Design Of Linear Systems Research Articles

Fault Detection Filter Design With Optimization and Partial Decoupling

For the fault detection filter design of linear time-invariant systems, we propose a novel problem formulation, which not only makes a tradeoff between fault sensitivity and disturbance sensitivity, but also incorporates partial fault decoupling and disturbance decoupling. This formulation compensates the drawbacks of the available frameworks such as ${\cal H}_{-}/{\cal H}_{\infty}$ , ${\cal H}_{2}/{\cal H}_{\infty}$ and ${\cal H}_{\infty}/H_{\infty} $ . One optimal fault detection filter design for this problem framework is derived. It is shown that the faults in a certain space have arbitrary sensitivities, while the faults in the complementary space have bounded and maximized sensitivities with the proposed filter. Both the decoupling and non-decoupling conditions are derived. Moreover, decoupling disturbances is discussed. Finally, an example is given to illustrate the results.

Robust [formula omitted] and [formula omitted] memory filter design for linear uncertain discrete-time delay systems

This paper is concerned with the problems of robust full-order H2 and H∞ filter design for linear uncertain discrete-time systems with multiple state delays. The uncertain parameters affecting the matrices of the system are supposed to be time-invariant and to belong to a polytopic domain. The main novelty is the fact that the filter contains an arbitrary number of past states and past output measures of the system, yielding a filtering system with memory. Linear matrix inequality relaxations based on polynomially parameter-dependent Lyapunov matrices and slack variables are proposed for the H2 and H∞ filter design. Due to the extra dynamics introduced through the delayed states, the robust memory filter is able to provide less conservative results in terms of the H∞ and the H2 performance when compared to the memoryless case. Throughout the paper, the multiple delays are considered to be fixed and time-invariant, but an extension of the conditions to cope with unknown delays belonging to a given interval is also presented for both time-varying and time-invariant delay cases. Numerical examples are given to demonstrate the improvements of the proposed approach with respect to other methods from the literature.

An approach to analysis and design for some large-scale linear systems

For a linear time invariant system, the system stability is equivalent to the stability of the system matrix. Thus, finding the conditions for the matrix stability becomes a key to analysis and design of large-scale linear systems. This paper is aimed at studying the large-scale matrix stability problem by means of matrix partitioning. The sufficient conditions for the large-scale matrix stability are proposed. For matrices with normal block diagonal submatrices, a concise and practical expression for testing matrix stability is derived. Additionally, for block diagonally dominant matrices, a sufficient condition, which is used to determine whether the matrix is stable, is proposed. Finally, numerical examples are provided that not only validate theoretical results obtained in this paper, but also demonstrate the analysis and design of large-scale linear systems.

Repetitive Learning Control Design for LED Light Tracking

A lighting system composed of three color light-emitting diode (LED) strings is considered. On the basis of a simplified dynamic model (with uncertainties) for the aforementioned system, the tracking of (possibly complex) periodic reference signals (with known period) for both the light color and intensity is achieved by designing, for each LED string, a decentralized repetitive learning control. Experimental results illustrate the effectiveness of the proposed approach in a practical user-friendly scenario: the color coordinates are obtained by an external low-cost red, green, blue sensor which allows for measuring the overall lighting effects (including external disturbances) while increasing the overall energy saving. A detailed theoretical analysis of the learning control design for first-order linear systems with zero relative degree under suitable assumptions is also included.

Multistage anti-windup design for linear systems with saturation nonlinearity: enlargement of the domain of attraction

This paper considers the multistage anti-windup (AW) design for linear systems with saturation nonlinearity, with the objective of enlarging the domain of attraction of the resulting closed-loop system. We present results for both static and dynamic AW compensation gains, in terms of linear matrix inequalities. Iterative algorithms are established to obtain the AW compensation gains that maximize the estimate of the domain of attraction. In addition, a particle swarm optimization-based systematic method is proposed to determine the design point of the multistage AW scheme and to set the initial conditions of the established iterative algorithms. Using the proposed method, benefits of the multistage AW on the domain of attraction are illustrated through a benchmark example.

