Controller Design For Discrete-time Systems Research Articles

Formal synthesis of non-fragile state-feedback digital controllers considering performance requirements for step response

This work describes an approach for synthesizing state-feedback controllers for discrete-time systems, taking into account performance aspects. The proposed methodology is based on counterexample-guided inductive synthesis (CEGIS), producing safe controllers based on step response performance requirements, such as settling time and maximum-overshoot. Controller candidates are generated through constrained optimization based on genetic algorithms. Each iteration that does not satisfy the initial system requirements is learned as a failed result and then used in another attempt. During the verification phase, it is considered the controller fragility to ensure deployable implementations. Such an approach assists the discrete-time control system design since weaknesses occur during implementation on digital platforms, where systems that meet design requirements are employed. The proposed method is implemented in DSVerifier, a tool that uses bounded (and unbounded) model checking based on satisfiability modulo theories. Experimental results showed that our approach is practical and sound regarding the synthesis of discrete state-feedback control systems that present performance requirements. It considers finite word-length effects, unlike other methods that routinely ignore them.

New Results on PID Controller Design of Discrete-time Systems via Pole Placement

This paper considers the problem of proportional-integral-derivative (PID) controller design for a discrete-time system via pole placement. We first provide a method on the determination of the discrete-time PID gains which can assign a pair of dominant poles of a closed-loop system to the desired positions and locate the other poles inside a given smaller circle centered at the origin to guarantee the dominance of the assigned poles. The procedure for ascertaining the gains of PID controllers can be achieved in a straightforwardly computational way. Further, besides dominant pole placement, we propose a novel result on PID controller design according to some requirements of non-dominant pole distribution, which is a more interesting topic in the present paper.

Networked iterative learning control design for discrete-time systems with stochastic communication delay in input and output channels

ABSTRACTThis paper develops two kinds of derivative-type networked iterative learning control (NILC) schemes for repetitive discrete-time systems with stochastic communication delay occurred in input and output channels and modelled as 0-1 Bernoulli-type stochastic variable. In the two schemes, the delayed signal of the current control input is replaced by the synchronous input utilised at the previous iteration, whilst for the delayed signal of the system output the one scheme substitutes it by the synchronous predetermined desired trajectory and the other takes it by the synchronous output at the previous operation, respectively. In virtue of the mathematical expectation, the tracking performance is analysed which exhibits that for both the linear time-invariant and nonlinear affine systems the two kinds of NILCs are convergent under the assumptions that the probabilities of communication delays are adequately constrained and the product of the input–output coupling matrices is full-column rank. Last, two illustrative examples are presented to demonstrate the effectiveness and validity of the proposed NILC schemes.

A Review of Fuzzy Logic and Neural Network Based Intelligent Control Design for Discrete-Time Systems

Over the last few decades, the intelligent control methods such as fuzzy logic control (FLC) and neural network (NN) control have been successfully used in various applications. The rapid development of digital computer based control systems requires control signals to be calculated in a digital or discrete-time form. In this background, the intelligent control methods developed for discrete-time systems have drawn great attentions. This survey aims to present a summary of the state of the art of the design of FLC and NN-based intelligent control for discrete-time systems. For discrete-time FLC systems, numerous remarkable design approaches are introduced and a series of efficient methods to deal with the robustness, stability, and time delay of FLC discrete-time systems are recommended. Techniques for NN-based intelligent control for discrete-time systems, such as adaptive methods and adaptive dynamic programming approaches, are also reviewed. Overall, this paper is devoted to make a brief summary for recent progresses in FLC and NN-based intelligent control design for discrete-time systems as well as to present our thoughts and considerations of recent trends and potential research directions in this area.

Robust partially mode delay dependent ℋ∞ control of discrete-time networked control systems

This article proposes a methodology for designing a partially mode delay dependent ℋ∞ controller design for discrete-time systems with random communication delays. Communication delays between sensors and controller are modelled by a finite state Markov chain where the transition probability matrix is partially known. Stability criteria are obtained based on Lyapunov–Krasovskii functional and a novel methodology for designing a partially mode delay dependent state feedback controller has been proposed. The controller is obtained by solving linear matrix inequality optimisation problems using cone complimentarity linearisation algorithm. A numerical example is provided to illustrate the effectiveness of the proposed controller.

