Control System Toolbox™

Using the SISO Design Task in the Controls & Estimation Tools Manager

Architecture

Use the Architecture pane for

• Modifying Block Diagram Structure

• Configuring Loops

• Importing Models

• Changing Sample Times

  Architecture Pane on the SISO Design Task Node

  

Modifying Block Diagram Structure

Click Control Architecture to change the feedback structure and label signals and blocks. The following pane appears:

Select an architecture from the list of block configurations. These include compensator in the forward path, compensator in the feedback path, feedforward controller, and various multi-loop configurations.

Each configuration has associated Signs and Blocks and Signals panes. This figure shows the Signs pane.

The Blocks and Signals pane displays the generic identifier, for example F for the prefilter block, and a default name.

Configuring Loops

Click Loop Configuration to configure loops for multi-loop design by opening signals to remove the effects of other feedback loops.

To specify openings for a given open loop, select the loop in the combo box. Click Highlight Feedback Loop to see the effects of the selected openings.

For an example of how to use this window in design, see Multi-Loop Compensator Design.

Importing Models

Click System Data on the Architecture pane to import models into your system. This opens the System Data dialog box, which is shown below.

You can import models for the plant (G), compensator (C), prefilter (F), and/or sensor (H). To import a model:

1. Select a system in the System column and click Browse. The Model Import dialog box opens, as shown below.

   

2. Select a model from the Available Models list. You can import models from:

   • The MATLAB workspace

   • A MAT-file

3. Click Import, then click Close. You can now see the model loaded into the system selected in the System Data dialog.

4. Click OK. The Graphical Tuning window is updated with the model you loaded.

Alternatively, you can import by entering a valid expression or variable (double or LTI object) in the Data column in the System Data window.

Changing Sample Times

Click Sample Time Conversion to convert the sample time of the system or switch between different sample times to design different compensators.

Choose from Zero-Order Hold, First-Order Hold, Impulse Variant, Tustin, Tustin w/Prewarping, and Matched Pole-Zero.

For a full description, see Continuous/Discrete Conversions Using the Sample Time Conversion Dialog Box.

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Compensator Editor

Use the Compensator Editor for adding or editing gains, poles, and zeros.

Compensator Editor Pane on the SISO Design Task Node

1. Enter the compensator gain in the text box in the top part of the pane.

2. Add or remove compensator poles and zeros by right-clicking in the Dynamics table.

3. Adjust pole and zero settings by entering values directly in the Edit Selected Dynamics group box.

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Graphical Tuning

Use the Graphical Tuning pane for

• Configuring Design Plots for the Graphical Tuning Window

• Selecting New Loops to Tune

• Refocusing on the Graphical Tuning Window

  Graphical Tuning Pane on the SISO Design Task Node

  

Configuring Design Plots for the Graphical Tuning Window

Click the Graphical Tuning tab to configure design plots displayed in the Graphical Tuning Window.

In the Graphical Tuning window, use design plots to graphically manipulate system response. These design plots are dynamically linked to the SISO Design Task. When you change the dynamics of your compensator in either the SISO Design Task or the Graphical Tuning window, the design updates in both places.

For open-loop responses, the available plot types are:

• Root locus

• Nichols

• Bode

For closed-loop responses, the available plot type is Bode.

Selecting New Loops to Tune

Click New Open/Closed Loops to Tune to open a window for specifying new loops to tune.

Use the pull down menus to select the desired closed loop to tune by specifying the input, output, and blocks for tuning. Using the dialog box, you can select additional closed loops to tune.

Any loop you specify is displayed in the Summary of Available Loops to Tune in the Graphical Tuning pane. The list is also available in the Design plots configuration table of the same pane. You can use the latter for configuring design plots.

Refocusing on the Graphical Tuning Window

Click Show Design Plot to change the focus to the Graphical Tuning window.

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Analysis Plots

Use the Analysis Plots pane for

• Customizing Loop Responses

• Adding New Response Plots

• Opening or Changing the Focus to the LTI Viewer

  Analysis Plots Pane on the SISO Design Task Node

  

Customizing Loop Responses

The following sections describe the main components of the Analysis Plots pane.

Analysis Plots.   You can have up to six plots in one LTI Viewer. To add a plot, start by selecting "Plot 1" from the list of plots. Then select a new plot type from the pull down menu. You can choose any of the plots available in the LTI Viewer. Select "None" to remove a plot.