Dynamic output feedback for switched linear systems based on a LQG design

The aim of this paper is to extend the LQG design for linear system to the case of switched linear systems in continuous time. The main result provides a control Lyapunov function and a dynamic output feedback law leading to sub-optimal solutions. Practically, the dynamic output feedback is easy to apply and the design procedure is effective if there exists at least one controllable and observable convex combination of the subsystems. Practical applications concern the large class of power converters.

Piecewise continuous hybrid systems based observer design for linear systems with variable sampling periods and delay output

The present paper deals with a new continuous undelayed state observer design approach by using only the sampled and delayed measurements where the sampling period and delayed value are variable and unknown. This proposed piecewise continuous observer (PCO), which is derived by using the theory of a particular hybrid systems called piecewise continuous hybrid systems (PCHS), has a very simple structure and can be easily implemented to the networked visual serving systems. This type PCO observer can be also adapted easily according to other kind feedbacks, such as sampled output, delayed output, sampled and delayed state, sampled state, or delayed state whose sampling periods and delayed values are unknown. The proposed PCO observer stability is also analyzed and demonstrated. Moreover, to show the proposed PCO observer performance, a comparison with a Lyapunov–Krasovskii technique and descriptor representation based observer is conducted via a numerical example.

An ISM-based CNF tracking controller design for uncertain MIMO linear systems with multiple time-delays and external disturbances

In this paper, a combination of integral sliding mode and composite nonlinear feedback method is proposed for fast and accurate robust tracking and model following of uncertain multiple-input multiple-output linear systems with multiple time-delays and external disturbances. The composite nonlinear feedback technique allows following the reference trajectory within a given accuracy and the invariance property of the integral sliding mode method rejects the disturbances and preserves the stability of the closed-loop system. By using the Lyapunov–Krasovskii functional, the conditions for asymptotic stabilization are obtained in the form of linear matrix inequalities. To improve the tracking performance for different reference amplitudes, a new nonlinear function is included in the control law and is optimally tuned using a modified random search algorithm. The selection of sliding surface and the existence of the sliding mode are two significant issues, which have been addressed. This scheme not only guarantees robustness against time-delays and uncertainties, but also avoids chattering phenomenon and reaching phase. Finally, the simulations are provided to verify the theoretical results. The results show that the proposed method leads to great improvement on the tracking error and the control effort compared to the available methods.

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.

FTC Structures with Virtual Actuators and Dynamic Output Controllers

The paper deals with the problem of the Hoo control design of continuous-time linear systems by bi-proper dynamic output controllers in the active fault tolerant structure with the virtual actuators. The design procedure is based on the solution of a set of linear matrix inequalities and one matrix equality and ensures the closed-loop stability using Lyapunov approach and the H∞ performance to guarantee the best robustness to a time-delay in fault detection and isolation. Numerical example is given to illustrate the design procedure and the relevance of the method as well as to validate the performances of the proposed approach.

Output Feedback Controller Sparsification via H2-Approximation

The problem of optimal sparse output feedback control design for continuous linear time invariant systems is considered. This work adopts the concept of %p-approximation to develop an optimization algorithm capable of synthesizing a structured sparse static controller gain for which the overall closed loop system exhibits empirical frequency characteristics resembling that of the system controlled with a pre-designed centralized controller. We, moreover, modify our optimization problem so that the control signal generated by the sparse controller falls into the vicinity of the centralized control input, in the sense of L norm. Furthermore, we show that our optimization problem can be equivalently reformulated into a rank constrained problem for which we propose to use a tailored version of Alternating Direction Method of Multipliers (ADMM) as a computationally efficient algorithm to sub-optimally solve it. Finally, we illuminate the effectiveness of our proposed method by testing it on randomly generated sample network models.

