Design Of Linear Control Systems Research Articles

ITADLS: An Interactive Tool for Analysis and Design of Linear Systems

Interactive software tools have proven as particularly useful techniques with high impact on education. This kind of tools make students more active and involved in their own learning process. The paper describes the basic functionality of ITADLS, an interactive tool for analysis and design of linear control systems. The tool, whose main feature is its simplicity and self-contained, has been developed using Sysquake, a MATLAB-like language with fast execution and excellent facilities for interactive graphics, and is delivered as a stand-alone executable that is readily accessible to students and instructors.

Virtual assistant for individualized practical training on controller design

In this work we present a virtual assistant to help instructors offer individualized practical training on controller design for linear systems. The virtual assistant is designed to be used together with Goodle GMS, a web application which offers services for the collection, storage and automatic grading of students exercises. Using the proposed scheme, an instructor can generate in an easy way and without having knowledge of programming, individualized exercises that can be graded automatically, ensuring that all the exercises have a solution and the same degree of difficulty. The platform has been tested in an automatic control course at the University of Seville during the 2013-14 academic year.

New Results on Reachable Set Estimation and Controller Design for Linear Systems with Mixed Delays via Triple Integral Functionals

This paper is concerned with the problem of reachable set estimation and controller design for a class of linear systems with mixed delays and bounded disturbance inputs. By constructing a newly augmented Lyapunov-Krasovskii functional, combining with triple integral technique and reciprocally convex approach, some new reachable set estimation conditions are derived in terms of linear matrix inequalities. Based on these conditions, a state-feedback controller has been designed to ensure the reachable set of the closed-loop system bounded by a given ellipsoid. Finally, two numerical examples are given to illustrate the effectiveness of the proposed analysis and designed method.

Multiobjective control system controllers design based on switching and applications

Many systems operate in an uncertain environment of limitations such as temperature, pressure, and physical acceleration/deceleration limitation, etc. Whatever the linear or nonlinear control system design methods are, the aircraft engine will encounter limitations on some occasions. So the aircraft engine control system consists of a family of continuous-time subsystems and switches from one to another depending on various environmental factors (see Figure 1). When the system switches from one subcontrol loop to another, the stability of the system is the basic performance that must be considered. The traditional control method is to switch slowly to avoid the dangers. Therefore, there is much space to improve the dynamic performance of the control system.

Networked predictive control for systems with unknown or partially known delay

This study is concerned with the problem of controller design for linear systems with unknown or partially known communication delay. A new networked predictive control scheme is proposed to deal with the unknown or partially known communication delay. The closed-loop system is modelled as a switched system under constraint switching taking an important property of communication delay into account. Sufficient stability conditions are derived using switched Lyapunov function approach. On the basis of stability conditions, the method of designing the controller gain matrix and some important parameters in the control scheme is investigated. Finally, a numerical example is given to confirm the effectiveness of the proposed method.

Extremal pole placement in control systems with a low order controller

We develop an optimizational approach to the design of linear control systems with a low order controller. The objective function is given by the right boundary of the location of poles in the closed-loop system, which depends on the values of controller parameters. We specify the types of mutual pole placements (root diagrams) corresponding to singular manifolds of such functions in the space of parameters and, in particular, their critical points. We establish the exact number of critical root diagrams depending on the dimension of the parameter space. With the example of finding a stabilizing control for a triple mathematical pendulum, we demonstrate the algebraic approach to finding the global minimum of the objective function.

A Finite Iterative Method for Solving the General Coupled Discrete-Time Periodic Matrix Equations

Analysis and design of linear periodic control systems are closely related to the discrete-time periodic matrix equations. In this paper, we propose an iterative algorithm based on the conjugate gradient method on the normal equations (CGNE) for finding the solution group of the general coupled periodic matrix equations $$\begin{aligned} \left\{ \begin{array}{l} A_{1,i}X_iB_{1,i}+C_{1,i}X_{i+1}D_{1,i}=E_{1,i},\\ A_{2,i}X_iB_{2,i}+C_{2,i}X_{i+1}D_{2,i}=E_{2,i}, \end{array} \right. ~~~\mathrm {for}~~~i=1,2,3,\ldots . \end{aligned}$$ A 1 , i X i B 1 , i + C 1 , i X i + 1 D 1 , i = E 1 , i , A 2 , i X i B 2 , i + C 2 , i X i + 1 D 2 , i = E 2 , i , for i = 1 , 2 , 3 , ? . By proving some properties of the algorithm, we show that the solution group of the periodic matrix equations can be obtained within a finite number of iterations in the absence of roundoff errors. Numerical examples are given to illustrate the efficiency and accuracy of the proposed algorithm.

