Tuning of Performance Index in Nonlinear Model Predictive Control by the Inverse Linear Quadratic Regulator Design Method

Abstract

: This paper proposes the use of the inverse linear quadratic (ILQ) regulator design method for the efficient tuning of the performance index in nonlinear model predictive control (NMPC). First, a linear quadratic regulator is designed for the linearized model using the ILQ regulator design approach and then the inverse optimality conditions are applied to the designed regulator to tune the quadratic weights in the performance index of NMPC. After that, the NMPC algorithm is applied to the nonlinear model. This approach provides some tuning parameters that give a trade-off between the speed of the system's response and the magnitude of the control input. Moreover, this tuning methodology provides a free parameter that can be utilized to adjust the transient response as well as to obtain a balance between the magnitudes of the control inputs.Key Words : tuning of performance index, nonlinear model predictive control, inverse linear quadratic regulator design method, coupled three-tank system.

MPC-Based Speed Tracking Control Design for Spark-Ignition Engines

“…Such ILQ regulator design method doesn't need to specify the weightings for the design of control performance, while it will give some choices for the weightings and meanwhile ensure the feedback law is optimal. In [13], a convenient design method based on the optimality conditions of the feedback control is provided that the quadratic weightings are determined by the only single tuning gain. The general design procedure is summarized in Appendix.…”

“…As is well known, the control performance of MPC depends on the weightings in the performance index and also relies on the model precison. In fact, the choices of the weightings P, Q and R contribute significantly to the response speed of the closed-loop system and the magnitude of the control inputs [13]. In this regard, the objective of the study will focus on the experimental validation of the MPC speed tracking control performance with different weightings' choice.…”

“…The basic idea of proposed control scheme is to perform the receding horizon optimization for the tracking error dynamics with respect to any given desired trajectory and to provide a systematic way to tuning the control parameter with ILQ method of linear systems [13]. To this end, the tracking error dynamics is derived with nonlinear compensation that renders the tracking dynamics linear and enables one to apply the ILQ tuning method.…”

“…The response sensitivity of the closedloop control system is also investigated and it can be simply adjusted by a single tuning gain which is derived according to the ILQ regulator design method. Considering the nonlinear characteristic of the engine speed tracking dynamics, the simple linear tracking dynamics is deduced based on the feedback linearization method and then the performance tuning problem can be solved in the framework of the already proposed tuning method in [13]. Moreover, an adaptive compensator is designed to improve the control precision and eliminate the tracking error which caused by the predictive model errors.…”

“…In this context, a convenient tuning approach for MPC performance has the important practical significance with consideration of the time and cost. Recently, a tuning method for MPC performance from the viewpoint of the inverse linear quadratic (ILQ) regulator design is presented in [12] and [13], which becomes a inspiration for this paper. The remarkable advantage of the given method is that it can provide a single tuning parameter for the selection of the MPC weightings while guarantee the optimality of the feedback control system.…”