Output‐feedback sliding‐mode control for systems subjected to actuator and internal dynamics failures

Abstract

This study presents an output-feedback control algorithm based on unit vector sliding mode for a class of multivariable systems. The control objective is to force each output signal to track a desired reference trajectory, while retaining good performance despite parameter uncertainties, unmatched disturbances and actuators faults that eventually may occur in the plant. Owing to the new approach proposed to tackle this problem, which involves a linear matrix inequality to be satisfied by the control distribution matrix, no upper bound on this matrix is required. Moreover, a remarkable result is that the proposed fault-tolerant controller can even handle variations in the order of the system dynamics. The analysis shows that the resulting closed-loop system is globally exponentially stable. A simulation example with a chain of trailers driven by redundant actuators illustrates the design and effectiveness of the proposed strategy.

Adaptive unit vector control of multivariable systems using monitoring functions

“…Remark 1. There are many possible choices for (k, t −t ) satisfying (38). For instance, an admissible choice is Unit vector control law u(t) = S p U(t), U(t) = − (t) (t)…”

“…Indeed, suppose that the system never enters in Phase 2. Then, from (34), (k, t −t ) will switch without stopping either due to || (t)|| → || (0)|| + Δ or to t → T. Therefore, from the -equation and taking (38) and (44) into consideration, it follows that, no matter how large d̄is, after at most finite switchings, we have…”

“…Since (k, t −t ) is assumed to switch without stopping, for any given positive constant C∕T, from (44), and taking into account (38), there exists an integerk ≥k, such that, ∀k ≥k, both (46) and the following inequalities hold:…”

“…The parameter b = 1.5 is chosen such that the amplitude of the modulation function (72) satisfies (38) at each switching. The parameter c = 0.2 is chosen such that the initial value of the modulation function given by (1, 0) = cb is small enough to prevent unnecessarily high-control amplitude that could damage the vessel.…”

Actuator multiplicative fault estimation in discrete-time LPV systems using switched observers

“…However, much of the recent research in FTC has considered systems affected by multiplicative faults, see e.g. the sliding mode control-based solutions developed in [13] and [14]. The main difference between an additive and a multiplicative fault is that, as a result of the additive faults, the mean value of the output changes, while if the fault is multiplicative, it generates changes on the system parameters [15].…”