracking or disturbance rejection.
When you open the PID Tuner, the tool starts in the Time
domain
design mode, displaying a step plot of the reference
tracking response. The new Transient behavior slider
is beneath the Response time slider.
You can use the Transient behavior slider when:
The tuned system's disturbance rejection response is too sluggish for your requirements. In this case, try moving the Transient behavior slider to the left to make the controller more aggressive at disturbance rejection.
The tuned system's reference tracking response has too much overshoot for your requirements. In this case, try moving the Transient behavior slider to the right to increase controller robustness and reduce overshoot.
In Frequency domain
design mode,
the PID Tuner has Bandwidth and Phase
margin sliders. These sliders are the frequency-domain
equivalents of the Response time and Transient
behavior sliders, respectively.
New Control Design Blocks allow you to specify more control structures and more types of constraints for fixed-structure control system tuning in MATLAB:
ltiblock.pid2
— Tunable
two-degree-of-freedom PID controller
loopswitch
— Control Design
Block for specifying feedback loop opening locations in a tunable genss
model
of a control system
You can use these Control Design Blocks to build control systems
for tuning with Robust Control Toolbox tuning commands such as systune
and looptune
.
For more information, see the ltiblock.pid2
and loopswitch
reference
pages.
New commands allow you to compute open-loop and closed-loop responses from a Generalized LTI model representing a control system.
getLoopTransfer
—
Compute point-to-point open-loop response of a Generalized LTI model
of a control system, at a loop-opening site defined by a loopswitch
block.
The new command getLoopID
returns
a list of such loop-opening sites.
getIOTransfer
—
Extract the closed-loop response from a specified input to a specified
output of a control system.
These commands are particularly useful for validating the response
functions of control systems tuned using Robust Control Toolbox tuning
commands such as systune
.
Additionally, the new showTunable
command
displays the current value of tunable components in a generalized
LTI model of a control system. This command is useful for querying
tuned parameter values of control systems tuned using Robust Control Toolbox tuning
commands such as systune
.
For more information, see the reference pages for these new commands and the following topics:
The new 'elem'
flag causes elementwise operation
on model arrays of the model query commands:
For example, for an array, sysarray
, of dynamic
system models,
B = hasdelay(sysarray,'elem');
returns a logical array. B
of the same size
as sysarray
indicating whether the corresponding
model in sysarray
contains a time delay. Without
the 'elem'
flag,
B = hasdelay(sysarray);
returns a scalar logical value that is equal to 1
if
any entry in sysarray
contains a time delay.
isfinite
and isstable
now
return a scalar logical value when invoked without the 'elem'
flag.
Previously, isfinite
and isstable
returned
a logical array by default.
If you have scripts or functions that use isfinite(sysarray)
or isstable(sysarray)
,
replace those calls with isfinite(sysarray,'elem')
or isstable(sysarray,'elem')
to
perform an elementwise query and obtain a logical array.
Control System Toolbox software includes two new frequency analysis commands:
getPeakGain
— Peak gain
of frequency response of a dynamic system model
getGainCrossover
— Frequencies
at which system gain crosses a specified gain level
For more information, see the getPeakGain
and getGainCrossover
reference
pages.
These functions use the SLICOT library of numerical algorithms. For more information about the SLICOT library, see http://slicot.org.
A new syntax for pidtune
lets you specify
a target crossover frequency directly as an input argument. For example,
the following command designs a PI controller, C
,
for a plant model sys
. The command also specifies
a target value wc
for the 0 dB gain crossover
frequency of the open-loop response L = sys*C
.
C = pidtune(sys,'pi',wc);
Previously, you had to use pidtuneOptions
to
specify a target crossover frequency.
For more information, see the pidtune
reference
page.
For discrete-time dynamic system models, the input signal applied
by impulse
is now a unit area pulse of length Ts
and
height 1/Ts
. Ts
is the sampling
time of the discrete-time system. Previously, impulse
applied
a pulse of length Ts
and unit height.
Results of this change include:
The amplitude of the impulse response calculated by impulse
and impulseplot
is
scaled by 1/Ts
relative to previous versions.
