Control Systems Design Part: Optimisation Slovak University of Technology Faculty of Material Science and Technology in Trnava 2007

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

Control Process Optimisation control process quality  control process stability  steady state - process variable deviation  dynamic control process overshooting time of control process t reg integral criteria f(dev) non oscillation control processes

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 T kr

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 = I part of controller; destabilisation of control loop stability versus quality - solution is compromise

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

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

Dynamic control process optimisation  standard forms of a characteristic polynomial Naslin form of characteristic polynomial The parameter  depends on the chosen overshooting  x max according the table:   x max

Dynamic control process optimisation  standard forms of a characteristic polynomial Graham - Lathrop form

Dynamic control process optimisation  Ziegler Nichols method  input data: GAIN cr - critical gain T cr - critical period measured or computed at the stability boundary of the single control loop with P - controller

Dynamic control process optimisation  Ziegler Nichols method

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 r 0, r -1 and r 1 :

Dynamic control process optimisation  method of optimum module PI controller

Dynamic control process optimisation  method of optimum module PID controller

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:

Dynamic control process optimisation  methods of integral criterions IAE: A B

Dynamic control process optimisation  methods of integral criterions ITAE: AB

Dynamic control process optimisation  methods of integral criterions For GAIN For time constants For Ti For Td

Dynamic control process optimisation  half dumping criterion

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

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

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