An iterative method for suboptimal control of linear time-delayed systems

This article presents a new approach for solving the Optimal Control Problem (OCP) of linear time-delay systems with a quadratic cost functional. The proposed method can also be used for designing optimal control time-delay systems with disturbance. In this study, the Variational Iteration Method (VIM) is employed to convert the original Time-Delay Optimal Control Problem (TDOCP) into a sequence of nonhomogeneous linear two-point boundary value problems (TPBVPs). The optimal control law obtained consists of an accurate linear feedback term and a nonlinear compensation term which is the limit of an adjoint vector sequence. The feedback term is determined by solving Riccati matrix differential equation. By using the finite-step iteration of a nonlinear compensation sequence, we can obtain a suboptimal control law. Finally, Illustrative examples are included to demonstrate the validity and applicability of the technique.     

Inverted pendulum stabilization: Characterization of codimension-three triple zero bifurcation via multiple delayed proportional gains

The paper considers the problem of stabilization of systems possessing a multiple zero eigenvalue at the origin. The controller that we propose, uses multiple delayed measurements instead of derivative terms. Doing so, we increase the performances of the closed loop in presence of system uncertainties and/or noisy measurements. The problem formulation and the analysis is presented through a classical engineering problem which is the stabilization of an inverted pendulum on a cart moving horizontally. On one hand, we perform a nonlinear analysis of the center dynamics described by a three dimensional system of ordinary differential equations with a codimension-three triple zero bifurcation. On the other hand, we present the complementary stability analysis of the corresponding linear time invariant system with two delays describing the behavior around the equilibrium. The aim of this analysis is to characterize the possible local bifurcations. Finally, the proposed control scheme is numerically illustrated and discussed.     

System identification with measurement noise compensation based on polynomial modulating function for fractional-order systems with a known time-delay

This study presents a system identification method based on polynomial modulating function for fractional-order systems with a known time-delay involving input and output noises in the time domain. Based on the polynomial modulating function and fractional-order integration by parts, the identified fractional-order differential equation is transformed into an algebraic equation. By using the numerical integral formula, the least squares form for the system identification is obtained. In order to reduce the effect of noises existing in the input and output measurements, the compensation method for the input and output noises is also studied by introducing an auxiliary high-order fractional-order system in the revised identification algorithm. Finally, the effectiveness of the proposed algorithm is verified by the simulation result of an illustrative example and the experimental result of temperature identification for a thermal system.     

Feedback linearization via state transformation using estimated states

This paper deals with the exact feedback linearization of nonlinear plants using estimated states. Under appropriate hypotheses, exact linearization can be achieved through transformation of states and feedback. We assume that the states cannot be measured so that a nonlinear observer, with exponential convergence, is included in the loop. We establish sufficient conditions to guarantee that the overall system trajectories asymptotically converge to those obtained with feedback linearization utilizing the true states. We apply our results to control an electrical drive using a permanent-magnet synchronous motor without mechanical and optical sensors. The behaviour of our control scheme is illustrated by simulations.     

Finite-time stability and stabilization for stochastic markov jump systems with mode-dependent time delays

This paper is concerned with the problems of finite-time stability and stabilization for stochastic Markov systems with mode-dependent time-delays. In order to reduce conservatism, a mode-dependent approach is utilized. Based on the derived stability conditions, state-feedback controller and observer-based controller are designed, respectively. A new N-mode algorithm is given to obtain the maximum value of time-delay. Finally, an example is used to show the merit of the proposed results.     

Designing an adaptive type-2 fuzzy logic system load frequency control for a nonlinear time-delay power system

In this paper, a combination of type-2 fuzzy logic system (T2FLS) and a conventional feedback controller (CFC) has been designed for the load frequency control (LFC) of a nonlinear time-delay power system. In this approach, the T2FLS controller which is designed to overcome the uncertainties and nonlinearites of the controlled system is in the feedforward path and the CFC which plays an important role in the transient state is in the feedback path. A Lyapunov–Krasovskii functional has been used to ensure the stability of the system and the parameter adjustment laws for the T2FLS controller are derived using this functional. In this training method, the effect of delay has been considered in tuning the T2FLS controller parameters and thus the performance of the system has been improved. The T2FLS controller is used due to its ability to effectively model uncertainties, which may exist in the rules and data measured by the sensors. To illustrate the effectiveness of the proposed method, a two-area nonlinear time-delay power system has been used and compared with the controller that uses the gradient-descend (GD) algorithm to tune the T2FLS controller parameters.     

Robust stability of homogeneous large-scale bilinear systems with time delays and uncertainties

This paper addresses the problem of stability analysis for homogeneous large-scale uncertain bilinear time-delay systems subjected to constrained inputs. Both nonlinear uncertainties and interval systems are discussed. Several delay-independent criteria are presented to guarantee the asymptotic stability of the overall systems. The main feature of the presented criteria is that although the Lyapunov stability theorem is used, they do not involve any Lyapunov equations that may be unsolvable. Three illustrative numerical examples are presented to verify the effectiveness of the proposed stability criteria.     

Generalized multi-scale control scheme for cascade processes with time-delays

The cascade control is a well-known technique in process industry to improve regulatory control performance. The use of the conventional PI/PID controllers has often been found to be ineffective for cascade processes with long time-delays. Recent literature report has shown that the multi-scale control (MSC) scheme is capable of providing improved performance over the conventional PID controllers for processes characterized by long time-delays as well as slow RHP zeros. This paper presents an extension of this basic MSC scheme to cascade processes with long time-delays. This new cascade MSC scheme is applicable to self-regulating, integrating and unstable processes. Extensive numerical studies demonstrate the effectiveness of the cascade MSC scheme compared with some well-established cascade control strategies.     

Synthesized sliding mode and time-delay control for a class of uncertain systems

In this note, the sliding mode control (SMC) is incorporated with time-delay control (TDC) during the sliding phase to reduce the switching gain. TDC identifies the unknown system dynamics and disturbance directly for every time-delay. For a system with a lumped perturbation which is relatively slow varying with respect to the sampling interval, a much low switching gain can be used if a reasonably good estimate of the derivative of system state can be obtained using the past information, hence chattering can be reduced or eliminated while retaining the tracking accuracy.