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• Signal ILC Controller Figure 2. AVR system. 20 40 60 80 100 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Iteration 2 4 6 8 10 Time Figure 3. ILC algorithm convergence. Figure 4. Comparing PID with ILC output. Effect of changing Q In this simulation, Q = q. I is changed 3 times: q = 1, 10, 100 . As is seen in Figures 6 and 7, the speed of the output increases as q increases, but overshoot in output and control signal increases, too. This is because the weight of the error is increased such that total error in one period must decrease and the process speeds up. It can be concluded that Q regulates the speed of output, but at the price of higher overshoot. Effect of changing R We suppose that R = rI and change r = 1, 10, 100 . It is observed that with higher R , output is slower and overshoots in both output and control signals reduce (Figures 8 and 9). Thus, by changing R, we can adjust the control signal overshoot by the adverse effect of slowing down the process. 2 4 6 8 10 -2 Time -1 -0.5 0.5 1 5 2 Time Figure 5. Control effort. Figure 6. Output for q = 1, 10, 100. -1 -0.5 0.5 1 5 2 -10 Time -1 1 2 3 4 5 6 Time Figure 7. Control effort for q = 1, 10, 100. Figure 8. Output for r = 0.1, 1, 10. Effect of changing the set point If it is known that in a certain time the set point changes in every cycle of working, the ILC can improve the tracking problem dramatically. Even without knowing the exact time, since the plant is linear, when a sudden set point change occurs we can apply a multiplication of the control signal that is obtained for the unit step (proportional to the set point change). The results for a set point change are shown in Figures 10 and 11. As is seen, the ILC acts much better than the standard PID, while having a lower overshoot than the PID. As mentioned before, in general the ILC algorithm responds very well to set point changes and disturbances that are repeated in every period. However, in the case of unpredictable set point changes or varying disturbances, it is better to use it with another controller like the PID to achieve better performance. Using ILC in parallel with PID One way to provide the ILC with better robustness is to use it with a PID controller either in series or in parallel Since the PID usually has good robustness and the ILC has good performance, it is expected that their combination has both good robustness and performance. Here a parallel PID-ILC combination is used to study the robustness of the response against system parameter changes, as shown in Figure 10. In this configuration, a conventional ZN-PID is designed for the loop. The ILC is then designed and its control signal is added to that of the PID. First the system is simulated under normal conditions with no parameter changes in the system. The comparison of the simulation results are given in Figure 11. It is seen that both the ILC and PID-ILC act well in this situation. -1 1 2 3 4 5 6 -0.5 Time e j u j PID YD Plant Dynamics 1 2 3 4 5 6 -0.2 Time Time C.I. Kang, C.H. Kim, “An iterative learning approach to compensation for the servo track writing error in high track density disk drives”, Microsystems Technologies, Vol. 11, pp. 623–637, 2005.
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