Modified composite nonlinear feedback control for output tracking of nonstep signals in singular systems with actuator saturation

Abstract

Summary This paper considers output tracking of nonstep reference signals for multi‐input multi‐output singular systems subject to actuator saturation and external disturbances. Singularity of the system alongside the actuator saturation constraint and external disturbances adds more complexity to stability analysis and controller design than normal systems. Moreover, the problem of output tracking of nonstep reference signals in singular systems via the composite nonlinear feedback (CNF) control law is not studied so far in the literature, and this article will investigate this problem for the first time by proposing the modified CNF control law. For this purpose, first, a singular reference generator system is constructed to produce the desired nonstep reference signal. Then, the dynamical error system is obtained by defining a new state vector as the tracking error and augmenting it to the main system. Different parts of the modified CNF control law are designed afterwards. Due to complexities caused by the singularity of the system and the saturation constraint, detailed mathematical calculations are done. In this regard, a theorem is given that guarantees the tracking problem for three different cases of the saturation function. Moreover, the given theorem will investigate the uniform ultimate boundedness analysis of the tracking error in the face of external disturbances. Finally, the theoretical results are affirmed by computer simulations through three examples to verify the performance and applicability of the proposed control law.

Sustained oscillations in MIMO nonlinear systems through limit cycle shaping

“…2 ) in hand, i , and i are calculated according to (25). The controlled blocks ∑ 11 , ∑ 21 , and ∑ 31 by (30a), (30b), and (30c), will have the same structures as the closed-loop system (12). The designed control input u 1 creates desirable oscillation in 1 = (1) 1 through shaping the stable limit cycle M 1 in ∑ 11 .…”

“…Motivated by this, a variety of approaches have been developed in the literature to achieve stable outputs with periodic behaviors . Most of the existing approaches are based on restating the dynamic equations of system in terms of tracking error and solving the stabilizing problem for the error dynamic system . Another solution for creating sustained oscillations in system's outputs is based on choosing a proper limit cycle according to the desired periodic response of the system's output (ie, its shape, amplitude, and frequency).…”

“…[8][9][10][11] Most of the existing approaches are based on restating the dynamic equations of system in terms of tracking error and solving the stabilizing problem for the error dynamic system. 12 Another solution for creating sustained oscillations in system's outputs is based on choosing a proper limit cycle according to the desired periodic response of the system's output (ie, its shape, amplitude, and frequency). Based on this approach, a method for obtaining stable elliptic limit cycles in a class of single-input single-output (SISO) nonlinear systems was introduced by Aracil et al 13 The wanted limit cycle was produced in a second-order subsystem by means of an appropriate feedback law and then was extended to the full system by a backstepping technique.…”

Robust output tracking of nonlinear systems with transient improvement via funnel-based sliding mode control

“…Singla et al (2014) and Chen et al (2017) have used a combination of a nonlinear approach and specific cost functions to progress the speed of the transient responses and to improve the amplitude of overshoot in the closed-loop system, simultaneously. Another control procedure that tries to improve the characteristics of the transient responses is composite nonlinear feedback (CNF) method (Binazadeh and Bahmani, 2018; Jafari and Binazadeh, 2018, 2019, 2020; Wang and Zhao, 2016). Model predictive control (MPC) scheme has also been used for improving the transient response (Köhler et al, 2018; Mehrivash and Shafiei, 2019; Aminsafaee and Shafiei, 2019).…”

Adaptive Robust Tracker Design for Nonlinear Sandwich Systems Subject to Saturation Nonlinearities

“…The existence of these nonsmooth nonlinearities limits the functionality of the system, causes oscillation and an undesirable error, or even may lead to instability in closed-loop systems. [11][12][13][14][15][16] Therefore, the effects of such factors must be considered in the procedure of controller design. Saturation is one of the common static nonlinearities that exist in many practical systems.…”