EE 461 Experiment #1 Digital Control of DC Servomotor 1 Objectives The objective of this lab is to introduce to the students the design and implementation of digital control. The digital control is implemented on a lab-scale DC Servomotor in the control systems laboratory. The performance of the resulted digital control system is compared with the continuous-time control system performance. The effect of sampling period T s (or sampling frequency f s = 1 T s ) is studied. When doing the lab, the software packages MATLAB with Control Systems Toolbox, and the Simulink are used for the analysis and design of control systems. 2 Introduction An important approach to digital controller (filter) design is to start with a well-designed analog controller. The digital controller C(z) is then implemented by discretizing the continuoustime controller C(s). This design method is also called design by emulation, which is widely used by control engineers in practice. It is known that for a properly chosen sampling period, this method can provide a useful digital controller with satisfactory performance. In this lab, students are asked to implement the digital controllers, obtained by discretizing a pre-specified analog controller using some common discretization methods. The effect of sampling frequency is also studied by comparing different system responses with respect to f s. In the last part of the experiment, the students are asked to implement a digital controller designed directly for the discrete-time dc-motor model, and the system response is obtained for comparison purpose. 1
3 Preparation Before the lab begins, students are required to read and understand the lab preliminary for the hardware and software description. In addition, it is recommended that the students complete the following pre-lab work. The Quanser dc-servomotor in the control systems laboratory has the following model (with a low gear ratio and in the load free case): P(s) = 20020. The analog control system can s(s+42) be implemented by using a continuous-time controller C(s): Figure 1: Analog Control System for a DC-Motor In this lab, the analog controller is given as a lead compensator C(s) = 0.08s+0.08 s+3, which can generate a satisfactory transient and steady-state performance of the system step response. By discretizing C(s), one can implement a digital control system: Figure 2: Digital Control System for a DC-Motor 1. With the sampling interval chosen as T s = 0.001, and T s = 0.01, use the Bilinear transformation (Tustin s method) to obtain the discrete-time models of C(s), denoted by C 1 (z) and C 2 (z), respectively. This can be done by using c2d command in Matlab. Record down C(s), C 1 (z), and C 2 (z), and they will be used in the following experiment procedure. 2
4 Experiment Procedure 1. Check and understand the wiring between the dc-motor, power module(upm) and the computer. 2. Start the MATLAB, and Simulink. It can be noticed that a Quanser toolbox is installed in the Simulink, and it contains the blocks to interface with the real system setup. 4.1 Part 1. Implementation of Analog Control 3. Build a simulink model (use Simulink and Quanser toolbox) to implement the analog control system in Figure 1, with C(s) given there. The motor shaft Encoder is used to measure the angular position, and a calibration gain of -360/4096 needs to be added to the encoder to convert the angular signal to degree. The reference input is set to a step signal of 30 degrees. 4. Compile your program by going to WinCon in the manual bar and clicking Build, a WinCon interface window will then appear if there is no error in your simulink model. Remember to adjust your motor shaft to zero position before start running the system every time. You can also select scopes to monitor the signals in real-time. For example, choose scopes to monitor the angular position Θ(t) and the control signal u(t) 5. Run the system by clicking Start, after 6 seconds (it can be seen from the scope), stop the program by clicking Stop and save the data for later analysis. Another way to stop the program is to add the following timer in your Simulink model, which allows the simulation to stop automatically. Figure 3: Timer 3
4.2 Part 2. Implementation of Digital Control by Emulation 6. Implement the digital control system in Figure 2. Set the sampling time as T s = 0.001 sec., then replace the analog controller in your Simulink model by the discretized one C 1 (z). Remember to set the same sampling time in the input block, and in the Simulation > Parameters... (change simulation method to discrete, and set the fixed step size as same as T s ). 7. Repeat steps (4) and (5), and save the data 8. Set T s = 0.01 sec., implement C 2 (z). Repeat steps (6) and (7) 4.3 Part 3. Digital Control by Direct Design In the following steps, we are going to implement a digital controller directly designed based on the discretized plant (i.e. the ZOH equivalent model of P(s)), rather than discretizing an analog controller. This method is referred to as direct design method. 9. By setting T s = 0.01 sec., a discrete-time compensator of the form C 3 (z) = K( z 0.657 z 0.35 ) is chosen. Implement C 3 (z) in your model, and repeat the steps (4) and (5). Observe the system response and save the data. Note: The gain K in C 3 (z), can be tuned to get a good performance. ( Warning: the system is very sensitive to the selection of K, too large K may result in instability, a suitable rang is [0.2, 0.05]), a suitable choice is K = 0.12) 10. When changing the sampling interval to T s = 0.1 (a rather slow sampling), one has to re-design the discrete-time compensator, it is chosen as C 4 (z) = 0.04( z 0.6 ). Implement C 4 (z), and observe the system z 0.35 response. Caution: during the experiment, the motor may run without control, such as turning extremely fast and making unpleasant noises, in these cases, stop the program immediately, and ask for assistance. 5 Analysis and Discussion Finally, after all the trials, load the data into Matlab and plot the time responses of the dcmotor angular position. Evaluate the performance by calculating the percent of overshoot (P.O.), settling time (T s, and steady-state error e ss. It is recommended to plot the reference input signal and the output signals that you want to compare in the same graph. 4
1. Compare the step responses of the dc-motor using the discretized controller C 1 (z), and C 2 (z) with that of analog controller C(s), in terms of P.O., T s, and e ss. What can you observe? 2. How does the sampling time affect the system responses in the experiment in Part 2? 3. Compare the system response by using C 3 (z) in Part 3, step (9), with the system response using C 2 (z) in step (8), what can you say about the performance of these two digital controllers? (remember that they are obtained by emulation and direct design ) 4. From all above procedures when trying different sampling intervals, make a discussion on the effects of sampling time to the system performance. 6 Lab Report Individual reports are required although the students may work in groups. should contain: The reports The pre-lab work A brief introduction of the experiment. Printouts of Simulink models, and all the plots. Your discussions by answering the question in section 5. Any conclusions you would like to draw. The lab report is due by 4pm on Feb. 14, 2011 for section H3 and 4pm on Feb. 28, 2011 for section H4. Please drop your report into the box assigned to EE461 LAB outside the main office at 2nd floor ECERF. 5