## Documentation |

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. Δ

*T*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.

Use 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.

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

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.

In 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:

By 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.

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.

The 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

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`.

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`.

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 TunerDesigning 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 pagesThe new Control System Toolbox demo Designing Cascade Control System with PI ControllersDesigning 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 ResponseApproximate 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.

Compensator Design for a Set of Plant ModelsCompensator Design for a Set of Plant Models demo.

Reference Tracking of a DC Motor with Parameter VariationsReference 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}*.

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')

now returns the transfer function

$$\frac{q+2}{{q}^{2}+3q+8}\equiv \frac{z+2}{{z}^{2}+3z+8}$$

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)

now returns the current regulator $$u\left[n\right]=-K\widehat{x}\left[n|n\right]$$ instead of the delayed regulator $$u\left[n\right]=-K\widehat{x}\left[n|n-1\right]$$.

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

at the MATLAB prompt.

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 defectiveExact 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 |
---|---|

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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