A Robust Controller Design Method Based on Parameter Variation Rate of RBF-ARX Model

Abstract

As an extension of the exponential autoregressive model and radial basis function (RBF) network, the RBF-ARX model has been widely used in nonlinear system modeling and control. Considering conservativeness of the previous method, which only uses the upper and lower limits of the RBF-ARX model parameters to construct a system's polytopic state space model, in this paper, the model's parameter variation rate information is also utilized to compress variation range of the coefficient matrices in the system's state space model. And then, a robust predictive control (RPC) strategy for output tracking without using system's steady state information is designed. The method of constructing the system's polytopic state space model takes advantage of the fact that the RBF-ARX model itself is a special quasi-LPV model, and there is no need to assume the time varying parameters and/or the variation rate of the parameters in the system model are known or measurable. The effectiveness of the proposed control strategy is verified on a continuous stirred tank reactor (CSTR) process. INDEX TERMS Robust predictive control, robustness and stability, nonlinear model, parameter variation rate.

An RBF-ARX Model-Based Variable-Gain Feedback RMPC Algorithm

“…Besides, the constraints max () | , 0 u u k i k i   in (19) can be described by conditions (33)(34) in bellow.…”

“…Based on the RBF-ARX model, Tian et al [33] designed an RMPC algorithm for a practical inverted pendulum system with high efficiency. Zhou et al [34] also studied an RMPC strategy designed based on the variation rate of RBF-ARX model parameters.…”

“…Although the existing RBF-ARX model-based RMPCs in Refs. [29][30][31][32][33][34] have some advantages, the state feedback control gains in the control policy of these robust controllers are all fixed as the constant. However, research results in Refs.…”

“…[31] (RMPC-2) and the RMPC algorithm proposed in Ref. [34] (RMPC-3). For a fair comparison, the three RMPCs and RMPC-P are designed with the same RBF-ARX model.…”

SD-ARX modeling and robust MPC with variable feedback gain for nonlinear systems

“…19,20 By approximating the functional coefficients in an SD-ARX model with radial basis function (RBF) neural networks, the RBF-ARX model can be obtained. [21][22][23] The SD-ARX model-based RMPC for systems without disturbance was first studied in the work of Peng et al 24 Based on this type of model, an RMPC with unknown steady-state information was proposed in Zhou et al 25 To decrease the conservativeness of the LPV models in studies such as Peng et al, 24 Zhou et al 25 Zhou et al 26 proposed an RMPC synthesis method using the model's parameter boundary information, and based on this model, they 27 further proposed a one-stage scheduling RMPC. So far, many meaningful researches of SD-ARX model-based RMPC have been reported, [24][25][26][27] whereas the research has mainly focused on studying single-constant feedback RMPC algorithms.…”