Showing papers in "Iet Control Theory and Applications in 2009"

Anti-windup design: an overview of some recent advances and open problems

Abstract: The anti-windup technique which can be used to tackle the problems of stability and performance degradation for linear systems with saturated inputs is dealt with. The anti-windup techniques which can be found in the literature today have evolved from many sources and, even now, are diverse and somewhat disconnected from one another. In this survey, an overview of many recent anti-windup techniques is provided and their connections with each other are stated. The anti-windup technique is also explained within the context of its historical emergence and the likely future directions of the field are speculated. The focus is on so-called ‘modern’ anti-windup techniques which began to emerge during the end of the 20th century and which allow a priori guarantees on stability to be made. The survey attempts to provide constructive LMI conditions for the synthesis of anti-windup compensators in both global and local contexts. Finally, some interesting extensions and open problems are discussed, such as nested saturations, the presence of time delays in the state or the input, and anti-windup for non-linear systems.

Dynamic inversion with zero-dynamics stabilisation for quadrotor control

Abstract: For a quadrotor, one can identify the two well-known inherent rotorcraft characteristics: underactuation and strong coupling in pitch-yaw-roll. To confront these problems and design a station-keeping and tracking controller, dynamic inversion is used. Typical applications of dynamic inversion require the selection of the output control variables to render the internal dynamics stable. This means that in many cases, perfect tracking cannot be guaranteed for the actual desired outputs. Instead, the internal dynamics of the feedback linearised system is stabilised using a robust control term. Unlike standard dynamic inversion, the linear controller gains are chosen uniquely to satisfy the tracking performance. Stability and tracking performance are guaranteed using a Lyapunov-type proof. Simulation with a typical nonlinear quadrotor dynamic model is performed to show the effectiveness of the designed control law in the presence of input disturbances.

Fast fault estimation and accommodation for dynamical systems

Abstract: The problem of fast active fault-tolerant control is studied using adaptive fault diagnosis observer (AFDO). Existence conditions for linear time-invariant system are first introduced to verify whether or not the adaptive observer for fault diagnosis exists. Then a novel fast adaptive fault estimation (FAFE) algorithm is proposed to enhance the performance of fault estimation. Using the on-line obtained fault information, the observer-based fault tolerant controller based on the separation property is designed to compensate for the loss of actuator effectiveness by stabilising the closed-loop system. Furthermore, an extension to a class of nonlinear systems is extensively investigated. Finally, simulation results are presented to illustrate the efficiency of the proposed techniques.

Robust control for uncertain switched non-linear systems with time delay under asynchronous switching

Abstract: The problem of robust control for uncertain switched non-linear systems with time delay under asynchronous switching is investigated. Firstly, when there exists asynchronous switching between the controller and the system, a sufficient condition for the existence of stabilising switching law for time-delay switched system is derived. Then, the proposed approach is extended to design stabilising controller and switching law for switched non-linear systems with time delay under asynchronous switching. Furthermore, the problem of robust control for uncertain switched non-linear systems with time delay under asynchronous switching is also investigated. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Adaptive backstepping dynamic surface control for systems with periodic disturbances using neural networks

Abstract: This paper addresses the adaptive neural network tracking control problem for a class of strict-feedback systems with unknown non-linearly parameterised and time-varying disturbed function of known periods. Radial basis function neural network and Fourier series expansion are combined into a new function approximator to model each suitable disturbed function in systems. Dynamic surface control approach is used to solve the problem of ‘explosion of complexity’ in backstepping design procedure. The uniform boundedness of all closed-loop signals is guaranteed. The tracking error is proved to converge to a small residual set around the origin. A simulation example is provided to illustrate the effectiveness of the control scheme designed.

Predictive control of networked systems with random delay and data dropout

Abstract: This study is concerned with the stochastic stability analysis of networked control systems with random network delay. A new control scheme termed networked predictive control is proposed. This scheme mainly consists of the control prediction generator and network-delay compensator. The control prediction generator provides a set of future control predictions to make the closed-loop system achieve the desired control performance and the network-delay compensator removes the effects of the network transmission delay and data dropout. The stochastic stability criteria of the closed-loop networked predictive control systems are derived. A numerical example and a practical experiment are given to show the potential of the proposed techniques.