Discretization using the impulse-invariant ('impulse'
)
method of c2d
returns a model that is scaled
by Ts
compared to previous releases. This scaling
ensures a close match between the frequency responses of the continuous-time
model and the impulse-invariant discretization as Ts
approaches
zero (for strictly proper models). In previous releases, the frequency
responses differed by a factor of Ts
.
The d2c
command now supports the first-order
hold (FOH) method for converting a discrete-time dynamic system model
to continuous time. The FOH method converts by performing linear interpolation
of the inputs, assuming the control inputs are piecewise linear over
the sampling period. For more information about using this method,
see the d2c
reference
page and Continuous-Discrete
Conversion Methods.
The tzero
command computes the invariant
zeros of SISO and MIMO dynamic system models. For minimal realizations, tzero
computes
transmission zeros. tzero
also returns the normal
rank of the transfer function of the system. For more information,
see the tzero
reference
page.
Identified linear models that you create using System Identification Toolbox software can now be used directly with Control System Toolbox analysis and compensator design commands. In prior releases, doing so required conversion to Control System Toolbox LTI model types.
Identified linear models can be used directly with:
Any Control System Toolbox or Robust Control Toolbox functions that operate on dynamic systems, including:
For a complete list of these functions, enter:
methods('DynamicSystem')
Analysis and design tools such as ltiview
, sisotool
and pidtool
.
The LTI System block in Simulink models.
Functionality | What Happens When You Use This Functionality? | Use This Instead | Compatibility Considerations |
---|---|---|---|
impulse(sys) and impulseplot(sys) ,
for discrete-time sys | Still works. | N/A | Amplitude of response is scaled by 1/Ts compared
to previous versions. Ts is sampling time of sys . |
c2d(sys,Ts,'impulse') | Still works. | N/A | Resulting discretized model is scaled by Ts compared
to previous releases. |
[y,t] = impulse(sys,Tfinal) [y,t]
= step(sys,Tfinal) [y,t,x] = initial(sys,Tfinal) | For discrete-time sys with undefined sample
time (Ts=-1 ), Tfinal is interpreted
as the number of sampling periods to simulate. | N/A | Expect the number of simulation data points to be Tfinal
+ 1 instead of Tfinal . |
You can now use formula strings to specify the behavior of summing
junctions with sumblk
. For example, to create
a summing junction, S
, that takes the difference
between signals r
and y
to produce
signal e
, enter the following command:
S = sumblk('e = r-y');
The following new commands allow you to examine and set the values of Control Design Blocks in Generalized LTI Models:
getValue
—
Get nominal value of Generalized Model (replaces getNominal
)
setValue
—
Modify value of Control Design Block
getBlockValue
—
Get nominal value of Control Design Block in Generalized Model
setBlockValue
—
Set value of Control Design Block in Generalized Model
showBlockValue
—
Display nominal values of Control Design Blocks in Generalized Model
For more information about these commands, see the reference pages for each command.
Functionality | What Happens When You Use This Functionality? | Use This Instead | Compatibility Considerations |
---|---|---|---|
delay2z | Errors | absorbDelay | Replace delay2z with absorbDelay . |
getNominal | Errors | getValue | Replace getNominal with getValue . |
Scale and Info properties
of realp parameter | Errors | None | None |
sumblk('a','b','c','+-') | Still works | sumblk('a=b-c') | Use new formula-based syntax for sumblk . |
Control System Toolbox includes new model objects that you
can use to represent systems with tunable components. You can use
these models for parameter studies or controller synthesis using hinfstruct
(requires Robust Control Toolbox).
The new model types include:
Control Design Blocks—Parametric components that are the building blocks for constructing tunable models of control systems. Control Design Blocks include:
realp
—Tunable
real parameter
ltiblock.gain
—Tunable
static gain block
ltiblock.tf
—Fixed-order
SISO transfer function with tunable coefficients
ltiblock.ss
—Fixed-order
state-space model with tunable coefficients
ltiblock.pid
—One-degree-of-freedom
PID controller with tunable coefficients
Generalized
Matrices—Matrices that include parametric (tunable)
values. Generalized matrices are genmat
models.
