Convert a discrete-time system to continuous time using d2c , and compares the results using two different interpolation methods.
Absorbing time delays into frequency response data can cause undesirable phase wrapping at high frequencies.
To reduce the order of a model by pole-zero cancellation at the command line, use minreal .
Convert a time delay in a discrete-time model to factors of 1/_z_.
Create a two-dimensional (2-D) array of transfer functions using for loops. One parameter of the transfer function varies in each dimension of the array.
Compute a reduced-order approximation of a system when the system has unstable or near-unstable poles.
Compute a low-order approximation in two ways and compares the results. When you compute a low-order approximation by the balanced truncation method, you can either:
Convert a compensator from continuous to discrete time using several discretization methods, to identify a method that yields a good match in the frequency domain.
Insert multichannel analysis points in a generalized state-space model of a MIMO control system.
Build a block diagram and insert analysis points at locations of interest using the connect command. You can then use the analysis points to extract various system responses from the model.
Extract SISO control components from a 2-DOF PID controller in each of the feedforward, feedback, and filter configurations. The example compares the closed-loop systems in all
Query model characteristics such as stability, time domain, and number of inputs and outputs. You can use the techniques of this example on any type of dynamic system model.
Query the size of model arrays, including the number of inputs and outputs of the models in the array, and the array dimensions. It also shows how to query characteristics of the models in the
Proper scaling of state-space models can be critical for accuracy and provides an overview of automatic and manual rescaling tools.
Construct a Linear Parameter Varying (LPV) representation of a system that exhibits multi-mode dynamics.
Focusing the energy-contribution calculation on a particular frequency region sometimes yields a good approximation to the dynamics of interest at a lower order than a reduction that
Sample a parametric model of a second-order filter across a grid of parameter values using sampleBlock .
Use the commands for continuous/discrete, discrete/continuous, and discrete/discrete conversions.
How the Control System Toolbox™ lets you represent, manipulate, and analyze any LTI model with a finite number of delays. The delays can be at the system inputs or outputs, between specific
Create a tunable model of the control system in the following illustration.
How choice of model type can affect numerical accuracy when interconnecting models.
Reduce model order while preserving important dynamics using the Model Reducer app. This example illustrates the Balanced Truncation method, which eliminates states based on their
Upsample a system using both the d2d and upsample commands and compares the results of both to the original system.
At the command-line, use balred to compute a reduced-order approximation of a model.
Improve the frequency-domain accuracy of a system with a time delay that is a fractional multiple of the sample time.
To reduce the order of a model by mode selection at the command line, use freqsep . This command separates a dynamic system model into slow and fast components around a specified frequency.
Create continuous-time linear models using the tf , zpk , ss , and frd commands.
Guidelines for building minimum-order models of LTI system interconnections.
Specify different Padé approximation orders to approximate internal and output delays in a continuous-time open-loop system.
When you create a dynamic system model, the software sets all property values. Properties that contain model dynamics are automatically set with the appropriate values. Other properties
High-multiplicity poles have high numerical sensitivity and can shift by significant amounts when switching model representation.
Switch between the transfer function (TF), zero-pole-gain (ZPK), state-space (SS), and frequency response data (FRD) representations of LTI systems.
Convert a numeric LTI model from one type ( pid ) to another type ( tf ).
Create a discrete-time transfer function with a time delay.
Create discrete-time linear models using the tf , zpk , ss , and frd commands.
Create a one-dimensional array of transfer functions using the stack command. One parameter of the transfer function varies from model to model in the array. You can use such an array to
Get the current value of a generalized model by converting it to a numeric model. This conversion is useful, for example, when you have tuned the parameters of the generalized model using a
The comparison of several techniques for discretizing a notch filter. While control system components are often designed in continuous time, they must generally be discretized for
This model shows how to use an LTI System block to represent a MIMO linear system in Simulink®.