On the sliding mode control of MIMO nonlinear systems: An input‐output approach

Abstract

Summary We address the sliding mode control design problem for output reference trajectory tracking problems in the special class of MIMO flat systems known as static feedback linearizable systems. We assume unavailable system state components but rely on available inputs and measurable flat outputs. Each controller will largely ignore state and control input couplings by adopting a standard sliding mode controller scheme derived from the SISO case and used this as decoupled input‐to‐flat‐output model. The standard controller arises from a vastly simplified pure integration, additively perturbed, system. The simplified pure integration system controlled trajectories are shown to be time‐scale homotopically equivalent to those of the nonlinear flat system. The basic sliding surface coordinate function design is approached from the perspective of structural integral reconstructors requiring only the inputs and the flat outputs of the system. Integral structural reconstructors were introduced by Fliess et al for the control of linear SISO and MIMO systems, giving rise to the generalized proportional integral control method. Simulations are presented for SISO and MIMO systems and experimental results are reported for a two‐degree‐of‐freedom fully actuated robotic manipulator.

Discrete‐time sliding mode output tracking control for a class of nonlinear perturbed systems

“…due to (23). Thus, as || k || decreases monotonically,ũ eq,k (21) does too, and there will be a time instant k such that ||ũ eq,k || ≤ u max , for k > k. At this time, the equivalent controlũ eq,k (18)-(19) is applied, bringing the closed-loop system trajectory in an ( 2 )-neighborhood of the sliding manifold, 26 that is…”

“…Since modern control systems are implemented by computers, the investigation of discrete time (DT) SMC has been an important topic of the SMC theory. [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] In the DT setting, SMC, similar to the continuous-time case allows decomposing the control design problem into two independent stages:…”

Cascade Second Order Sliding Mode Control for Permanent Magnet Synchronous Motor Drive

“…In [19], a feedback linearization was combined with optimization to deal with parametric changes and applied to a pendulum like a robot. In [20], a standard SMC scheme was derived from the SISO case and used as a decoupled input-to-flat-output model for a robot manipulator with good performance. Despite the good performance of such control strategies, it is difficult to assess the behavior of SMC strategies when dealing with both mechanical and electrical models of the PMSM system.…”

Sustained oscillations in MIMO nonlinear systems through limit cycle shaping

“…Many practical systems have been modeled as multiple‐input multiple‐output (MIMO) systems and not necessarily in the standard strict feedback form. Such systems include an important class of dynamic systems, for example, multilink robots and quadrotors . In literature, different procedures have been developed for solving the regulation or tracking problems in MIMO nonlinear systems .…”

“…Such systems include an important class of dynamic systems, for example, multilink robots and quadrotors. [23][24][25] In literature, different procedures have been developed for solving the regulation or tracking problems in MIMO nonlinear systems. 23,[26][27][28][29] So far, there is no result on stable limit cycle shaping for MIMO nonlinear systems.In this paper, the limit-cycle shaping problem of MIMO nonlinear systems is considered.…”