Robust stabilization and tracking control schemes for disturbed multi-input multi-output Hammerstein model in presence of approximate polynomial nonlinearities

Abstract

This article presents robust stabilization and tracking control problems for multi-input multi-output Hammerstein model with external disturbances. This model is characterized by static nonlinear elements followed by a linear dynamic block. Moreover, the unknown parameters of the identified mathematical model are estimated using the multivariable output error state space subspace algorithm. Unlike the general control strategy that used the nonlinearity inversion method, the nonlinearities are supposed not bijective. In this context, inverse nonlinear functions of polynomial structure are suggested in this article. Furthermore, the composition of the static nonlinear elements and their approximate inverses in series with the linear dynamic block are then decomposed into a set of linear parts using the Takagi–Sugeno fuzzy representation. Consequently, new sufficient stability conditions with decay rate and disturbance attenuation using the [Formula: see text] criterion and linear matrix inequality tools are discussed. Finally, simulation studies are provided to illustrate the merit of our purpose.

Nonfragile H∞ Stabilizing Nonlinear Systems Described by Multivariable Hammerstein Models

“…where ΔV Lyap (x k ) � V Lyap (x k+1 ) − V Lyap (x k ) and P ∈ R n×n is a symmetric positive definite matrix. By considering (27) in (24), we may write…”

“…In this view, many algorithms and approximations are used in the literature to determine the corresponding nonlinearity inverse. One may refer to latest research works based on polynomial form approximation [23,27,28], Bernstein-Bezier neural network [29], De Boor algorithm [30], and rational B-spline model approximation [31].…”

“…Remark 1. Consider system (19) with no uncertainty, i.e., ΔK � 0. en, the origin of the closed-loop system ( 26) is globally asymptotically stable if [27] minimize…”

Digital twin-based subspace model predictive control for thermal power plant

“…The parameter perturbations always exist in actual power plants and affect the coordinated control performance. Generally speaking, common control methods such as active disturbance rejection control, 30,31 robust control, [32][33][34] output feedback integral control, 35 and MPC 13,36 have certain robustness and anti-interference ability so that the influence of parameter perturbations on outputs can be eliminated by adjusting the inputs. For the complex controlled object with large inertia and large time delays like power plants, although the system can maintain stable operation, the control performance will inevitably deteriorate.…”