Input-delay Systems Research Articles

Formulas on Preview and Delayed $H^{\infty}$ Control

A generalized Hinfin control problem, which covers preview and delayed control strategies, is discussed based on a state-space approach. By introducing a Hamiltonian matrix, which is associated with a delay-free generalized plant, the analytic solution to the corresponding operator Riccati equation is newly established. Based on the result obtained here, the Hinfin control problem is solved and, for typical control problems (e.g., Hinfin and linear quadratic (LQ) control for multiple input delay systems, Hinfin preview control), some interpretations are provided on the resulting control system

Stabilization of Input Delay Systems by Using Sliding Mode Control

In this paper, we consider the stabilization problem of linear systems with time-delay at the input by using a sliding mode control. Sliding Mode Control (SMC) is a well-known robust control method for systems with model uncertainties and disturbances and a large number of the design methods for finite dimensional systems have been proposed. However there are a few design methods which are applicable for input-delay systems. To overcome the drawback, we analyze the stability of input-delay systems with switching inputs by transforming the systems into the equivalent systems with time-varying feedback gain. As a result, we show that input-delay systems cannot be asymptotically stabilized by the SMC with signal function. Then we derive a sufficient condition for asymptotic stability of the systems with SMC. Thereafter we propose a SMC design method for systems with uncertain delay at the input. The effectiveness of the proposed methods are illustrated by numerical simulations.

Optimal Tracking Design for Hybrid Uncertain Input-Delay Systems under State and Control Constraints via Evolutionary Programming Approach

A novel digital redesign methodology based on evolutionary programming (EP) is introduced to find the 'best' digital controller for optimal tracking design of hybrid uncertain multi-input/ multi-output (MIMO) input-delay systems with constraints on states and controls. To deal with these multivariable concurrent specifications and system restrictions, instead of conventional interval methods, the proposed global optimization scheme is able to practically implement optimal digital controller for constrained uncertain hybrid systems with input time delay. Further, an illustrative example is included to demonstrate the efficiency of the proposed method.

Robust stabilization of uncertain systems with unknown input delay

This paper is concerned with the robust controller design for uncertain input-delayed systems. The time delay is assumed to be an unknown constant. A controller with delay feedback for the robust stabilization of the system is proposed. The stability criterion of the closed-loop system is derived in terms of linear matrix inequalities (LMIs). Examples show that in many cases our method can give less conservative results than those by the existing methods. Moreover, for the same cases, our controllers have lower feedback gains than the existing ones.

Optimal digital redesign of hybrid cascaded input-delay systems under state and control constraints

This paper presents a new multi-objective evolutionary programming (MOEP)-based digital redesign scheme to find an optimal low-gain digital tracking controller for hybrid control of multi-input, multi-output (MIMO) cascaded analog systems with input time delays, having the constraints on the states and inputs. The proposed global optimization searching technique enables one to find a high-gain optimal analog controller for analog control of MIMO analog systems with specified performances and constrained states. Then, a new MOEP-based digital redesign method, taking into account the inter-sample behavior of the digitally controlled state, is developed to determine the longest possible sampling period under the state and input constraints and to reconstruct the low-gain pulse amplitude modulated (PAM) digital controller for hybrid control of the cascaded input-delay systems. The resulting controlled hybrid system is able to satisfy the state and actuator constraints without significantly affecting the overall performance of the hybrid cascaded systems with input time delays.

Synthesis of Controllers Which Explicitly Contain Plant States Generators

This paper deals with multiobjective control problems for systems whose partial states can be generated by a stable system. For given problems we propose a method to synthesize controllers which explicitly contain the stable system. The synthesis method is proposed as a consequence of the following results : (a) there exists an equivalent problem where partial states of a given generalized plant are exactly available; (b) the resultant controller is constructed by the stable system and another controller for the equivalent problem. The proposing method is advantageous owing to the following reasons : (1) it is possible to synthesize, based on LMIs, controllers which explicitly contain stable systems; those stable systems generate partial states of generalized plants; (2) computational complexity in LMI synthesis can be reduced; (3) computational time to produce control input can be shorten. Moreover, numerical experiments clarify the effectiveness of the proposed method in the case of discrete input delay systems.

H∞ Control for Preview and Delayed Strategies

Achievable performance of preview and delayed control is investigated in terms of H∞ criterion. We defined a generalized class of H∞ problem, in which both control and disturbance involve multiple delays, and provide a check method of solvability based on a solution to matrix Riccati equation. The posed problem covers robust H∞ preview control problem, the H∞ control for multiple input delay systems, and further it enables to derive formulas of LQ control for multiple input delay systems.

Finite spectrum assignment for input delay systems

The problenl of polynomial invariant factors assignment of input delay systems with classical spectrum assigment control laws with distributed delays is adressed. The multiplicities of the invariant factors are shown to be restricted by specified Rosenbrock type inequalities. The results are proved with the help of an equivalent linear assignment problem with no delay, and within the Bezout domain ε. A bidinlensional illustrative example is given.

Delay robustness of closed loop finite assignment for input delay systems

The problem of the robustness with respect to delay uncertainty for the finite spectrum closed loop assignment of input delay systems is addressed. Numerically exploitable conditions in terms of the maximal deviation of the design delay, and of the assigned closed loop are given. An analytic expression of a lower bound of this deviation guaranteeing stability in the monovariable and multivariable case are obtained. The Smith predictor and related schemes are also revisited.