An Active Reconfiguration Scheme for Systems with Single Sensor Faults

The paper presents a modified method of the reconfigured control design for discrete-time systems with single sensor faults, using stabilizing full state feedback principle. The method is based on discrete-time constrained control techniques with state constraints defined by linear equalities, where a single sensor fault is described by an equality constraint given on the state variable associated with the faulty sensor. Using an enhanced form of bounded real lemma to solve this singular problem, the design conditions are outlined in the form of linear matrix inequalities. The validity of the proposed method is illustrated by a numerical example to demonstrate effectiveness and performance of the reconfiguration structure.

New method of fault-distribution-dependent memory-reliable controller design for discrete-time systems with stochastic input delays

A new memory-reliable controller design for a class of discrete-time systems with time-varying input delays is proposed. By assuming that the actuator fault obeys a certain probabilistic distribution, a new practical actuator fault model is presented. Based on this fault model and the known past information, an augmented system with time-varying delay or non-delay, similar to switched systems, is established. By using the Lyapunov–Krasovskii approach, a sufficient condition for the existence of reliable controller is expressed by linear matrix inequalities. An illustrative example is exploited to show the effectiveness of the proposed design procedures.

Quantized robust ℋ∞ control of discrete-time systems with random communication delays

The article considers stability and robust ℋ∞ controller design of discrete-time systems with random communication delays and state quantization. A finite state Markov process is used to model communication delays between sensors and controllers. Measurements are assumed to be quantized by a logarithmic quantizer, and the effect of quantization errors are incorporated into the controller design. Based on a Lyapunov–Krasovskii approach, novel methodologies for analysing stability and designing a time-delay mode-dependent quantized state feedback controller are proposed. The controller is obtained through solving bilinear matrix inequalities (BMIs) using the cone complementarity linearisation algorithm.

Robust mode delay-dependent ℋ ∞ control of discrete-time systems with random communication delays

This study considers stability and robust mode delay-dependent ℋ∞ controller design for discrete-time systems with random communication delays. Communication delays between sensors and controllers are modelled by a finite state Markov process. Based on Lyapunov–Krasovskii functional, a novel methodology for designing a mode delay-dependent state feedback controller has been proposed. The authors also show that the existing delay-dependent approach is a special case of the mode delay-dependent approach proposed in this study. The mode delay-dependent controller is obtained by solving linear matrix inequality optimisation problems using the cone complementarity linearisation algorithm. The effectiveness of the proposed design methodology is verified by a numerical example.

Improved stability criterion and its applications in delayed controller design for discrete-time systems

This paper is concerned with the problem of delay-dependent stability analysis for discrete-time systems with interval-like time-varying delays and the problem of stabilization for discrete-time linear systems via time-delayed controllers. The first problem is solved by applying a novel Lyapunov functional, and an improved delay-dependent stability criterion is obtained in terms of a linear matrix inequality. Based on this, a sufficient condition for the solvability of the second problem is presented. The reduced conservatism of the proposed stability result is shown through a numerical example, while the applicability of the time-delayed controller design method is demonstrated by an inverted pendulum system.

ROBUST POLE PLACEMENT VIA REFLECTION AXES POLYTOPES

A robust version of the output controller design for discrete-time systems is introduced. Instead of a single stable point a stable polytope is preselected in the closed loop characteristic polynomial coefficient space. A constructive procedure for generating stable polytopes is given starting from the unit hypercube of reflection coefficients of monic polynomials. This procedure is quite straightforward because for a special family of polynomials the linear cover of so-called reflection vectors is stable. The roots placement of reflection vectors is studied. A stability measure in a polytope is introduced in order to solve the problem by quadratic programming approach.

ROBUSTNESS GRADIENTS FOR DISCRETE-TIME CONTROL SYSTEMS

ABSTRACT This article addresses gradients for discrete-time control system design. First, the stability margin is investigated based on the minimum distance of the Mikhailov hodograph to the origin or on the minimum distance of the closed-loop poles to the unit circle. The gradients with respect to the output state controller matrix are derived and applied for stepwise, improving the dynamics of the closed-loop system. Second, the maximum admissible uncertainty of the plant is considered based on the unstructured type of uncertainty. For robustification, gradients to attain maximum admissible uncertainty are introduced.

Robust pole assignment via reflection coefficients of polynomials

A robust version of the output controller design for discrete-time systems is introduced. Instead of a single stable point a stable polytope (or simplex) is preselected in the closed-loop characteristic polynomial coefficients space. A constructive procedure for generating stable polytopes is given starting from the unit hypercube of reflection coefficients of monic polynomials. This procedure is quite straightforward because for a special family of polynomials the linear cover of so-called reflection vectors is stable. The roots placement of reflection vectors is studied. If a stable target simplex is preselected then the robust output controller design task is solved by quadratic programming approach.