Generalized and Uncertain LTI Models—Models representing systems that have both fixed and tunable coefficients. Generalized LTI models include:
These models arise from interconnections between numeric LTI
models (such as tf
, ss
,
or frd
) and Control Design Blocks. You can also
create genss
models by using the tf
or ss
commands
with one or more realp
or genmat
inputs.
This release also adds new functions for working with generalized models:
getNominal
—Nominal value
of generalized model
replaceBlock
—Replace
Control Design Blocks in generalized model
nblocks
—Number
of blocks in generalized model
isParametric
—
Determine if model has tunable blocks
getLFTModel
—Decompose
generalized model
For more information about the new model types and about modeling systems that contain tunable coefficients, see the following in the Control System Toolbox User's Guide:
All linear model
objects now have a TimeUnit
property for
specifying unit of the time variable, time delays in continuous-time
models, and sampling time in discrete-time models. The default time
units is seconds. You can specify the time units, for example, as
hours. See Specify
Model Time Units for examples.
Frequency-response data ( frd
and genfrd
)
models also have a new FrequencyUnit
property for
specifying units of the frequency vector. The default frequency units
is rad/TimeUnit
, where TimeUnit
is
the system time units. You can specify the units, for example as KHz,
independently of the system time units. See Specify
Frequency Units of Frequency-Response Data Model for examples.
If your code uses the Units
property of frequency-response
data models, it continues to work as before.
See the model reference pages for available time and frequency units options.
Changing the TimeUnit
and FrequencyUnit
properties
changes the overall system behavior. If you want to simply change
the time and frequency units without modifying system behavior, use chgTimeUnit
and chgFreqUnit
,
respectively.
The time and frequency units of the model appear on the response plots by default. For multiple systems, the units of the first system are used. You can change the units of the time and frequency axes:
Graphically, using the following editors:
Programmatically, by setting the following properties of plots:
TimeUnits
for time-domain plots
using timeoptions
FreqUnits
for frequency-domain
plots using, for example, bodeoptions
New requirements for creating pid
and pidstd
controller
objects ensure that the derivative filter pole is always stable.
For a discrete-time pid
controller
with a derivative filter (Tf
≠ 0) and Dformula
set
to 'ForwardEuler'
, the sampling time Ts
must
be less than 2*Tf
.
For a discrete-time pidstd
controller
with a derivative filter (N
≠ Inf
)
and Dformula
set to 'ForwardEuler'
,
the sampling time Ts
must be less than 2*Td/N
.
The Trapezoidal
value for DFormula
is
not available for a discrete-time pid
or pidstd
controller
with no derivative filter (Tf = 0
or N
= Inf
).
On loading pid
or pidstd
controllers
saved under previous versions, the software changes certain properties
of controllers that do not have stable derivative filter poles.
For a discrete-time pid
controller
with a derivative filter (Tf
≠ 0), Dformula
set
to 'ForwardEuler'
, and sampling time Ts
≥ 2*Tf
,
the derivative filter time is reset to Tf = Ts
.
For a discrete-time pidstd
controller
with a derivative filter (N
≠ Inf
), Dformula
set
to 'ForwardEuler'
, the sampling time Ts
≥ 2*Td/N
,
the derivative filter constant is reset to N = Td/Ts
.
For a discrete-time pid
or pidstd
controller
with no derivative filter and DFormula = 'Trapezoidal'
,
the derivative filter integrator formula is reset to DFormula
= 'ForwardEuler'
.
The software issues a warning when it changes any of these values. If you receive such a warning, validate your controller to ensure that the new values achieve the desired performance.
You can now express discrete-time tf
and zpk
models
in terms of the inverse shift operator q^-1
. The
variable q^-1
is equivalent to z^-1
.
Note:
This new definition is consistent with the System Identification Toolbox definition
of |
Use the new variable by setting the Variable
property
of a tf
or zpk
model to q^-1
.