Developing CGNE algorithm for the periodic discrete-time generalized coupled Sylvester matrix equations

The discrete-time periodic matrix equations often arise in analysis and design of linear periodic control systems. This paper studies the problem of finding the solutions of the periodic continuous-time generalized coupled Sylvester matrix equations $$\begin{aligned} \left\{ \begin{array}{ll} A_kX_kB_k+C_kY_kD_k=M_k,&{} \hbox {} \\ E_kX_{k+1}F_k+G_kY_kH_k=N_k,&{} \hbox {} \end{array} \right. \quad {\mathrm {for}} \quad k=1,2,\ldots ,\phi . \end{aligned}$$ We propose an iterative method based on the idea of conjugate gradient method on the normal equations (CGNE) for solving this problem. By proving some properties of the iterative method, it is shown that the iterative method can solve the problem within a finite number of iterations in the absence of roundoff errors. Finally, numerical results are carried out to confirm the theoretical conclusions.

Reachable set estimation and controller design for distributed delay systems with bounded disturbances

This paper is concerned with the problems of reachable set estimation and state-feedback controller design for linear systems with distributed delays and bounded disturbance inputs. The disturbance inputs are assumed to be either unit-energy bounded or unit-peak bounded. First, based on the Lyapunov–Krasovskii functional approach and the delay-partitioning technique, delay-dependent conditions for estimating the reachable set of the considered system are derived. These conditions guarantee the existence of an ellipsoid that contains the system state under zero initial conditions. Second, the reachable set estimation is taken into account in the controller design. Here, the purpose is to determine an ellipsoid and find a state-feedback controller such that the determined ellipsoid contains the reachable set of the resulting closed-loop system. Sufficient conditions for the solvability of the control synthesis problem are obtained. Based on these results, the problem of how to design a controller such that the state of the resulting closed-loop system is contained in a prescribed ellipsoid is studied. Finally, numerical examples and simulation results are provided to show the effectiveness of the proposed analysis and design methods.

Improved State Space Model Predictive Control Design for Linear Systems with Partial Actuator Failure

This paper presents a new state space model predictive control scheme for linear systems with partial actuator faults. To consider dealing with the uncertainties caused by actuator faults, the proc...

Realization of Try-Once-Discard in Wireless Multihop Networks

In networked control systems, the Try-Once-Discard (TOD) protocol is of high interest because its properties can be characterized by Lyapunov functions. This feature makes it practical to incorporate TOD into Lyapunov-based design of linear and nonlinear control systems, yielding a self-contained theory for system stabilization. In previous work, candidates for TOD realizations for single-hop (wired and wireless) networks have been proposed. However, it has been a hitherto open question whether TOD can be realized in wireless multihop networks. In fact, it is far from obvious how dynamic value-based competition with deterministically bounded maximum delay, as required by TOD, is achievable in wireless multihop networks. In this paper, we give a positive answer to this question, by presenting a functionally complete realization of TOD in wireless multihop networks. Our solution is based on highly accurate multihop tick synchronization, and applies an algorithm for collision-protected network-wide value arbitration with deterministic delay. We provide experimental evidence for the feasibility of our solution on existing micro controller platforms, and assess our TOD realization in a batch reactor scenario.

Novel criteria on H ∞ filter design of linear networked control systems

This study considers H ∞ filter design for a class of linear networked control systems with quantisation. The effects of network-induced delay, data loss and signal quantisation on the system is considered, where the quantiser is selected to be logarithmic. Based on the modified delay-central-point method and using the convexity property of the matrix inequality, new criteria are derived for the H ∞ performance analysis of the filtering-error systems, which can lead to a less conservative analysis results and thus reduce the overdesign of the filter. Two examples are provided to show the less conservatism of the derived analysis results and also to illustrate the design procedures of the filters’ parameters.