Robust pole assignment via stable polytopes of reflection vectors

A robust version of the output controller design for discrete-time systems is introduced. Instead of a single stable point a stable polytope (or simplex) is preselected in the coefficient space of closed-loop characteristic polynomials. A constructive procedure for generating stable simplexes is given starting from the unit hypercube of reflection coefficients of monic polynomials. This procedure is quite straightforward, because for a special family of polynomials the linear cover of so-called reflection vectors is stable. The root placement of reflection vectors is studied. If a stable target simplex is preselected, then the robust output controller design task is solved by the quadratic programming approach.

ROBUST POLE PLACEMENT BY QUADRATIC PROGRAMMING

A robust version of the output controller design for discrete-time systems is introduced. Instead of a single stable point a stable polytope (or simplex) is preselected in the closed loop characteristic polynomials coefficients space. A constructive procedure for generating stable simplexis is given starting from the unit hypercube of reflection coefficients of monic polynomials. This procedure is quite straightforward because for a special family of polynomials the linear cover of so-called reflection vectors is stable. The roots placement of reflection vectors is studied. If a stable target simplex is preselected then the robust output controller design task is solved by quadratic programming approach.

ON THE ROBUST OUTPUT CONTROL VIA REFLECTION VECTORS

A robust version of the output controller design for discrete-time systems is introduced. Instead of a single stable point a stable polytope (or simplex) is defined in the closed loop characteristic polynomials coefficients space. A constructive procedure for generating simplexis inside the “nicely stable” region is given starting from the unit hypercube of reflection coefficients of monic polynomials. This procedure is quite straightforward because for a special family of polynomials the linear cover of so-called reflection vectors is stable. The roots placement of reflection vectors is studied. If the stable simplex is preselected then the robust output controller design task is solved by quadratic programming approach. If the stable simplex (or polytope) of reflection vectors is not given then a simple search procedure is needed.

ON–LINE IMPROVEMENT FOR THE DECENTRALIZED PREDICTIVE CONTROL OF THE HEAT DYNAMICS OF A GREENHOUSE

A decentralized model-based predictive controller is used for the design of discrete-time control systems aiming at regulating the air temperature and heat supply in greenhouses. Moreover, alternative techniques are proposed for the approximation of the decentralized part of the control and the on-line improvement of the overall control problem. A state space model is used to predict the corresponding local indoor temperature over a long-range time-period and approximate models are used to predict the interactions among the subsystems. The sun radiation and outdoor temperature are treated as external disturbances that affect the overall system dynamics. A series of energy fluxes consist the heating system and the predictive controllers have proved to be powerful in controlling the supply temperature.

Decentralized Predictive Control ofthe Heat Dynamics of a Greenhouse

This paper proposes a decentralized model - based predictive controller approach for the design of discrete-time control systems for the regulation of the air temperature and heat supply in greenhouses. A state space model is used at the greenhouse to predict the corresponding indoor temperature over a long-range time period. The sun radiation and outdoor temperature are treated as external disturbances tliat affect the overall system dynamics. A series of energy fluxes consist the heating system and the predictive controllers have proved to be powerful in controlling the supply temperature.

On the frequency response of scalar discrete-time systems

A detailed understanding of the gain and phase characteristics of discrete-time zeros and poles is obtained. This new knowledge extends and complements previous results available in the control systems and digital signal processing literature. The results introduced in the paper also substantiate the view that discrete-time zeros and poles have much more intricate frequency domain features than their continuous-time counterparts. A simple loop-shaping example is used to illustrate the feasibility of discrete-time control system design developed entirely in the z-plane.

On the robust control via reflection coefficients

Abstract A robust version of the modal controller design for discrete-time systems is introduced. Instead of a single stable point a stable simplex must be preselected in the closed loop characteristic polynomials coefficients space. A constructive procedure for generating simplexis inside the “nice stability region” is given starting from the unit hypercube of reflection coefficients of monic polynomials. This procedure is quite straightforward because, first, n edges are generated by a linear Schur invariant transformation and, second, the most critical edge is determined by the difference of reflection coefficients numbers. The procedure of robust controller design makes use of a stability measure defined as the minimal distance between a preselected stable simplex and vertices of an uncertain polytopic plant.