Contents of plots.   Once you have selected a plot type, you can include several open- and closed-loop transfer function responses for display. You can plot open-loop responses for each of the components of your system, including your compensator (C), plant (G), prefilter (F), or sensor (H). In addition, various closed loop and sensitivity response plots are available.

Adding New Response Plots

Click Add Responses to open a window with three drop-down menus for selecting open and closed loop responses for various input and output nodes in the control architecture block diagram. This allows you to select additional responses for viewing. The Response table updates automatically to include the selected response.

Opening or Changing the Focus to the LTI Viewer

Click Show Analysis Plot to open a new LTI Viewer for SISO Design with the response plots that you selected. All the plots open in one instance of the LTI Viewer.

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Automated Tuning

Use the Automated Tuning pane to select a method for automatic tuning of your compensator design. Automated tuning methods help you design an initial compensator for a SISO loop that satisfies your design specifications.

You can choose among the following algorithms:

• Optimization-Based Tuning — Optimizes compensator parameters using design requirements implemented in graphical tuning and analysis plots.

• PID Tuning — Searches for initial PID controller parameters using the Ziegler-Nichols, IMC Based, and Singular Frequency Based methods.

• Internal Model Control (IMC) Tuning — Obtains a full-order stabilizing feedback controller using the IMC design method.

• LQG Synthesis — Designs a full-order stabilizing feedback controller as a Linear-Quadratic-Gaussian (LQG) tracker.

• Loop Shaping — Finds a full-order stabilizing feedback controller with a desired open loop bandwidth or shape.

After you select a tuning algorithm, the pane updates to display the corresponding options.

Note   If the particular automated tuning method you are using does not apply or fails, try selecting different tuning specifications or switch to a different tuning algorithm.

Stability of an Effective Plant for Automated Tuning

Knowing the stability of the effective plant in your model may help you understand which automated tuning methods work for your model. Some of the automated tuning methods only apply to compensators whose open loops ( ) have stable effective plants ( ).

An effective plant is the system controlled by the compensator you design and contains all elements of the open loop in your model other than this compensator. The following figure shows two examples of effective plants.

Generic Work Flow

For each method, follow these steps to do your design:

1. Select an automated tuning algorithm from the Design method drop-down menu.

2. If you select Optimization-Based Tuning, stop here and see Optimization-Based Tuning.

3. Select a compensator from the drop-down menu.

4. Determine how you want the compensator to perform and set the tuning specifications.

5. Click Update Compensator and notice the changes in the associated design and analysis plots.

   Note   If you encounter a disabled Update Compensator button, try selecting different tuning specifications (Step 4) or switch to a different tuning algorithm (Step 1). The disabled button means that the current method does not work for your model.

Optimization-Based Tuning

Optimization-based tuning creates a subdesign task to assist in the tuning and optimization of control systems. If you have Simulink Response Optimization software installed, you can use this method to either:

• Directly tune response signals within Simulink^® models.

• Tune responses of LTI systems using a SISO Design Task.

See "Frequency Domain Response Optimization Example" in the Simulink Response Optimization documentation for more details.

PID Tuning

PID (proportional-integral-derivative) control is the most popular control technique used in modern industry. Four PID tuning algorithms are provided in the SISO Design Tool, including one that supports unstable systems (Singular frequency based tuning). In most cases, the PID controllers resulting from PID tuning provide acceptable performance.

To do a PID design:

1. Select a controller type from the following options:

   • P — Proportional-only control ( )

   • PI — Proportional-integral control ( )

   • PID — Proportional-integral-derivative control ( )

   • PIDF — PID control with a lowpass filter

     If you choose this controller type, specify the N frequency (bandwidth) in rad/s.

2. Select an algorithm from the Tuning algorithm list:

   • Singular frequency based tuning — This method implements robust control design techniques to locate stabilizing PID regions in parameter space. This method supports unstable systems.

   • Ziegler-Nichols open loop — Controller settings are based on a first-order model with a time delay that approximates the plant. This method uses the Chien-Hrones-Resnick (CHR) setting with 20% overshoot.

   • Ziegler-Nichols closed loop — Controller settings are obtained from a modified Ziegler-Nichols lookup table, based on the ultimate gain and frequency of the system.

