Contents

Physical setup

In this section, we show how to build the DC Motor model using the physical modeling blocks of the Simscape extension to Simulink. The blocks in the Simscape library represent actual physical components; therefore, complex multi-domain models can be built without the need to build mathematical equations from physical principles as was done previously by applying Newton's laws and Kirchoff's laws to generate the model implemented in DC Motor Speed: Simulink Modeling.

The following figure shows a schematic of the DC Motor system we will be modeling in this page.

The system parameters are as follows:

(R)    Armature Resistance                   1 ohms

(L)    Armature Inductance                   0.5 H

(K)    Torque Constant/Back emf Constant     0.01 Nm/A or Vs/rad

(J)    Rotor Inertia                         0.01 kgm^2

(b)    Rotor damping                         0.1 Nms/rad

Open a new Simscape model by typing ssc_new in the MATLAB command window. A new model will open, shown below, with a few commonly used blocks already in the model. The PS-Simulink and Simulink-PS blocks define the boundary between Simulink input/output models where the blocks are evaluated sequentially and Simscape models where the equations are evaluated simultaneously.

Create the motor model

To create the motor model a number of blocks have to be added to the model.

Tips for adding blocks:

Add the following blocks:

* DC Motor block
* Current Sensor block (be sure to use the one from the Foundation Library)
* Controlled Voltage Source block (be sure to use the one from the Foundation Library)
* Electrical Reference block (be sure to use the one from the Foundation Library)
* Ideal Rotational Motion Sensor block
* Mechanical Rotational Reference block
* Step

The DC Motor block models both the electrical and mechanical characteristics of the motor.

Note that since the motor torque constant and the back emf constant are equal if the units are consistent, we only need to define one of the two.

We need to measure the position, speed, and current drawn by the motor.

Next, we have to connect the input signals and measurements to the input and output blocks. This will let us control the motor using Simulink.

The Solver Configuration block defines how the equations of a Simscape network are handled. Connect it to any electrical connection. We do not need to modify the parameters; we will use the defaults.

Delete any other unconnected items in the block diagram. The resulting model should appear as follows.

Running the simulation (CTRL-T or press the green arrow run button) will produce the following plot.

Create a subsystem

We will now place the motor into a subsystem.

Set up the controller: lag compensation

To generate the closed-loop step response with the current model, we will add a lag compensator in series with the motor subsystem and will feed back the motor's speed for comparison to a desired reference. The design of the compensator is detailed in the DC Motor Speed: Root Locus Controller Design page.

Insert the following blocks:

Make the following adjustments to model the lag compensator:

Make the following connections to close the loop:

Your completed model should now have the following form.

Then run the simulation (press CTRL-T or press the green arrow run button). Examining the generated plot, shown below, this step response matches the closed-loop performance observed in the DC Motor Speed: Root Locus Controller Design page where the lag compensator was originally designed. Furthermore, the simulation results achieved with this Simscape model also agree with the physics-based Simulink model implemented in the DC Motor Speed: Simulink Controller Design page.

Set up controller: lead compensation

The lag compensator we have designed meets all of the stated design requirements. Instead of a lag compensator, we could have also designed a lead compensator to meet the given requirements. More specifically, we could have designed a lead compensator to achieve a similar DC gain and phase margin to that achieved by the lag compensator, but with a larger gain crossover frequency. You can refer back to the DC Motor Speed: Frequency Domain Methods for Controller Design page for more details on the design of the lag compensator, but the fact that the DC gains and phase margins are similar indicate that the responses under lag and lead control would have similar amounts of error in steady state and similar amounts of overshoot. The difference in response would come in that the larger gain crossover frequency provided by the lead compensator would make the system response faster than with the lag compensator. We will specifically use the lead compensator that was used in the DC Motor Speed: Simulink Controller Design page.

To see the precise effect of the lead compensator as compared to our lag compensator, make the following changes to the model

Next, modify the compensator as follows:

Your model should appear as shown in the following figure:

Running the simulation produces the following plots. From inspection, you will see that both responses have a steady-state error that approaches zero. Comparing the two graphs, the response belonging to the lead compensated system has a much smaller settle time and slightly larger, but similar, overshoot as compared to the blue response produced by the lag compensated system.

Lead compensation vs. lag compensation

It is generally preferred that a system respond to a command quickly. Why then might we prefer to use the lag compensator even though it is slower than the lead compensator? The advantage of the lag compensator in this case is that by responding more slowly it requires less control effort than the lead compensator. Less control effort means that less power is consumed and that the various components can be sized smaller since they do not have to supply as much energy or withstand the higher voltages and current required of the lead compensator.

You can download the final Simscape model created here by right-clicking here and then selecting Save link as ....

Published with MATLAB® 9.7