Robust stabilization of uncertain input-delayed systems using reduction method

This paper concerns a robust stabilization problem that arises when applying the so-called reduction method to multiple input-delayed systems with parametric uncertainties. A robust stabilizing controller that can be constructed easily by solving convex problems in terms of linear matrix inequalities is presented. Numerical examples are provided to show that in many cases the proposed controller is less conservative and easier to obtain than the existing controllers.

Sliding mode control with uncertainty adaptation for uncertain input-delay systems

This paper deals with a sliding mode control with uncertainty adaptation for the robust stabilization of uncertain input delay systems. The types of uncertainties comprise unknown time-varying non-linear parameter perturbations and external disturbance. A sliding surface including a state predictor is employed to compensate for the input delay. The proposed method does not need a priori knowledge of upper bounds on the norm of the uncertainties, but estimates them by using the adaptation scheme based on the sliding surface. Then, a robust control law with uncertainty adaptation is derived to ensure the existence of the sliding mode.

Robust stabilization of uncertain input-delay systems by sliding mode control with delay compensation

In this paper, a sliding mode control is proposed for the robust stabilization of uncertain linear input-delay systems with nonlinear parametric perturbations. The proposed sliding surface includes a predictor to compensate for the input delay of the system. A robust control law is derived to ensure the existence of a sliding mode and to overcome the effects of the delay and uncertainty in the sliding mode. A numerical example is given to illustrate the design procedure and results of the proposed approach.

Stochastic stabilizability and H∞ control for markovian jump time-delay systems

This paper is concerned with the stochastic stabilizability and H∞ disturbance attenuation for linear time-delay systems that possess randomly jumping parameters. The transition of the jumping parameters is governed by a finite-state Markov process. Sufficient conditions on the existence of a stochastic stabilizing and γ-suboptimal H∞ state feedback controller are presented using the Lyapunov functional approach. It is shown that the stochastic stabilizing H∞ state feedback controller can be constructed through numerical solution of a set of coupled LMIs. Both state-delay and input-delay systems are considered.

Formulas for Hankel singular values and vectors for a class of input delay systems

This paper gives explicit formulas for Hankel singular values and vectors for a class of multiple input delay systems. The class consists of systems whose gramian is reducible to an integral operator with semi-separable kernel. This structure is exploited in deriving a transcendental equation for singular values.

Balanced Reduction for a Class of Time Delay Systems

A calculation method of Hankel singular values is discussed for input and unilateral time delay systems. For input time delay systems, whose channels involve different value of time delays independently, the Hankel singular values are obtained based on a matrix Lyapunov equation. By introducing auxiliary systems for the unilateral time delay system, it is shown that the singular values are characterized based on the preliminary results for input time delay systems. When Hankel singular values and vectors are derived for input and unilateral time delay systems, the calculation method of balanced reduction is constructed. We investigate balanced reduction with numerical examples.

A stabilizing output-feedback linear quadratic control for pure input-delayed systems

This paper proposes the design of a stabilizing output-feedback linear quadratic controller for a pure input-delayed system. By reducing a pure input-delayed system into a non-delayed system and modifying the linear quadratic cost, a simple, stabilizing output-feedback linear quadratic controller is formulated in terms of linear matrix inequalities. The worst-case output-feedback LQ controller is also presented with respect to the unknown initial states. A numerical example is given to illustrate the performance of the proposed controllers.

A Case Study on Balanced Reduction of Time Delay Systems

Explicit formulas of balanced reduction are derived for a class of retarded delay systems. We focus on a unilateral time delay systems and provide analytic solutions on controllability/observability gramians. The unilateral time delay system is addressed as natural extension of input delay systems and enables to describe a wind tunnel or a rolling mill. By characterizing the Hankel singular values based on the gramians, calculation procedure is given with finite-dimensional operations. Finally, the properties of resulting systems are illustrated with examples.

入力むだ時間系の可制御性・可観測性グラミアン

入力むだ時間系の可制御性・可観測性グラミアン

Loop transfer recovery for linear systems with delays in the state and the output

This paper presents robustness properties of the Kalman filter and the associated LQG/LTR method for linear time-invariant systems having delays in both the state and the output. A circle condition relating to the return difference matrix associated with the Kalman filter is derived. Using this circle condition, it is shown that the Kalman filter guarantees (1/2, ∞) gain margin and ±60° phase margin, which are the same as those for non-delay systems. However, it is shown that, even for minimum phase plants, the LQG/LTR method cannot recover the target loop transfer function. Instead, an upper bound on the recovery error is obtained by using an upper bound of the solution of the Kalman filter Riccati equations. Finally, some dual properties between output-delayed systems and input-delayed systems are exploited.

Design of a stable digital output feedback controller for continuous-time input-delay plants

This paper presents a stable multirate output-feedback controller for digital control of a continuous-time input-delay system. It is shown that an arbitrary digital state feedback controller for an observable input-time-delay plant can be realized by using multirate sampled output data. The developed digital multirate-output feedback controller enables us to achieve results similar to those of the state feedback controller, without constructing an observer.