     Ziegler-Nichols closed loop does not apply to first-order or second-order systems with time delay. If you select Ziegler-Nichols closed loop for these cases, the tuning algorithm will automatically be switched to Ziegler-Nichols open loop.

   • Internal Model Control (IMC) based tuning — Controller settings are derived from a full-order IMC controller (note that this is different from selecting Internal Model Control (IMC) Tuning as the full-order compensator tuning method).

   

3. Set the tuning options available for your selected tuning algorithm type.

   • If you chose singular frequency based tuning, select one of these options from the Performance metric list:

     • Integral Absolute Error (IAE)

     • Integral Square Error (ISE)

     • Integral Time Absolute Error (ITAE)

     • Integral Time Square Error (ITSE)

     These are typical controller performance criteria based on time response.

     

   • If you chose Ziegler-Nichols open loop, select a tuning preference by clicking one of these option buttons:

     • Setpoint tracking

     • Load disturbance rejection

     

   • If you chose Ziegler-Nichols closed loop, select a tuning formula by clicking one of these option buttons:

     • Ziegler-Nichols

     • Tyreus-Luyben

     • Astrom-Hagglund

     

   • If you chose Internal Model Control (IMC) based tuning, use the slider bar to set the Dominant closed-loop time constant.

     

4. Click Update Compensator.

Internal Model Control (IMC) Tuning

IMC design generates a full-order feedback controller that guarantees closed-loop stability when there is no model error. It also contains an integrator, which guarantees zero steady-state offset for plants without a free differentiator. You can use this tuning method for both stable and unstable plants.

To design an IMC controller:

1. Specify a value in the Dominant closed-loop time constant field. The initial value is set as 5% of the open-loop settling time. In general, increasing this value slows down the closed system and makes it more robust.

2. Specify a value in the Desired controller order field using the slider. After you obtain a full-order feedback controller, you can try to reduce its order. You may lose performance and closed-loop stability if you reduce the order.

3. Click Update Compensator.

LQG Synthesis

LQG tracker design generates a full-order feedback controller that guarantees closed-loop stability. It also contains an integrator, which guarantees zero steady-state error for plants without a free differentiator.

To design an LQG controller:

1. Specify your preference for controller response using the Controller response slider.

   • Move the slider to the left for aggressive control response.

     This means that large overshoot is more heavily penalized so that the controller acts more aggressively. If you believe your model is accurate and that the manipulated variable has a large enough range, an aggressive controller is more desirable.

   • Move the slider to the right for robust control response.

2. Specify your estimation of the level of measurement noise using the Measurement noise slider.

   • Move the slider to the left for small measurement noise.

     This means that you expect low noise from the process output measurement. Because this measurement is used by the Kalman estimator, process disturbances are picked up more accurately by the estimated states. In this case, the controller is freer from robustness considerations.

   • Move the slider to the right for large measurement noise. This results in a controller that is more robust to measurement noise.

3. Specify your preference for controller order using the Desired controller order slider.

4. Click Update Compensator.

Loop Shaping

Loop shaping generates a stabilizing feedback controller to match as closely as possible to a desired loop shape. You can specify this loop shape as a bandwidth or an open loop frequency response. If you have Robust Control Toolbox™ software installed, you can use loop shaping for SISO systems. For more information see the section on H-Infinity Loop Shaping in the Robust Control Toolbox User's Guide.

To design a controller using loop shaping:

1. Select a tuning preference by clicking one of these option buttons:

   • Target bandwidth — Allows you to specify a target loop shape bandwidth ( ). This results in a loop shape of your specified bandwidth over an integrator ( ).

   • Target loop shape — Allows you to specify the target open loop shape in one of the following representations: state-space, zero-pole-gain, or transfer functions.

2. Set the tuning options available for your selected tuning preference as follows:

   • If you chose Target bandwidth, specify the desired Target open-loop bandwidth in the editable box.

     

   • If you chose Target loop shape, do the following:

     • Enter the desired Target open-loop shape (LTI).

       This can be a state-space representation, a zero-pole-gain representation, or a transfer function.

     • Enter the desired Frequency range for loop shaping [wmin,wmax].

     

3. Specify your preference for controller order using the Desired controller order slider.

4. Click Update Compensator.

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Using the SISO Design Task Node

SISO Design Task Graphical Tuning Window