For example, entering:
H = tf([1 2 3],[5 6 7],0.1,'Variable','q^-1')
creates the following discrete-time transfer function:
Transfer function: 1 + 2 q^-1 + 3 q^-2 ------------------- 5 + 6 q^-1 + 7 q^-2 Sampling time (seconds): 0.1
When you set Variable
to q^-1
, tf
interprets
the numerator and denominator vectors as ascending powers of q^-1
.
This release introduces specialized tools for modeling and designing PID controllers.
The new PID Tuner GUI lets you interactively tune a PID controller for your required response characteristics. Using the GUI, you can adjust and analyze your controller's performance with response plots, such as reference tracking, load disturbance rejection, and controller effort, in both time and frequency domains.
The PID Tuner supports all types of SISO plant models, including:
Continuous- or discrete-time plant models
Stable, unstable, or integrating plant models
Plant models that include I/O time delays or internal time delay
For more information about using PID Tuner, see:
Designing PID Controllers in the Control System Toolbox Getting Started Guide
The new demo Designing PID for Disturbance Rejection with PID Tuner
The new pidtune
command lets you tune PID
controller gains at the command line.
pidtune
automatically tunes the PID gains
to balance performance (response time) and robustness (stability margins).
You can specify your own response time and phase margin targets using
the new pidtuneOptions
command.
pidtune
supports all types of SISO plant
models, including:
Continuous- or discrete-time plant models.
Stable, unstable, or integrating plant models.
Plant models that include I/O time delays or internal time delays.
Arrays of plant models. If sys
is
an array, pidtune
designs a separate controller
for each plant in the array.
For additional information, see:
The pidtune
and pidtuneOptions
reference
pages
The new Control System Toolbox demo Designing Cascade Control System with PI Controllers
The new LTI model objects pid
and pidstd
are
specialized for modeling PID controllers.
With pid
and pidstd
you
can model a PID controller directly with the PID parameters, expressed
in parallel (pid
) or standard (pidstd
)
form. The pid
and pidstd
commands
can also convert to PID form any type of LTI object that represents
a PID controller.
Previously, to model a PID controller, you had to derive the controller's equivalent transfer function (or other model), and could not directly store the PID parameters.
For additional information, see the pid
and pidstd
reference
pages
This release includes improvements to the PID Tuning options in the Automated Tuning pane of SISO Design Tool.
In addition to the Robust Response Time tuning algorithm, SISO Design Tool offers a collection of classical design formulas, including the following:
Approximate M-Constrained Integral Gain Optimization (MIGO) Frequency Response
Approximate MIGO Step Response
Chien-Hrones-Reswick
Skogestad Internal Model Control (IMC)
Ziegler-Nichols Frequency Response
Ziegler-Nichols Step Response
For information about using SISO Design Tool, see SISO Design Tool in the Control System Toolbox User's Guide. For specific information about the automatic PID Tuning options in SISO Design Tool, see PID Tuning in the Control System Toolbox User's Guide.
You can now analyze a controller design for multiple models simultaneously using the SISO Design Tool. This feature helps you analyze whether the controller satisfies design requirements on a system whose exact dynamics are not known and may vary.
System dynamics can vary because of parameter variations or
different operating conditions. You represent variations in system
dynamics of the plant (G
), sensor (H
),
or both in a feedback structure using arrays of LTI
models. Then, design a controller for a nominal model in the
array and analyze that the controller satisfies the design requirements
on the remaining models using the design and analysis plots. For more
information, see:
Control Design Analysis of Multiple Models in the Control System Toolbox documentation.
Reference Tracking of a DC Motor with Parameter Variations demo in Simulink Control Design™ software.
The output of the repsys
command
when called with a single dimension argument has changed.
In prior versions, the output of repsys(sys,N)
was
the same as that of append(sys,...,sys)
.
Now, repsys(sys,N)
returns the same result
as repsys(sys,[N N])
.
The results of other syntaxes for repsys
have
not changed.
Code that depends upon the previous result of repsys(sys,N)
no
longer returns that result. To obtain the previous result, replace repsys(sys,N)
with sys*eye(N)
.
The c2d
command can now approximate fractional
time delays when discretizing linear models with the tustin
or matched
methods.
