Control Systems Design Part: Optimisation

1. Slovak University of Technology Faculty of Material Science and Technology in Trnava ControlSystemsDesign Part: Optimisation 2007

2. Control Process Optimisation • Optimisation Process • control loop structure design • optimum criteria selection • optimum control parameters computation • control process simulation • control parameters refinement • control process quality evaluation • documentation production • ...SAT

3. Control Process Optimisation • control process quality • control process stability • steady state - process variable deviation • dynamic control process • overshooting • time of control process treg • integral criteria f(dev) • non oscillation control processes

4. Control Process Optimisation • control process stability • characteristic polynomial • characteristic polynomial roots • negative part of complex roots! • degree of the stability • critical parameters • single control loop with P controller • critical GAIN • critical period Tkr

5. Control Process Optimisation • steady state - process variable deviation • should be = 0; Deviation = Set Point - Process • the P controller problem: GAIN has to be as large as possible; (!) stability violation for higher order systems • else process deviation = 0 --- I part of controller; destabilisation of control loop • stability versus quality - solution is compromise

6. Control Process Optimisation • Dynamic control process optimisation • standard forms of a characteristic polynomial • Ziegler Nichols method • method of optimum module • methods of integral criterions

7. Dynamic control process optimisation • standard forms of a characteristic polynomial • Naslin form of characteristic polynomial is according the i = 1,2, .... n-1

8. Dynamic control process optimisation • standard forms of a characteristic polynomial • Naslin form of characteristic polynomial The parameter a depends on the chosen overshooting Dxmax according the table: a 1.7 1.75 1.8 1.9 2.0 Dxmax 20 16 12 8 5

9. Dynamic control process optimisation • standard forms of a characteristic polynomial • Graham - Lathrop form

10. Dynamic control process optimisation • Ziegler Nichols method • input data: GAINcr - critical gain Tcr - critical period measured or computed at the stability boundary of the single control loop with P - controller

11. Dynamic control process optimisation • Ziegler Nichols method

12. Dynamic control process optimisation • method of optimum module The transfer function of a controlled system is supposed in the form The control parameters are for the ideal parallel PID algorithm r0, r-1 and r1:

13. Dynamic control process optimisation • method of optimum module • PI controller

14. Dynamic control process optimisation • method of optimum module • PID controller

15. Dynamic control process optimisation • methods of integral criterions • IAE Integral of Absolute Error • ITAE Integral of Absolute Error multiplied by Time • Dynamic system approximation by K, T and D:

16. Dynamic control process optimisation • methods of integral criterions IAE: A B

17. Dynamic control process optimisation • methods of integral criterions ITAE: A B

18. Dynamic control process optimisation • methods of integral criterions For GAIN For time constants For Ti For Td

19. Dynamic control process optimisation • half dumping criterion

20. Dynamic control process optimisation • half dumping criterion Dynamic system approximation by K, T and D:

21. Control Process Optimisation • half dumping criterion • PI controller: Auxiliary parameter For GAIN For integral time constant Ti

22. Control Process Optimisation • half dumping criterion • PID controller: Auxiliary parameter For GAIN For integral time constant Ti For derivative time constant Td