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This section continues the magball example from Selecting an Operating Point. At this stage in the example, a compensator design task has been created, and tunable blocks, closed-loop signals, and an operating point have been selected.
In this step of the compensator design task, you will create and configure a SISO Design Task in the Control and Estimation Tools Manager. The SISO Design Task includes several tools for tuning the response of SISO systems:
A graphical editing environment in the SISO Design Tool window that contains design plots such as root-locus, and Bode diagrams
An LTI Viewer window where you can view time and frequency analysis plots of the system
A compensator editor where you can directly edit the block mask parameters or the poles and zeros of compensators in your system
A tool that automatically generates compensators using PID, internal model control (IMC), or linear-quadratic-Gaussian (LQG) methods (uses the Control System Toolbox software)
A response optimization tool that automatically tunes the system to satisfy design requirements (available when you have the Simulink Response Optimization product)
The Design Configuration Wizard guides you through the selection of the open- and closed-loop systems you want to design and the configuration of the design and analysis plots you want to use in the SISO Design Task. To launch the wizard, click the Tune Blocks button in the Simulink Compensator Design Task node. The wizard opens in a separate window.
The first page of the wizard provides an overview of the design configuration process and lists some issues to consider when selecting design and analysis plots. Click Next to continue to step 1 of the design configuration process on the second page of the wizard.
In step 1, select the open- and closed-loop systems that you want to design in your model, and up to six corresponding design plots you want to use.
Open-loop design allows you to design the response of a closed feedback loop in your model by artificially opening the loop and designing the response of this open-loop system. The open-loop design plots use rules of linear control theory to determine the dynamics of the closed-loop system from those of the open-loop system. Open-loop design is typically used to tune compensators that lie inside feedback loops.
A set of default open-loop systems is created for your model, shown in the lower half of the wizard. To create these open-loop systems, the software artificially opens the feedback loop at the output signal of each tunable block (at the X in the following figure) and unwraps the closed-loop system to create the corresponding open-loop system.
The unwrapped open-loop system, which is -CPH, is shown in the following figure. The open-loop design plots show the negative of the unwrapped open-loop, which is CPH. This configuration allows you to design controllers using a negative feedback architecture.
Note that elements that are outside the feedback loop, such as the prefilter F, are not seen in the open-loop system.
In this example, you will tune the response of Open Loop 1 which is defined by a loop opening at the output of the Controller block. This open-loop system contains the plant model and the controller. To design this system, select Open Loop 1 from the menu next to Plot 1 in the wizard.
Next, select a design plot to use for this open-loop system. Design plots are interactive plots within the SISO Design Tool. You can use them to graphically tune parameters and manually move, add, or remove poles and zeros of the tunable blocks to tune and design the dynamics of open- and closed-loop systems in your model. The following table shows the design plots, along with their uses, available in the SISO Design Tool.
| Type of Design Plot | Available Plots in the SISO Design Tool | Use to tune blocks that act as |
|---|---|---|
| Open-loop | Root Locus, Nichols, Open-loop bode | Feedback elements |
| Closed-loop | Closed-loop bode | Feedforward or prefilter elements |
You can also use the design plots to specify requirements for stability, performance, or both to use in using optimization-based automated tuning.
For this example, select Root Locus from the menu next to Plot 1 to use this plot type as the design plot for Open Loop 1. Step 1 of the wizard should now look similar to the following figure.
Click Next to proceed to step 2 of the wizard.
In this step, select the closed-loop responses that you want to view while designing your model, and the corresponding analysis plots you want to use to view them.
Analysis plots are plots that show the responses or dynamics of a closed or open loop systems or tunable blocks in your model. Although you cannot directly edit the analysis plots by graphically moving gains, poles, zeros, etc., changes that you make in the design plots, compensator editor, or automated design tools will affect the responses in the analysis plots. Possible analysis plots include
Step response
Impulse response
Bode and Bode magnitude
Nyquist
Nichols
Pole/Zero
You can use analysis plots to
Analyze closed-loop, open-loop, and tuned block responses in your control system.
Define stability and performance requirements for optimization-based automated tuning.
For this example, select Step from the menu for Plot 1 to create a step response analysis plot.
Next, select the closed-loop system that you want to display in this plot. A closed-loop system is a system that has not had any feedback loops opened for open-loop design. It typically defines the system whose response you want to control and it lies between the input and output signals of interest, for example between a reference signal and the plant output signal.
Linearization input and output points placed on signal lines in your model define closed-loop systems. The closed-loop system includes all blocks in the path between the input and the output.
The software automatically displays a list of up to four closed-loop systems in your model, based on the input and output points on the signal lines. In this example, only one closed-loop system appears in the wizard, the closed-loop from the Desired Height signal to the output of the Magnetic Ball Plant Model, because the system only has one input and one output point. You can add additional closed-loop responses, as well as open-loop and tunable block responses. To add a new response, click the Add Responses button and complete the Select a New Response to Analyze dialog box.
To display the current closed-loop system in the step response plot of Plot 1, select the check box under Plot 1 to the left of the closed-loop system. Step 2 of the wizard should now look similar to the following figure.
Click Finish to complete the wizard and create the SISO Design Task underneath the Simulink Compensator Design Task node within the Control and Estimation Tools Manager, as shown in the following figure.
The SISO Design Task also includes the design plots you configured in the Design Configuration Wizard. They appear within the SISO Design Tool window, as shown in the following figure.
In addition, the SISO Design Task also includes the analysis plots you configured in the Design Configuration Wizard. They appear within the LTI Viewer window, as shown in the following figure.
| Selecting an Operating Point | Completing the Design | |
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