N. Okaeme, P. Zanchetta , M. Sumner PEMC group University of Nottingham, UK

1. ECON2 Marie Curie Mini-Conference July 9, 2008, School of EEE, University of Nottingham, UK N. Okaeme,P. Zanchetta, M. SumnerPEMC groupUniversity of Nottingham, UK Automated Online Design of Robust Speed Digital Controllers For Variable Speed Drives

2. Outline • Aim of the research • Genetic Algorithm • Digital Controller • Mechanical Loads Investigated • Experimental Approach • Theoretical Approach • Results • Conclusion

3. More complex control strategies have been proposed in literature: • Sliding mode control • Fuzzy logic control • Fuzzy-sliding mode control Aim of the research Traditional controllers such as Proportional plus Integral (PI), which are widely used in industrial drives, may not give satisfactory results in all operative conditions, above all in the presence of largely variable loads. Keep straightforward control implementation Provide excellent performance and robustness to variable loads

4. Aim of the research To investigate a control design procedure: Robustness to variable loads and different load types Traditional discrete linear control implementation (z domain controllers) (Most likely need higher order controllers) No need for a fixed control structure Automated design No need for plant modelling On-line optimization procedure for experimental control system design using Genetic Algorithm (GA)

5. Aim of the research

6. Outline • Aim of the research • Genetic Algorithm • Digital Controller • Mechanical Loads Investigated • Experimental Approach • Theoretical Approach • Results • Conclusion

7. Genetic Algorithm Stochastic global search method based on biological evolution • Developed as a Part of Evolutionary Computing introduced in 1960s By I. Rechenberg • GA proposed by John Holland in the mid-1970s • Random Numerical Search and Optimisation Technique that operates on a population of potential solutions, termed individuals, applying the principle of evolution, simulated by means of mathematical operations that mimic the process of selection, crossover and mutation. • A “fitness function” measures the fitness of an individual to survive in a population of individuals. GA

8. Genetic Algorithm Evaluate Fitness Value (Using Fitness Function) Are Optimisation Criteria met? (Max. No of Generations) Best Individuals Ps Result Selection Generate New Population Pc Crossover Pm Mutation Randomly Generate Initial Population Yes No

9. Genetic Algorithm Fitness function evaluation • The quality of the system response to each load operative condition is quantified online using the Fitness function. • The fitness function is defined as a linear function of the target specifications: overshoot (OS), rise time (tr), steady state error (ess), steady state ripple (rss), system bandwidth (BW) - Further requirements can be added • These indices are weighted individually and are summed up to give a fitness value. The overall quality of the closed loop response under different load conditions is obtained by weighting and then summing all of the relative fitness values FF = (k1*OS+ k2*tr+ k3*ess+ k*4 rss + k5* BW)J=Jnom+ (k1*OS+ k2*tr+ k3*ess+ k*4 rss + k5* BW)J=2Jnom+………

10. Roulette wheel example Genetic Algorithm Selection • Process that chooses the fittest individuals from a population to continue into the next generation. Principle of “Survival of the fittest” • Proportionate selection: the probability that an individual advances to the next generation it`s proportional to its relative fitness • Expected offsprings of an individual = product of the individual`s relative fitness times the number of individuals in the population.

11. Genetic Algorithm Crossover • Crossover generates new individuals by exchanging genetic material between individuals • Individual coding uses real number representation • A random number between 0 and 1 is generated. If it is smaller than a fixed crossover probability then two individuals are randomly chosen and crossed. The resulting offspring replaces the parents in the new population. C1 and C2 = parents individuals; C1new and C2new = offsprings C1new =  C1+(1-) C2 C2new =  C2+(1-) C10<<1 Crossover parameter

12. Genetic Algorithm Mutation • Mutation effects a random variation upon the gene of an individual with a fixed mutation probability • A random number between 0 and 1 is generated. If it is smaller than the mutation probability then a gene is randomly chosen and mutated. The resulting offspring replaces the parents in the new population • Uniform Mutation: Ci = [Ci1,…., Cij …., Cin] Individual Cinew = [Ci1,…., Cijnew …., Cin] New individual after mutation where Cijnew is a random value (with uniform probability distribution) within the domain of Cij

13. Outline • Aim of the research • Genetic Algorithm • Digital Controller • Mechanical Loads Investigated • Experimental Approach • Theoretical Approach • Results • Conclusion

14. F1 F2 F3 F4 F5 kpi Zpi P1 Z1 P2 Z2 … Structure Binary Flags Real Parameters Digital Controller Encoding unstructured controllers e(k) u(k) F1 F2 F3 F4 F5 Chromosome of a single controller :

15. Outline • Aim of the research • Genetic Algorithm • Digital Controller • Mechanical Loads Investigated • Experimental Approach • Theoretical Approach • Results • Conclusion

16. Mechanical Loads Investigated • Stiff shaft mechanical load • J1≤ Jem ≤ 5J1 and B≤ Bem ≤ 5B • Flexible shaft mechanical load • J2≤ JLem ≤ 5J2, D≤ Dem ≤ 5D, backlash=1.5rad/sec

17. Outline • Aim of the research • Genetic Algorithm • Digital Controller • Mechanical Loads Investigated • Experimental Approach • Theoretical Approach • Results • Conclusion

18. The online experimental GA optimisation is performed on the controller of the drive motor Hardware system for control implementation and GA optimisation The dynamics of the load motor control loop is manipulated to emulate the characteristics of different mechanical loads Experimental Approach Two identical permanent magnet DC servomotors coupled along the same shaft. One serves as the Driving motor and the other as the load motor.