The new c2dOptions
command lets you specify an
optional Thiran all-pass filter. The Thiran filter approximates fractional
delays for improved phase matching between continuous and discretized
models. Previously, c2d
rounded fractional time
delays to the nearest multiple of the sampling time when using the tustin
or matched
methods.
For more information, see the c2d
and c2dOptions
reference
pages and Continuous-Discrete
Conversion Methods in the Control System Toolbox User
Guide.
New commands c2dOptions
, d2dOptions
,
and d2cOptions
make it easier to specify options
for
Discretization using c2d
Resampling using d2d
.
Conversion from discrete to continuous time using d2c
.
This release deprecates the prewarp
method
for c2d
, d2d
, and d2c
.
Instead, use c2dOptions
, d2dOptions
,
or d2cOptions
to specify the tustin
method
and a prewarp frequency. For more information, see Continuous-Discrete
Conversion Methods and the c2d
, d2d
,
and d2c
reference
pages.
You can now remove selected data from frd
models
using the new fdel
command.
For example, use fdel
to:
Remove spurious or unneeded data from frd
models
you create from measured frequency response data.
Remove data at intersecting frequencies from frd
models
before merging them into a single frd
model with fcat
,
which can only merge frd
models containing no
common frequencies.
For more information, see fdel
reference
page.
In the SISO Design Tool, you can now design compensators for plants models that:
Contain time delays
Previously, you had to approximate delays before designing compensators.
You specify as frequency-response data (FRD)
For more information on designing compensators using the SISO Design Tool, see SISO Design Tool.
You can now tune compensators using a new automated PID tuning algorithm called Robust Response Time, which is available in the SISO Design Tool. You specify the open-loop bandwidth and phase margin, and the software computes PID parameters to robustly stabilize your system.
For information on tuning compensators using automated tuning methods, see Automated Tuning.
The variable q is now defined in the standard way as the forward shift operator z. Previously, q was defined as z^{-1}.
Note: This new definition is consistent with the System Identification Toolbox definition of q. |
If you use the q variable, you may receive different results than in previous releases when you:
Create a transfer function
Modify the num
or den
properties
of an existing transfer function
The resulting transfer function differs from previous releases when both the
Variable
property is set to q
num
and den
properties
have different lengths
For example, the following code:
H = tf([1,2],[1 3 8],0.1,'Variable','q')
$$\frac{q+2}{{q}^{2}+3q+8}\equiv \frac{z+2}{{z}^{2}+3z+8}$$
Previously, the code returned the transfer function
$$\frac{1+2q}{1+3q+8{q}^{2}}\equiv \frac{1+2{z}^{-1}}{1+3{z}^{-1}+8{z}^{-2}}\equiv \frac{{z}^{2}+2z}{{z}^{2}+3z+8}$$
The two transfer functions have different numerators.
You can now design a Linear-Quadratic-Gaussian (LQG) servo controller
for set-point tracking using the new lqi
and lqgtrack
commands.
This compensator ensures that the system output tracks the reference
command and rejects process disturbances and measurement noise.
For more information on forming LQG servo controllers, see Linear-Quadratic-Gaussian
(LQG) Design, the lqi
reference
page, and the lqgtrack
reference
page.
The 'current'
flag was moved from the lqgreg
function
to the kalman
function.
The following code:
kest = kalman(sys,Qn,Rn) c = lqgreg(kest,k)
To update your code to return the same results
as in previous releases, use the following code with the added string 'delayed'
in
the kalman
command:
kest = kalman(sys,Qn,Rn,'delayed') c = lqgreg(kest,k)
For information on using these functions with the current flag
in the kalman
function, see the kalman
and lqgreg
reference
pages.
You can now upsample a discrete-time system to an integer multiple
of the original sampling rate without any distortion in the time or
frequency domain using the upsample
command.
For more information on upsampling, see the upsample
reference
page and Upsample
a Discrete-Time System in the Control System Toolbox User's
Guide.
