Tune 2-DOF PID Controller (PID Tuner)
This example shows how to design a two-degree-of-freedom (2-DOF) PID controller usingPID Tuner。例子还比较了二自由度控制器performance to the performance achieved with a 1-DOF PID controller.
In this example, you represent the plant as anLTI model。For information about usingPID Tunerto tune aPID Controller (2DOF)block in a Simulink®model, seeDesign Two-Degree-of-Freedom PID Controllers(Simulink Control Design)。
2-DOF PID controllers include setpoint weighting on the proportional and derivative terms. Compared to a 1-DOF PID controller, a 2-DOF PID controller can achieve better disturbance rejection without significant increase of overshoot in setpoint tracking. A typical control architecture using a 2-DOF PID controller is shown in the following diagram.
For this example, first design a 1-DOF controller for the plant given by:
G = tf(1,[1 0.5 0.1]); pidTuner(G,'PID')
Suppose for this example that your application requires a faster response than thePID Tunerinitial design. In the text box next to theResponse Timeslider, enter 2.
The resulting response is fast, but has a considerable amount of overshoot. Design a 2-DOF controller to improve the overshoot. First, set the 1-DOF controller as the baseline controller for comparison. Click theExportarrowand selectSave as Baseline
。
Design the 2-DOF controller. In theTypemenu, selectPID2
。
PID Tunergenerates a 2-DOF controller with the same target response time. The controller parameters displayed at the bottom right show thatPID Tunertunes all controller coefficients, including the setpoint weightsb
andc
, to balance performance and robustness. Compare the 2-DOF controller performance (solid line) with the performance of the 1-DOF controller that you stored as the baseline (dotted line).
Adding the second degree of freedom eliminates the overshoot in the reference tracking response. Next, add a step response plot to compare the disturbance rejection performance of the two controllers. SelectAdd Plot>Input Disturbance Rejection。
You can move the plots in thePID Tunersuch that the disturbance-rejection plot side by side with the reference-tracking plot.
The disturbance-rejection performance is identical with both controllers. Thus, using a 2-DOF controller eliminates reference-tracking overshoot without any cost to disturbance rejection.
You can improve disturbance rejection too by changing thePID Tunerdesign focus. First, click theExportarrowand selectSave as Baseline
again to set the 2-DOF controller as the baseline for comparison.
Change thePID Tunerdesign focus to favor reference tracking without changing the response time or the transient-behavior coefficient. To do so, clickOptions, and in theFocusmenu, selectInput disturbance rejection
。
PID Tunerautomatically retunes the controller coefficients with a focus on disturbance-rejection performance.
智慧h the default balanced design focus,PID Tunerselects ab
value between 0 and 1. For this plant, when you change design focus to favor disturbance rejection,PID Tunersetsb
= 0 andc
= 0. Thus,PID Tunerautomatically generates an I-PD controller to optimize for disturbance rejection. (Explicitly specifying an I-PD controller without setting the design focus yields a similar controller.)
The response plots show that with the change in design focus, the disturbance rejection is further improved compared to the balanced 2-DOF controller. This improvement comes with some sacrifice of reference-tracking performance, which is slightly slower. However, the reference-tracking response still has no overshoot.
Thus, using 2-DOF control can improve disturbance rejection without sacrificing as much reference tracking performance as 1-DOF control. These effects on system performance depend strongly on the properties of your plant and the speed of your controller. For some plants and some control bandwidths, using 2-DOF control or changing the design focus has less or no impact on the tuned result.