Robust controller design for input‐delayed systems using predictive feedback and an uncertainty estimator

Abstract

This paper deals with the problem of stabilizing a class of input-delayed systems with (possibly) nonlinear uncertainties by using explicit delay compensation. It is well known that plain predictive schemes lack robustness with respect to uncertain model parameters. In this work, an uncertainty estimator is derived for input-delay systems and combined with a modified state predictor, which uses current available information of the estimated uncertainties. Furthermore, based on Lyapunov-Krasovskii functionals, a computable criterion to check robust stability of the closed-loop is developed and cast into a minimization problem constrained to an LMI. Additionally, for a given input delay, an iterative-LMI algorithm is proposed to design stabilizing tuning parameters. The main results are illustrated and validated using a numerical example with a second-order dynamic system. 1827 robustness (which was a common practice in frequency-based methods). Works in this line are scattered. Regarding disturbance rejection, in [25] a low-pass filtered prediction is shown to improve disturbance rejection capabilities and, in [26], better disturbance rejection is achieved by introducing a modified state prediction. Regarding robustness improvement, which is the problem this paper is concerned with, a sliding mode control with delay compensation is proposed in [27] to deal with matched uncertainties; in [28], adaptive schemes are introduced to estimate uncertain plant parameters and input delay, and a control strategy is proposed in [29] to deal with Euler-Lagrange-like nonlinear systems with time-varying input delay.In this paper, the disturbance observer based control is adopted to improve the robustness of the state predictor. The basic idea behind this technique is to use a model of the system along with its input/output information to identify uncertainties and disturbances [30]. There are slightly different techniques that pursue the same goal, which have been recently summarized and explained in [31] (see also the references therein). Most of them make use of some sort of low-pass filter which is needed to obtain a realizable control law. In general, the bandwidth of this filter is desired to be as high as possible to estimate uncertainties in a wide range of frequencies. However, in [32], by means of the Bode's integral formula, it is shown that there is a severe limitation in the choice of the bandwidth if the plant includes time delay. Intuitively, the uncertainties can be estimated arbitrarily fast, but they cannot be counteracted in the same way. This inconvenient can be seen as analogous to the need of detuning PID controllers for open-loop unstable systems [33]. An attempt of combining the state predictor with a disturbance observer based control technique known as the active disturbance rejection control can be found in [34], but neither the analysis nor the design problems are tackled, presenting only numerical case studies. Also, a similar idea was explored in [35], where work in [36] is extended to the case of st...

Predictor‐based output feedback control design for sampled systems with input delay subject to disturbance

“…Remark 1 An assumption that the input dynamics matches with that of disturbance, i.e. , was made in [27, 28], while the system state was assumed available for control design. Herein these two assumptions are exempted for output feedback control design so as to facilitate practical applications.…”

“…Following the delayed control approach [25], a modified Artstein predictor‐based control design [26] was proposed for continuous LTI systems with dead time and unknown disturbance. Recently, a robust controller design [27] was developed in continuous‐time domain for input‐delayed systems with non‐linear uncertainties, by constructing an uncertainty estimator together with a state predictor. Using a linear tracking differentiator, an enhanced disturbance rejection design for continuous‐time LTI systems with input delay was developed in [28].…”

“…In this paper, a predictor‐based output feedback control design is proposed for sampled systems with input delay subject to disturbance, taking into account not only the advantage of state prediction for improving control performance [24, 26, 27], but also the advantage of using an ESO to estimate disturbance dynamics for anti‐disturbance control design [29, 30]. Based on only the output measurement, an ESO is constructed to simultaneously estimate the plant state and disturbance dynamics.…”

Regional Stabilization of Input-Delayed Uncertain Nonlinear Polynomial Systems

“…The stability analysis and control synthesis of dynamical systems under delayed inputs is a problem that has been attracting the interest of control practitioners over the last decades due to the inherent transport delays in practical applications, and more recently because of induced communication delays in the context of networked control systems (see, for instance, [1]- [4] and references therein). For linear systems, there exist several approaches to deal with input delay in the frequency and state-space domains such as the predictorbased approach [5], the model reduction technique [6], and the ones employing either Lyapunov-Razumikhin or Lyapunov-Krasovskii stability theories to take model uncertainties and varying delays into account -see, e.g., [7], [8] and the references therein.…”

Rejection of mismatched disturbances for systems with input delay via a predictive extended state observer

“…For unknown sinusoidal disturbances, cancelation by means of adaptive control schemes have been also achieved in the works of Basturk. () Uncertainty observers have been also used in the work of Sanz et al to deal with norm‐bounded nonlinearities.…”