You can now scale state-space models to maximize accuracy over
the frequency band of interest using the prescale
command
and associated GUI. Use this functionality when you cannot achieve
good accuracy at all frequencies and some tradeoff is necessary. A
warning alerts you when accuracy may be poor and using prescaling
is recommended.
For more information on setting the frequency band for scaling
state-space realizations, see Scaling State-Space
Models and the prescale
reference
page.
You can now reorder the states of state-space models according
to a specified permutation using the xperm
command.
For more information on reordering states, see the xperm
reference
page.
You can now make the following changes to your Control System Toolbox response plots using the figure plotting tools:
System name
Line color
Line style
Line width
Marker type
For more information on customizing the appearance of response plots using plot tools, see Customizing Response Plots Using Plot Tools in the Control System Toolbox User's Guide.
The Control System Toolbox demos have been reformatted and expanded to include more examples and content. Demos in the following categories now have new and improved content:
Getting Started with LTI Models
Discretization and Sampling Rate Conversions
How to Get Accurate Results
To open the Control System Toolbox demos, type
demo toolbox control
Control System Toolbox software now lets you:
Model, simulate, and analyze any interconnection of linear systems with delays, such as systems containing feedback loops with delays.
Exactly analyze and simulate control systems with long delays. You can evaluate control strategies, such as Smith Predictor and PID control for first-order-plus-dead-time plants.
Use new commands for modeling state-space models with
delays including:
, delayss
,
and getDelayModel
.setDelayModel
For more information, see the section on Models with Time Delays in the Control System Toolbox documentation.
Control System Toolbox software now provides the following new and updated automated tuning methods:
New Singular Frequency Based Tuning lets you design PID compensators for both stable and unstable plants.
New H-infinity Loop Shaping lets you find compensators based on a desired open-loop bandwidth or loop shape. This feature requires Robust Control Toolbox software.
Updated Internal Model Control (IMC) Tuning now supports unstable plants.
For more information, see the section on automated tuning in the Control System Toolbox documentation.
The d2d
function now includes the following
new options for the resampling method:
'tustin'
—Performs Bilinear
(Tustin) approximation
'prewarp'
—Performs Tustin
approximation with frequency prewarping
For more information, see the d2d
reference
pages.
Two new loop configurations are available from the SISO Design Tool. See Modifying Block Diagram Structure for more information.
The LTI Viewer now supports step response and upper/lower time bound design requirements. See Adding Design Requirements to the LTI Viewer for more information.
The SISO Design Tool now provides one-click automated tuning using systematic algorithms such as Ziegler-Nichols PID tuning, IMC design, and LQG design. In addition, you can calculate low-order approximations of the IMC/LQG compensators to keep the control system complexity low.
If you have installed Simulink Response Optimization™ software,
you can now optimize the compensator parameters inside the SISO Design
Tool GUI. You can specify time- and frequency-domain requirements
on SISO Design Tool plots such as bode
and step
,
and use numerical optimization algorithms to automatically tune your
compensator to meet your requirements. See the Simulink Response Optimization documentation
for more details.
The Compensator Editor used to edit the numerical values of poles and zeros has been upgraded to better handle common control components such as lead/lag and notch filters.
Many control systems involve multiple feedback loops, some of which are coupled and need joint tuning. The SISO Design Tool now lets you analyze and tune multi-loop configurations. You can focus on a specific loop by opening signals to remove the effects of other loops, gain insight into loop interactions, and jointly tune several SISO loops.
To improve workflow and better leverage other tools, such as Simulink Control Design software and Simulink Response Optimization software, the SISO Design Tool is now fully integrated with the Controls & Estimation Tools Manager (CETM). This provides a signal environment for the design and tuning of compensators.
When you open the SISO Design Tool, the CETM also opens with a SISO Design Task. Many SISO Design Tool features, such as importing models, changing loop configurations, etc., have been moved to the SISO Design Task in CETM. In addition, related tasks such as Simulink based Tuning and Compensator Optimization are seamlessly integrated with the SISO Design Task. See the Control System Toolbox Getting Started Guide for details on the new work flow.
