Getting Started with the Control System Designer

Open Live Script

This example shows how to tune compensators for a feedback control system usingControl System Designer.

UsingControl System Designeryou can:

1) Define control design requirements on time, frequency, and pole/zero response plots.

2) Tune compensators using:

Automated design methods, such as PID tuning, IMC, and LQG.
Graphically tune poles and zeros on design plots, such as Bode and root locus.
Optimization-based control design to meet time-domain and frequency-domain requirements using Simulink® Design Optimization™.

3)可视化闭环和开环反应that dynamically update to display the control system performance.

Compensator Design Problem

For this example, design a compensator for the system

$G (s) = \frac{1}{s + 1}$

with the following design requirements:

Zero steady-state error with respect to a step input.
80% rise time less than 1 second.
Settling time less than 2 seconds.
Maximum overshoot less than 20%.
Open-loop crossover frequency less than 5 rad/s.

Open Control System Designer

Use the standard feedback structure with the controller in the forward path. This structure is the defaultControl System Designerarchitecture.

OpenControl System Designerwith the specified plant.

controlSystemDesigner(tf(1,[1,1]))

On theControl Systemtab, you can select a compensator tuning method, and create response plots for analyzing your controller performance. You can also store, compare, and export different control system designs.

For this example, graphically tune your compensator using theRoot Locus Editorand open-loopBode Editor, and validate the design using the closed-loopStep Response. By default,Control System Designerdisplays these responses when it opens. To add additional response plots, clickNew Plot.

Add Design Requirements

Add the time-domain design requirements to theStep Responseplot. Right-click the plot area, and selectDesign Requirements > New. In theDesign requirement typedrop-down list, selectStep response bound. Enter the time-domain design requirements.

ClickOK. The app adds the design requirement to the step response plot as a shaded exclusion region. To meet the requirement, the step response must remain outside of this region.

To specify the frequency-domain crossover requirement, right-click theBode Editorplot area, and selectDesign Requirements > New. In theDesign requirement typedrop-down list, selectUpper gain limit, and specify the design requirement.

ClickOK.

Tune Compensator

To meet the zero steady-state error design requirement, add an integrator to the compensator. Right-click theRoot Locus Editorplot area, and selectAdd Pole or Zero > Integrator.

To create a desirable shape for the root locus plot, add a real zero near -2. Right-click the root locus plot area and selectAdd Pole or Zero > Real Zero. In the root locus plot, left-click the real axis near -2.

To create a faster response by increasing the compensator gain, in theBode Editor, drag the magnitude response upward. To satisfy the crossover frequency requirement, keep the response below the exclusion region in the Bode editor.

To view the compensator, right-click in theBode EditororRoot Locus Editorplot area, and selectEdit Compensator...

You can also tune the compensator parameters using the Compensator Editor dialog box.

Automated Compensator Tuning

In addition to graphical tuning, you can also use automated tuning methods. To select an automated tuning method, clickTuning Methods.

PID Tuning,IMC Tuning, andLQG Synthesis- Compute initial compensator parameters based on tuning specifications such as closed-loop time constants. For an example, seeDesign LQG Tracker Using Control System Designer.
Optimization-Based Tuning- Optimize compensators using both time-domain and frequency-domain design requirements (requires Simulink Design Optimization). For an example, seeDC Motor Controller Tuning(Simulink Design Optimization).
Loop Shaping——指定一个分ed target loop shape (requires Robust Control Toolbox™).