Real-time Controller Parameter's Optimal Tuning With Receding Horizon Performance

The formal PID control algorithm was first developed at the early twentieth century with many years5 practical experience.Automatic control theory based on information feedback has been extensively and deeply studied,since the basic feedback concept of cybernetic systems was published by Norbert Wiener.Though control theory has developed from the stage of classi-cal control,modern control and intelligent control,the traditional PID feedback control is still widely used in many industry processes.It is more suitable for dealing with fast tracking prob-lem of the controlled plant in the lower level control loop.The control effect of PID control is directly dependent on the selection of the controller parameters.Many researches have been done on the design of PID controller parameters.How-ever,most studies are confined to the control performance with less consideration on the control energy and the trade-ofF relation between them.In this paper,combining the idea of modern op-timum control,the real-time tuning under constraints for PID controller parameters is proposed based on the receding horizon optimization(RHO)strategy,which satisfies the requirements on the system performance with both tracking performance and weighted control energy contained in the cost function.The main contents are as follows,1)Traditional tuning methods of PID controller parameters,like Ziegler-Nichols(Z-N)method,are difficult to guarantee the best system performance.In this paper,the effects of PID controller parameters on the system tracking performance and control energy are discussed with classical control theory analysis method.Firstly,the ranges of controller parameters are given to make the closed-loop system of two simple low-order controlled plants stable.Then the func-tions of two performance indexes(integral indexes of squared tracking error and control signal)on the controller parameters are established respectively.Combining the theory analysis and simulation results,the nonlinear effects on both system performances are founded.This conclu-sion provides a theory foundation of the finite time receding optimization on PID parameters in discrete domain.2)The former conclusion on the selection of PID parameters between the optimum points,which optimize the system tracking performance and eontrol energy respectively,shows a trade-off between the two system performances.To extend the design of PID parameters to a general high-order controlled plant,we further propose a real-time PID controller parameter optimiza?tion method with a weighted multi-objective performance index in discrete domain.This RHO-PID method can intuitively deal with the constraints on the manipulated variable and tracking signal,and the problem of selection of three PID controller parameters is transferred to be the trade-ofF problem between the tracking performance and control energy.3)The control weight in the receding horizon performance index,which reflects the trade-off relation between the tracking performance and control energy,plays a crucial role in the RHO-PID controller parameter's on-line tuning.Considering the zero steady-state error situa-tion,the system performance mainly reflects in the dynamic response.The control weight can be optimized according to the given requirements on the control energy or dynamic response index within the allowed longest adjusting time.Meanwhile,the design of variable weighted coefficient,which optimize the system performance with input-output constraints,is further dis-cussed.4)The parameters of actual controlled plant may change with time under different working conditions.A data-driven RHO-PID controller parameters tuning method is proposed based on on-line subspace identification.Subspace method,which has robustness of the numerical calculation,requires little priori knowledge of the controlled plant.The future system output in a finite time horizon,described as a function of the PID controller parameters,can be directly obtained by a series of numerical calculation on the Hankel matrices,which are constructed by historical data.Combining with the proposed RHO-PID strategy,the parameters of PID controller can be well tuned.