The LTI Viewer now lets you plot the response of a system to
user-defined input signals (lsim
) and initial conditions
(initial
). A new GUI lets you select input signals
from a signal generator library, or import signal data from a variety
of file formats.
There is now full support for descriptor state-space models
with a singular E
matrix. This now lets you build
state-space representations, such as PID, and manipulate improper
models with the superior accuracy of state-space computations. In
previous versions, only descriptor models with a nonsingular E
matrix
were supported.
The new stepinfo
and lsiminfo
commands
compute time-domain performance metrics, such as rise time, settling
time, and overshoot. You can use these commands to write scripts that
automatically verify or optimize such performance requirements. Previously,
these metrics were available only from response plots.
The commands connect
, feedback
, series
, parallel
,
and lft
now
let you connect systems by matching names of I/O channels. A helper
function, sumblk
, has also been added to simplify
the specification of summing junctions. Altogether this considerably
simplifies the task of deriving models for complicated block diagrams.
In previous releases, only index-based system connection was supported.
The ioDelay
property is deprecated from state-space
models. Instead, these models have a new property called InternalDelay
for
logging all delays that cannot be pushed to the inputs or outputs.
Driving this change is the switch to a representation of delays in
terms of delayed differential equations rather than frequency response.
See Models
with Time Delays in the Control System Toolbox documentation
for more details on internal delays, and ss/getdelaymodel
for
details on the new internal representation of state-space models with
delays.
This new property lets you attach a name (string) to a given LTI model. The specified name is reflected in response plots.
The new exp
command simplifies the creations
of continuous-time transfer functions with delays. For more information,
type help lti/exp
at the MATLAB prompt.
The frd
object
has the following new methods:
fcat
—
Concatenates one or more FRD models along the frequency dimension
(data merge).
fselect
—
Selects frequency points or range in frd
model.
fnorm
—
Calculates pointwise peak gain of frd
model.
The .*
operation is supported for transfer
functions and zero-pole-gain objects. This allows you to perform element-by-element
multiplication of MIMO models.
There have been several major improvements in the Control System Toolbox numerical algorithms, many of which benefit the upgraded SISO Design Tool:
New scaling algorithm that maximizes accuracy for badly scaled state-space models
Performance improvement in time and frequency response computations through MEX-files
More accurate computations of the zero-pole-gain and transfer function representations of a state-space model
More accurate state-space representations of zero-pole-gain models
Better handling of nonminimal modes in model reduction
commands (balred
, balreal
)
canon
now computes a block modal
form for A
matrices that are not diagonizable or
are nearly defective
Exact phase computation for zero-pole-gain models
in bode
and nichols
Accurate handling of improper models using the descriptor state-space representation
The Control System Toolbox software now provides a command-line API for customizing units, labels, limits, and other plot options. You can now change default plot options before generating a plot, or modify plot properties after creation.
For a detailed description of the commands, see the Control System Toolbox documentation.
You can now create
Single piecewise linear constraints for root-locus and Bode plots
Gain/phase exclusion regions for Nichols plots
Design constraints are displayed as shaded regions.
When editing Bode and Nichols plots, you can now
Set the lower limit of the magnitude manually.
Adjust the phase offsets by multiples of 360 degrees to facilitate comparing multiple responses.
Release | Features or Changes with Compatibility Considerations |
---|---|
R2015b | None |
R2015a | |
R2014b | |
R2014a | damp command display includes time constant
information |
R2013b | |
R2013a | None |
R2012b | Option for elementwise operation of model query commands on model arrays |
R2012a | |
R2011b | Functionality Being Removed or Changed |
R2011a | Discrete-Time PID Controller Objects Have Stable Derivative Filter Pole |
R2010b | Change in Output of repsys Command |
R2010a | New Commands for Specifying Options for Continuous-Discrete Conversions |
R2009b | None |
R2009a | Variable q Now Defined as the Forward Shift Operator z |
R2008b | New Design Tools for Linear-Quadratic-Gaussian (LQG) Servo Controllers with Integral Action |
R2008a | None |
R2007b | None |
R2007a | None |
R2006b | None |
R2006a | None |
R14SP3 | None |
R14SP2 | None |
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