The Design and Realization of Linear Calibration System of a Large Dynamic Range Readout Unit for a BGO Calorimeter

The DArk Matter Particle Explorer (DAMPE) is proposed by the Purple Mountain Observatory, Chinese Academy of Sciences. This project expects to find the evidence of the existence of dark matter particles in the universe via the detection of the high-energy electrons and gamma-ray particles produced possibly by the annihilation of dark matter particles. The major component of the satellite payload is a BGO (Bismuth Germanate Oxide) calorimeter, which is used to detect the particles in the energy range from 5GeV to 10 TeV. According to a physical simulation, the dynamic range of each BGO detection unit is about 1.5×105. In order to test the readout linearity of the BGO detection unit, we have implemented a simple linear calibration system covering such a large dynamic range. The experimental result shows that the readout nonlinearity of the BGO detection unit in the entire dynamic range is less than 2.7%.

Robust Fault-Tolerant Control based on a Functional Observer for Linear Descriptor Systems

A novel robust fault-tolerant control design for linear descriptor systems is proposed in this paper, with fault tolerant control action achieved via a normal state estimate feedback derived using H∞ optimization and fault compensation. A robust functional (reduced order) observer approach is proposed to estimate the controller directly. Necessary and sufficient conditions are given to ensure the asymptotic stability of the functional observer. H∞ optimization with LMI regional pole placement is used to design the functional observer so that satisfactory estimation and closed-loop system transient performances are achieved, subject to bounded faults and disturbance. Then, a step-by-step fault-tolerant control design procedure for obtaining both the controller and observer design parameters is given. Finally, the effectiveness of the proposed design is illustrated using a numerical example.

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.

Data-driven Filter Design for Linear Systems with Quantized Measurements

This paper is concerned with the problem of data-driven filter design for linear systems with bounded noise by using quantized measurements. Since the mathematical model of the plant studied is unavailable, most of the existing model-based filter design approaches cannot be used to solve this problem. Another challenge lies in the fact that all the measurement data accessible is quantized. To solve this issue, a quasi-feasible filter set within the set membership framework is proposed, and a data-driven optimal worst-case filter is designed. Furthermore, an l2-l∞ almost-optimal worst-case filter design algorithm is presented by means of linear programming technique. A numerical example is given to illustrate the effectiveness of the proposed algorithms.

An enhanced approach to actuator fault estimation design for linear continuous-time systems

An enhanced approach to fault estimation systems design, adjusted for linear continuous-time systems, is proposed in the paper. Based on LMI principle the method exploits state-space observer principle in an adaptive fault estimation scheme for single actuator faults. A simulation example, subject to different type of failures, demonstrates the effectiveness of the proposed form of the fault estimation technique.

Feedback control for parabolic systems with in‐domain actuation

AbstractState feedback design for linear parabolic systems with in‐domain actuation and general Robin boundary conditions is considered. To this end the system is shown to be state equivalent to a boundary controlled system. By means of the backstepping transformation the latter system is shown to be feedback equivalent to a stable parabolic equation. Within the contribution previous results concerning such systems are supplemented by numerical simulation studies. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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.

Vibration control performance of tuned mass dampers with resettable variable stiffness

Vibration control of civil engineering structures using tuned mass dampers (TMDs) is a widely acknowledged control strategy based on numerous analytical and experimental verifications. Although the design and application of traditional linear TMD systems are well established, nonlinear TMD systems that may have better control performance remain in the developmental stage. The TMD systems have two main problems, i.e. detuning effect and excessive TMD’s stroke. To improve the overall performance of TMD systems, a novel semi-active TMD named resettable variable stiffness TMD (RVS-TMD), is proposed. The RVS-TMD consists of an undamped TMD and a resettable variable stiffness device (RVSD). This RVSD is composed of a resettable element and a controllable stiffness element. By varying the stiffness of controllable stiffness element in the RVSD, force produced by the RVSD can be controlled smoothly through a semi-active control law. By operating the resettable element, the hysteretic loops of the RVSD can cover all four quadrants in the force–deformation diagram and, thus, increases energy dissipation. In other words, both stiffness and damping of the RVS-TMD are adjustable via only the RVSD device. The harmonic and seismic responses of a building equipped with the RVS-TMD were investigated. Numerical results show that the proposed RVS-TMD system can avoid detuning effect automatically and assure the optimal control performance as desired when the frequency of primary structure is changed.