1. Matteo MacchiniStudent meeting – October 2014 Motion control design for the new BWS Matteo Macchini Technical student BE-BI-BL Supervisor: Jonathan Emery

2. Matteo Macchini Outline Student meeting – October 2014 Saturation problem and Anti-Windup controller Quantization problem and Kalman Filter

3. Matteo Macchini Saturation problem Student meeting – October 2014 Saturation non-linearity in the output can lead to performance drops or even instability in PID controllers due to integral action. This effect is know as “Windup”. It can cause: -Slow down in dynamics -Reaction delay

4. Matteo Macchini Anti-Windup controllers Student meeting – October 2014 Anti-Windup controllers are designed to solve the problems caused by saturating effects on their outputs. The origin of the issue is that a “classic” saturated controller will increase its output trying to chase a reference that it won’t be able to reach. By doing this, the integrator will keep charging, causing a delay in the reaction and a dynamic different from the expected. Simple example: Thermostat with VERY low environmental temperature

5. Matteo Macchini Anti-Windup controllers Student meeting – October 2014 Two architectures were implemented and compared: Conditioned AW PIDTracking AW PID

6. Matteo Macchini Anti-Windup controllers Student meeting – October 2014 Results: Conditioned AW PIDTracking AW PID

7. Matteo Macchini Anti-Windup controllers Student meeting – October 2014 Results comparison: Conditioned AW PIDTracking AW PID Conditioned PID shows better performance

8. Matteo Macchini Quantization problem Student meeting – October 2014

9. Matteo Macchini Quantization problem Student meeting – October 2014 Causes of quantized speed : -High sampling frequency -Low resolution Additional problem: - Too high resolution can lead to slow dynamics (lag) with current hardware

10. Matteo Macchini Quantization problem Student meeting – October 2014 10121416 0.006136 rad0.001534 rad0.000383 rad0.000096 rad 98.175 rad/s24.544 rad/s6.136 rad/s1.534 rad/s Resolution too lowSlow response Good trade-offs

11. Matteo Macchini Quantization problem Student meeting – October 2014 In our system we will have to deal with a quantized speed (and angle, but it’s much less of an issue!) This can input some spikes in the control loop with bad effects on performance and stability. Solution?FILTERING!

12. Matteo Macchini Filter comparison Student meeting – October 2014

13. Matteo Macchini Filter comparison Student meeting – October 2014 Finite Impulse Response linear filter, 2 samples

14. Matteo Macchini Filter observations Student meeting – October 2014 Observations Filtering, either analogic or digital, will produce: -Lag (even worse!) -“Noisy” outputs

15. Matteo Macchini Kalman filter Student meeting – October 2014 Second solution: OBSERVER! Instead of filtering the signal, we can try to predict how it is going to behave basing on a model, and then correct our predictions taking in account the measures. Such an observer is called a Kalman Filter.

16. Matteo Macchini Kalman filter performance Student meeting – October 2014

17. Matteo Macchini Kalman filter overview Student meeting – October 2014 Advantages: -High response quality -No lag -(Possibility of tuning) Drawbacks: -Need of a good model -Sensitive to parametrical variation -Sensitive to unexpected inputs g = g/10 g = g*4

18. Matteo Macchini Experimental results Student meeting – October 2014 The latter method was implemented on the test bench with good results 2 steps FIR filter Kalman filter In the real system, an estimation of the acceleration is computed by the measurement of currents and angle.

19. Matteo Macchini Conclusions Student meeting - October 2014 CONCLUSIONS Implemented new version of Anti-Windup PID controller with quick response Kalman filter can solve the quantization problem if a trustworthy model of the system is available