Real-time identification of tire-road friction conditions

Abstract: Tire-road friction characteristics are deeply interlaced with all vehicle dynamics control systems, as road conditions strongly affect the control schemes behaviour. This work aims at the real-time estimation of the wheel slip value corresponding to the peak of the tire-road friction curve, in order to provide anti-lock braking systems (ABS) with reliable information on its value upon activation. Different techniques based on recursive least squares and the maximum likelihood approach are used for friction curve fitting and their merits and drawbacks thoroughly examined. In addition, since one of the main issues in slip-based friction estimation during braking is vehicle speed estimation, an effective algorithm for addressing this task is developed. The proposed peak slip value estimation strategy is analysed and tested both in simulation and on data collected on an instrumented test vehicle. In the latter case, the vehicle speed estimation algorithm is used, and the estimated vehicle speed provided as input for friction estimation. Practical applicability constraints posed by typical ABS systems are also considered.

Robust H∞ filtering for uncertain discrete Markov jump singular systems with mode-dependent time delay

Abstract: The robust H∞ filtering problem for mode-dependent time-delay discrete Markov jump singular systems with parameter uncertainties is discussed. Based on delay-dependent linear matrix inequalities, a Markov jump filter is designed, which guarantees that the filtering error system is regular, causal, stochastically stable and satisfies H∞ performance for all admissible uncertainties. The H∞ filter can be of full or of a reduced order. A numerical example is given to illustrate the effectiveness of the proposed method.

A delay-partitioning projection approach to stability analysis of continuous systems with multiple delay components

Abstract: An effective approach is introduced to study the stability of continuous systems with multiple timevarying delay components. By employing a new Lyapunov?Krasovskii functional form based on delay partitioning, delay-dependent stability criteria are established for cases with or without the information of the delay rates. The contribution of the paper is 2-fold. First, it provides an improvement, as well as generalisation, of the existing stability criteria for continuous systems with multiple time-varying delay components. Second, it is illustrated numerically that the approach can be applied to estimate the delay bound for system stability in the single delay case with reduction both in conservatism and computational complexity when compared with the existing methods.

Robust adaptive terminal sliding mode-based synchronised position control for multiple motion axes systems

Abstract: A novel robust adaptive terminal sliding mode position synchronised control (RATSMPSC) approach is developed for the operation of multiple motion axes systems. The RATSMPSC structure is designed in cross-coupling error space to stabilise position tracking of each axis while coordinating its motion with other axes in finite time. The criterion for the design is that any position error and synchronisation error should be converged to zero in finite time simultaneously. An adaptive mechanism is employed to estimate controller parameters so that the request of prior knowledge of the bounds of system uncertainty can be alternatively resolved. The corresponding stability analysis is presented to lay a foundation for a theoretical understanding to the underlying issues as well as safely operating real systems. The proposed approach has strong rejection capacity against external disturbances and robustness to deal with model uncertainties. An illustrative example is initially simulated to demonstrate the performance of the approach.

Nonlinear sliding-mode control of a multi-motor web-winding system without tension sensor

Abstract: A sliding-mode (SM) feedback linearisation control system is designed for a multi-motor web-winding system. First, an ideal feedback linearisation control system is adopted in order to decouple the tensions and velocity of the web-winding system; then to enhance the performance of the control system in the presence of uncertainties, an SM feedback linearisation control system is applied, which consists of an SM velocity controller and two SM tension controllers; a decentralised version of the proposed controller is developed. Two tension observers are suggested to eliminate the need of load cells in a web-winding system. Finally, the effectiveness and capability of the proposed control strategy is verified by computer simulation.

Average dwell time approach to L 2 -L∞1 control of switched delay systems via dynamic output feedback

Abstract: This study is concerned with the L 2 -L infin control problem for continuous-time switched systems with time-varying delay. A dynamic output feedback (DOF) controller is designed, which is assumed to be switching with the same switching signal as in the original system. By using an average dwell time approach and the piecewise Lyapunov function technique, a delay-dependent sufficient condition is proposed to guarantee the exponential stability and a weighted L 2 -L infin performance for the closed-loop system with the decay estimate explicitly given. The corresponding solvability condition for a desired DOF controller is established, and an explicit parametrisation of all desired DOF controllers is also given. Finally, a numerical example is given to illustrate the effectiveness of the proposed theories.

