Control System Toolbox
This example shows how the SISO Design Tool facilitates the compensator design process by providing interactive and automated tools to tune compensators for a feedback control system.
The SISO Design Tool allows:
1) The design problem to be setup graphically by defining the control design requirement on time, frequency, and pole/zero response plots.
2) Tuning the compensator with:
automated design methods such as Ziegler Nichols, IMC, and LQG.
graphically tuning poles and zeros on design plots such as Bode and root locus.
optimization to meet time and frequency-domain requirements using Simulink® Design Optimization™.
3) While tuning the compensators, the closed-loop and open-loop responses are dynamically updated to display the performance of the control system.
The design process using the SISO Design Tool will be illustrated with an example problem.
For this example we will design a compensator for the system
with the following design requirements:
Zero steady state error with respect to a step input.
80% rise time < 1 second.
Settling time < 2 seconds.
Maximum overshoot < 20%.
Open-loop crossover constraint of less than 5 rad/s.
For this example we will use the standard feedback structure with the controller in the forward path which happens to be the default feedback structure when launching the SISO Design Tool. To launch the SISO Design Tool with the specified plant G type
This will bring up two windows. The first window is Control and Estimation Tools Manager (CETM)
and the second window is the SISO Design graphical editors
In the CETM the SISO Design Task node contains tabbed panels which are used to configure the compensator design options as well as manipulate the compensators. For complete details of the functionality for each of the panels refer to the documentation.
For this design example we will use the root-locus plot and open-loop Bode plot for graphically tuning the compensator and validate the design by viewing the step response.
To view the closed-loop step response, click on the Analysis Plot tab in the CETM. Now configure the plot by selecting "Step" for the first plot and checking the first check box for the response "Closed-Loop r to y". This will bring up the SISO Tool Viewer.
Now add the time domain design requirements to the step response plot by right clicking on the axis and selecting the Design Requirements -> New menu item. We will use the "Step response bounds" design requirement type to specify the rise time, settling time and overshoot requirements.
We can now use this time response with its requirements to view the performance of the compensator design.
To specify the frequency domain crossover requirement, right click the bode axis in the SISO Design window and select the Design Requirement->New menu item and specify an upper gain limit.
Now that the problem has been set up we will begin to design the compensator to satisfy the problem specifications.
Compensators can be manually tuned from the graphical editors or the Compensator Editor tab of the CETM. For this example we will use the graphical editors to tune the compensator. To begin the design an integrator will be added to achieve zero steady state error to a step input. To add the integrator to the compensator use the right-click menu on the root-locus plot and select Add Pole/Zero->Integrator. To create a desirable shape for the root locus plot we will add a zero at approximately -2. To add the zero, use the right-click menu on the root-locus plot and select Add Pole/Zero->Real Zero menu item and then left-click at approximately -2 on the real axis of the root locus plot. Now in the bode plot adjust the open-loop gain by clicking and dragging the curve on the magnitude plot such that the cross-over and time domain constraints are satisfied.
To view the compensator go to Compensator Editor tab. Note that the steps performed in the graphical tuning plots to tune the compensator can also be accomplished from this panel.
In addition to the manual tuning interfaces, the SISO Design Tool also provides the following automated tuning algorithms:
Use the PID tuning, IMC tuning, and LQG synthesis options in the Automated Tuning panel to compute initial parameters for the compensators based on tuning parameters such as closed-loop time constants. See the example "Automated Controller Design in the SISO Design Tool".
Use the Optimization based tuning option in the Automated Tuning panel (requires Simulink Design Optimization) to tune the compensators using both time and frequency domain design requirements. See the example "DC Motor Controller Tuning".
Using the SISO Design Tool we were able to successfully design a compensator such that all of the specified design requirements were satisfied. The tool facilitated the heuristic process of compensator design by providing an interactive and visual environment for
Specifying the design requirements
Tuning the compensator, and
Evaluating the performance of the design.