In this video you will see how to design a controller for a set of plant models simultaneously using Control System Toolbox.
Here we have a variable sys that represents an array of 11 continuous-time state-space models.
Those models were obtained by linearizing a nonlinear Simulink model at 11 different operating conditions.
If we look at the Bode plot of this array of models, we will see the variations in plant dynamics
from one operating condition to another.
What we want to see is if we can design a single controller to provide stable closed-loop performance
across different operating conditions and meet some design requirements,
for example, an overshoot of less than 3 percent.
To see that let’s launch Control System Designer app.
We’ll use Bode editor for tuning the controller, and let’s provide the array of models as the input argument.
The app opens up, let’s maximize it.
In the app we have two plots – the Bode editor and the closed-loop step response.
Let’s put those two plots side by side.
Now let’s go to the Bode editor and change the frequency range for our calculations.
The solid blue line that we see in the Bode plot corresponds to the nominal plant model.
By default, it’s the first state-space model in our array.
And then we have light blue lines that you can see here, especially if I zoom in here,
that correspond to 10 other state-space models in our array.
Let’s go ahead and lower the gain of the system to make our closed-loop step response stable.
It is stable now, but it has nonzero steady-state error, and from the Bode plot we can clearly see that we need integral action here to fix that.
So let’s go ahead and add an integrator, and let’s now lower the gain a little bit to bring our overshoot down to about 3 %.
To actually help us see if we meet this requirement, let’s go here, and under “Design Requirements�?
specify a new design requirement that our amplitude should not exceed the value of 1.03.
This way we can visually see this design requirement and we can continue tuning, lowering the gain, until we meet it.
So we meet it for the nominal plant model. But what about 10 other state-space models in our array
that correspond to ten other operating conditions?
Let’s go here to the step response, right-click on “Multimodel Display�?, and here we can choose to look at bounds or individual responses.
Let’s do that.
Now if we zoom in, we see that even though we are very close to meeting the overshoot requirement for the nominal plant,
we are definitely not meeting it for 10 other operating points.
So let’s go ahead and zoom out.
And let’s lower our controller gain to make sure that we satisfy the overshoot requirement even in the worst case.
So now we see that with a single controller we have fast response,
stable closed-loop step response at all the different operating conditions,
and an overshoot of less than 3%.
If we needed to get faster performance, we probably would have to design individual controllers for each operating condition
and then schedule them as we change from one operating condition to another.
That’s a technique called gain scheduling.
In summary, you saw how to use Control System Designer app
to tune one controller against a set of different plant models.
This concludes the video.