Motor Control Model

The model shows the control of angular position for two motors. Open the Simulink Model.

open_system('sdoMultipleMotors')

Model references are used for the two controllers, which are instances of the same model. Open the controller.

open_system('sdoRateLimitedController')

Each controller has PID gains Kp, Ki, and Kd, and a slew rate, Slew. The Slew value limits the rate at which the control signal changes, so that currents drawn from the power supply stay within the power supply's limits. The Slew value is common to both instances of the controller. In contrast, the PID gains need to be different for each instance of the controller, since the motors being controlled have different characteristics. Therefore, the PID gains are specified as model arguments in the controller's model workspace. The PID gain values are set at the level of the sdoMultipleMotors model.

Design Problem

The control reference signal is a step change in position, which occurs at 1 second. Each motor's angular position should follow the reference signal, but the first motor has a smaller moment of inertia and can respond more quickly to changes in the reference signal. We want the angular position of the first motor to satisfy the following requirements:

The second motor has a larger moment of inertia so it can't respond as quickly. We want the angular position of the second motor to satisfy the following requirements:

Also, the derivative of each controller signal is required to be in the range from -5 to 5, so that currents drawn from the power supply stay within the power supply's limits.

All these requirements are specified using blocks in the Simulink model.

Open the Response Optimization Tool

In the Simulink model from the Apps tab, click Response Optimizer under Control Systems to launch the Response Optimization tool. With the current settings of the controller variables, observe that neither step response requirement is satisfied.

Specify Design Variables

In the Design Variables Set list, select New. The dialog shows tunable variables. The Slew variable is listed as sdoRateLimitedController:Slew, indicating that the variable is set at the level of the sdoRateLimitedController model. The colon is a delimiter between the model and variable. The Slew variable has the same value for all instances of the controller model. In contrast, the derivative gain for the first controller is listed as sdoMultipleMotors/Control_1:Kd, indicating that the variable is set at the level of the sdoMultipleMotors model, where it appears in the Control_1 block. The forward slash is the delimiter for Simulink blockpaths.

Select the common Slew variable, as well as the Kd, Ki, and Kp parameters for each model. Add these variables to the design variable set. Specify the minimum value for the Slew variable as 0.

Click OK. A new variable, DesignVars, appears in the Response Optimization Tool Workspace. Create a plot of the design variables to see how they evolve during optimization. Under Data to Plot, select DesignVars. Click Add Plot and add an iteration plot. You can use the View tab to arrange the plots so they are all visible.

Optimize the Design

To optimize the design, click Optimize. The plots are updated during optimization. When optimization is complete, observe that all design requirements are satisfied. The step responses are within the prescribed bounds, as are the controller output signal derivatives.

Close the models.

bdclose('sdoMultipleMotors')
bdclose('sdoRateLimitedController')