19. Experimental Approach Power conversion stages: DC to DC converter based on a MOSFET H-Bridge configuration switching at 20kHz with nominal current of 5A Control: xPC target toolbox in Matlab-Simulink and interfaced with the motors using the National Instrument PCI-MIO-16XE-10 I/O board

20. Experimental Approach • High Flexibility Original Software tool in Matlab - every type of application and control structure - fitness function adjustable to specs requirements • The software defines the more appropriate order and the best structure of the controller and determines the optimum values of its parameters • Structure can include: gain, pure integrator, PI regulator, real poles and zeros, complex poles and zeros • The user can set: - bounds for the parameters values - probability of mutation and crossover - guidance on the controller structure

21. Current reference Controller Parameters Control processor DC drive with bult-in current control Speed, Response Fitness function evaluation Speed Speed control test Summary on Experimental approach Robust control design for loads with variable inertia • The GA software is written in Matlab language and runs on the host PC • Each individual is then tested experimentally online on the actual real rig • The speed closed loop dynamic for the range of different mechanical loads is measured Host PC runs GA in Matlab

22. Summary on Experimental approach Optimization time: • Optimisations are performed through 30 generations with each generation having 40 individuals; Each experiment takes approximately 5s. Total time for the optimisation is approximately two hours • Experience has shown that improvements obtained with longer optimizations are not substantial for the sake of control robustness. Protections: • During the experiments, it is necessary to prematurely stop the experimental test of badly performing individuals (to reduce the time duration of the experiments, as well as the risks of damages to the hardware). • Suitable logical protection schemes both in the control software and hardware implementation.

23. Outline • Aim of the research • Genetic Algorithm • Digital Controller • Mechanical Loads Investigated • Experimental Approach • Theoretical Approach • Results • Conclusion

24. Background

26. Identification of Nominal Model • Offline simulation model • Sub-optimal controller • Model of mechanical loads • Achieved using GA • Run of 50 generations & 50 individuals • Identified over drive’s speed range • Parameters identified at particular speeds • Range of operation 0 – 3000 rpm • Parameters values vs. speed plots • Nominal model = average of parameters

27. Identification of Nominal Model • Mechanical load with stiff shaft Variation of the friction of the nominal load Variation of the Inertia of the nominal load

28. Identification of Nominal Model • Mechanical load with stiff shaft GA identified nominal model response matched with experimental data reference speed = 105 rad/s GA identified nominal model response matched with experimental data reference speed = 210 rad/s

29. Identification of Nominal Model • Mechanical load with flexible shaft Variation of the Inertia of the nominal load Variation of Damping coefficient of nominal load with speed

30. Identification of Nominal Model • Mechanical load with flexible shaft Backlash causes oscillations; reference speed = 105 rad/s reference speed = 210 rad/s

31. Plant Uncertainty Model • Feedback Uncertainty Model for Gp is selected • Models Unstructured Uncertainty • Poles crossing from left & right-half plane

32. Plant Uncertainty Model • Define weighting function, W2 Load with flexible Shaft W2 = 0.002(0.004s + 1) Load with Stiff Shaft W2 = 0.00075(0.325s + 1)

33. - Sensitivity function Performance criteria • Robust stability condition Where S is: and C is the controller transfer function

34. Closed loop control design • Optimization implemented using GA • Offline model of experimental system • Fitness function • Nominal performance & Robust Stability

35. Outline • Aim of the research • Genetic Algorithm • Digital Controller • Mechanical Loads Investigated • Experimental Approach • Theoretical Approach • Results • Conclusion

36. Results • GA designed controller response Load with Stiff Shaft Inertia = 5J, Friction = 5B Tr = 100ms, Ts = 110ms Load with Stiff Shaft Inertia = J, Friction = 5B Tr = 50ms, Ts = 55ms

37. Results • GA designed controller response Load with flexible shaft with backlash Inertia = 5J, Damping = 5D Tr = 60ms, Ts = 65ms Load with flexible shaft with backlash Inertia = J, Damping = 5D Tr = 52ms, Ts = 57ms

38. Outline • Aim of the research • Genetic Algorithm • Digital Controller • Mechanical Loads Investigated • Experimental Approach • Theoretical Approach • Results • Conclusion

39. Conclusion • Simple & effective approach • Reduces commissioning time for drives • Requires little user interaction • Experimental robust control design • Does not require modelling • Optimization implemented directly on rig • Theoretical robust control design • Faster implementation within computer • Less stress experienced by load machine