A gain‐tuning method for almost disturbance decoupling problems of nonlinear systems with zero dynamics

Abstract

In this paper, a gain-tuning method for almost disturbance decoupling problems of nonlinear systems with zero dynamics is developed. Firstly, a linear subsystem is formed by linearizing the nonlinear system. Then, a linear matrix inequality can be formed for the linear subsystem. After that, a linear state-feedback controller can be obtained by solving the linear matrix inequality. A nonlinear state-feedback controller can be obtained for the original nonlinear system by using backstepping design method. Another linear state-feedback controller can be derived by linearizing the nonlinear state-feedback controller. Finally, the backstepping gains can be solved by equating the two linear controllers. The detailed derivations of the method are provided. Some comparisons with the existing techniques are discussed. Moreover, the designed method is verified by simulations and some comparisons are made accordingly.

Observer-Based Adaptive Finite-Time Neural Control for Constrained Nonlinear Systems With Actuator Saturation Compensation

“…B ACKSTEPPING technology as a recursive Lyapunov policy has attracted wide attention, and many constructive results have been reported to control nonlinear systems in [1]- [5]. However, the "explosion of complexity" issue severely hinders the application of backstepping control (BC) [1].…”

“…B ACKSTEPPING technology as a recursive Lyapunov policy has attracted wide attention, and many constructive results have been reported to control nonlinear systems in [1]- [5]. However, the "explosion of complexity" issue severely hinders the application of backstepping control (BC) [1]. To overcome this issue, a dynamic surface control (DSC) was primarily in [2] by using the low-pass filter to approximate the derivative of the virtual control law in each iteration.…”

“…The primary innovations of this study are highlighted, as (1) Unlike the multi-objective adaptive CFB [8], the neural CFB [10], and the event-triggered DSC [3], the proposed controller, which integrates the CFB technology and the filtering-error compensation system, not only solves the problems of "explosion of complexity" and the filtering error but also realizes the fast finite time convergence. Compared to previous studies in [1]- [3], [20], [36], this study does not require the availability of system states, which means that the state observation and the controller can be designed independently. This makes proposed controller more flexible for practical applications.…”

“…(1) Squared error (SE):µ SE = N i=1 x1 (i) − y d (i) 2 ; (2) Absolute error (AE): µ AE = N i=1 |x 1 (i) − y d (i)|; (3) Time-weighted absolute error (TWAE): µ T AE = N i=1 i|x 1 (i) − y d (i)|.For the Example 4, the evaluation indices are modified as µ SE = 3 j=1 N i=1 xj,1 (i)−ϕ d (i) 2 , µ AE = 3 j=1 N i=1 |x j,1 (i)− θ d (i)|, and µ T AE = 3 j=1 N i=1 i|x j,1 (i) − ψ d (i)|.…”

Weak disturbance decoupling of high‐order fully actuated nonlinear systems

“…With sampled‐data output feedback controller, the ADD problem for a class of strict feedback‐like systems subject to time‐delays was solved in References 16. Reference 17 proposed a gain‐tuning method for ADD problems of nonlinear systems with zero dynamics. Some practical applications about ADD problems were studied as well, such as the satellite attitude control, 18 web tension control 19 and ball and beam system 20 …”