Robust adaptive control of Hammerstein nonlinear systems and its application to typical CSTR problems

Abstract

This paper considers the robust adaptive control of Hammerstein nonlinear systems with uncertain parameters. The control scheme is derived from a modified criterion function which can overcome non-minimum phase property of the linear subsystem. The parameter adaptation is performed by using a robust recursive least squares algorithm with a deadzone weighted factor. The control law compensates the model error by incorporating the unmodeled dynamics estimation. An online pole assignment technique is also presented to guarantee that Assumption 2 always holds. Rigorous theoretical analysis indicates that the parameter estimation convergence and the closed-loop system stability can be guaranteed under mild conditions. Simulation examples including two typical continuous stirred tank reactor problems are studied to verify the effectiveness of the control scheme. ROBUST ADAPTIVE CONTROL OF HAMMERSTEIN NONLINEAR SYSTEMS 165 where f i .u.t // are user-chosen basis functions. This work employs the following polynomial basis functions to approximate the static nonlinearities Figure 2. Adaptive control scheme for Hammerstein system. The initialization is that O Â.0/ D OE1:4; 0:12; 0:8; 0:1; 0:35; 0:7; 0:05; 0:2 T y.0/ D v.0/ D u.0/ D 0, P .0/ D 10 5 I , $ D 0:75, D 0:02 for noise-free case or D 0:1 for noisy case. Simulations are conducted under the following initial conditions: Condition 1 x 3 .0/ D 0:8467; x 4 .0/ D 1:3796; y R .0/ D x 5 .0/ D 1:2737; u Q .0/ D 0 Condition 2. x 3 .0/ D 1; x 4 .0/ D 0:3796; y R .0/ D x 5 .0/ D 0:7737; u Q .0/ D 0

Three‐stage least squares‐based iterative estimation algorithms for bilinear state‐space systems based on the bilinear state estimator

“…Another problem occurs because the parameter matrix A 1 (t) and vector b are unknown. Therefore, the state estimation in (26) to (31) cannot be realized. The solution is to use the parameter estimatesâ k ,b k , andm k obtained by Equations (21) to (25) to construct the estimates k ,M k andb k of A, M, and b aŝ…”

“…Then, the estimate 1,k (t) of A 1 (t) can be obtained by 1,k (t) ∶= k + M k u(t). Replacing A, M, b, and A 1 (t) in (26) to (31) with their estimates k ,M k ,b k , and 1,k (t) giveŝ…”

“…25 However, it needs heavy computational cost when calculating the inversion of the covariance matrix of large sizes. 26 In order to overcome this problem and improve the identification results of bilinear systems, we employ the hierarchical identification principle to deal with the computational cost problem. So-called hierarchical identification was inspired initially by the hierarchical control for large-scale systems based on the decomposition-coordination principle.…”

Design of an H∞ PI controller with given relative stability and its application to the CSTR problem

“…The mathematical model of CSTR has the form [29][30] The goal of the control systems is to control the CSTR composition (y) by manipulating the cool rate through the control signal (u). Different control strategies are presented in literature [31][32]34].…”

“…Great attention has been paid to the control of CSTR processes and different approaches have been developed such as the predictive control strategy [31] and the Hammerstein model [32], which yielded a robust adaptive controller.…”