Constrained Control Design for Linear Systems with Geometric Adversary Constraints

Inspired by some practical applications concerning collision avoidance topics, this paper focuses on the optimal control of linear dynamical systems in the presence of a set of adversary constraints. One of the novelties is the type of constraints introduced in the receding horizon optimization problem. These constraints can be considered as “adversary” by their non convex characteristics which make the convergence of the system dynamics towards the “zero” equilibrium position an impossible task. The present paper proposes a dual-mode control strategy which builds on an optimization based controller and a fixed constrained control law whenever the adversary constraints are activated. In order to illustrate the benefits of the proposed method, typical applications involving the control of multi-agent systems are considered.

Robust PI controller design with respect to fuzzy sensitivity margins

The paper deals with PI controller design for linear systems with parametric uncertainty with respect to sensitivity margin. The plant is considered as possibility distribution on a plant space and the closed loop specifications are given in terms of the peak of sensitivity function described by fuzzy numbers. The controller design is understood as the inclusion of respective α-cuts. Such consideration makes it possible to degrade the closed loop specifications towards the uncertainty that occurs very rarely. The proposed procedure is applied on the speed control of a hydraulic turbine – a non-minimum phase system.

Approximate Controllability of Fractional Neutral Stochastic System with Infinite Delay

The concept of controllability plays an important role in analysis and design of linear and nonlinear control systems. Further, fractional differential equations have wide applications in engineering and science. In this paper, the approximate controllability of neutral stochastic fractional integro-differential equation with infinite delay in a Hilbert space is studied. By using Krasnoselskii's fixed point theorem with stochastic analysis theory, we derive a new set of sufficient conditions for the approximate controllability of nonlinear fractional stochastic system under the assumption that the corresponding linear system is approximately controllable. Finally, an example is provided to illustrate the obtained theory.

Quantized feedback fault‐tolerant H ∞ controller design for linear systems with adaptive mechanism

SUMMARYThis paper addresses the design problem of fault‐tolerant H ∞ controller for linear systems with state quantization. By combining linear matrix inequality technique and indirect adaptive method, a new method is proposed to design a fault‐tolerant controller against actuator faults via quantized state feedback. The controller gains are updating according to the online estimation of eventual faults, which are dependent on the quantized state signals. Meanwhile, the proposed designs conditions with variable gains can be proved to be less conservative than those of the traditional controller with fixed gains. A numerical example is presented to illustrate the effectiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.

Control With Markov Sensors/Actuators Assignment

This note is concerned with the stability analysis and controller design for linear systems involving a network of sensors and actuators, which are triggered in groups by random events. These events are modeled by two independent Markov chains. A novel stability criterion is obtained by considering transmission delays in the measurement and control signals. Based on the stability criterion, the controller gain is designed. A numerical example is given to show the effectiveness of the proposed method.

Control design of linear systems with saturating actuators: A survey

In this paper, a survey of the extensive research investigation performed on linear systems subject to saturation including actuator, output and state types is presented. The survey takes into consideration several technical views on the analysis and design procedures leading to global or semi-global stability results and outlines basic assumptions. Research works on the design of linear feedback laws, decentralized controllers are equally emphasized. Results related stability with enlarging the domain of attraction and systems subject to multi-layered nested saturations are provided. Some typical examples are given to illustrate relevant issues.

Design and Simulation of Urban Road Intersection Signal Linear Control System

In order to solve the contradiction between the supply and demand of traffic system, reduce traffic delay and improve the motor vehicle traffic capacity, the traffic engineering related theory knowledge is used and the existing research results at home and abroad is combined with. The purpose is to design the program: linear control system, based on the systemic analysis of some aspects such as the motor vehicle traffic capacity, traffic delay, signal period and peak hour traffic demand, which takes traffic delay time and capacity as evaluation index, by VISSIM microscopic simulation software, to compare and analyze the condition of traffic signal timing before and after optimization, which verifies that the linear control system effectively improve traffic capacity of the crossing and reduce the delay in the intersection.

LMI based control design for linear systems with distributed time delays

LMI based control design for linear systems with distributed time delaysThe paper concerns the problem of stabilization of continuous-time linear systems with distributed time delays. Using extended form of the Lyapunov-Krasovskii functional candidate, the controller design conditions are derived and formulated with respect to the incidence of structured matrix variables in the linear matrix inequality formulation. The result give sufficient condition for stabilization of the system with distributed time delays. It is illustrated with a numerical example to note reduced conservatism in the system structure.