Further results on decentralised coordination in networks of agents with second-order dynamics

Abstract: This study investigates consensus problems for networks of second-order agents, where each agent can only access the relative position information from its neighbours. We first introduce two new protocols with and without time-delay. Then we provide a convergence analysis in three cases: (a) networks with fixed topology; (b) networks with switching topology; (c) networks with switching topology and time-delays. Several conditions are presented to make all agents asymptotically reach consensus while accomplishing some tasks such as moving to a common value and moving together with a constant velocity or with a constant acceleration. Finally, simulation results are provided to demonstrate the effectiveness of our theoretical results.

Tracking control of sampled-data fuzzy-model-based control systems

Abstract: The tracking control approach for the sampled-data fuzzy-model-based control systems is presented Compared with the stabilisation problem, tracking control problem is more difficult as the system states of the nonlinear plant are required to be driven to follow those of the stable reference model A sampled-data fuzzy controller is proposed to realise the tracking control problem The sampling activity introduces discontinuity, which complicates the closed-loop system dynamics and makes the system analysis difficult As a result, the stability analysis approach used in pure-continuous fuzzy control systems cannot be applied Furthermore, favourable characteristics that lead to relaxed stability analysis results vanish because of the existence of the sampling activity The system stability is investigated using the Lyapunov-based approach The membership function information of both fuzzy model and fuzzy controller is employed to alleviate the conservativeness of the stability analysis results LMI-based stability conditions are derived to aid the design of stable sampled-data fuzzy-model-based tracking control systems An application example is given to illustrate the merits of the proposed approach

Robustness analysis of input shaping commands for two-mode flexible systems

Abstract: A robustness evaluation of input-shaping techniques to reduce residual vibration of two-mode flexible systems is presented. Using a benchmark two-mode system, the robustness problem is illustrated by first applying input shapers designed for only one mode. These simple shapers are effective for a wide array of two-mode systems because the amplitude of the second mode is often small, perhaps near the noise level. However, single-mode shapers are ineffective when the second mode contributes substantial oscillation amplitude. Therefore the robustness analysis for both single- and two-mode input shapers reveals an inherent compromise between shaper robustness to parameter uncertainties and rise time of the command. A specified-insensitivity shaper can result in command profiles that are significantly more robust to modelling errors than profiles produced with alternative input shapers. The robustness evaluation is verified with a numerical simulation of double-pendulum dynamics and experimentally validated on a 10 ton industrial bridge crane.

Simultaneous fault detection and control for uncertain linear discrete-time systems

Abstract: This paper studies the simultaneous fault detection and control problem for linear uncertain discrete-time systems. A design procedure dealing with polytopic uncertainties is proposed for residual generation, where both the fault detection objectives and some control objectives are considered simultaneously through certain performance indexes. To cope with the fault sensitivity performance index in a given frequency range directly, the generalised KYP lemma is introduced in this framework. A two-step procedure is adopted to obtain the solutions through satisfying a set of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed methods.

Efficient iterative method for solving the second-order sylvester matrix equation EVF 2 -AVF-CV=BW

Abstract: The second-order Sylvester matrix equation EVF2−AVF−CV=BW (including the generalised Sylvester matrix equation, normal Sylvester matrix equation and Lyapunov matrix equation as special cases) over unknown matrix pair [V, W], has wide applications in many fields. In the present study, the authors propose an iterative method to solve the second-order Sylvester matrix equation. The proposed iterative method does not depend on the Jordan form of the matrix F. By this iterative method, the solvability of the matrix equation can be determined automatically over unknown matrix pair [V, W]≠0. When the matrix equation is solvable, its solution pair can be obtained within finite iterative steps, and its least Frobenius norm solution pair can be obtained by choosing suitable initial matrix pair. Furthermore, its optimal approximation solution pair to a given matrix pair can be derived by finding the least norm solution pair of a new matrix equation. A numerical example is given to show the efficiency of the proposed method.

Hybrid adaptive and impulsive synchronisation of uncertain complex dynamical networks by the generalised Barbalat's lemma

Abstract: Robust local and global hybrid adaptive and impulsive synchronisation for a class of uncertain complex dynamical networks are investigated in this study, respectively. For the complex dynamical network with unknown but bounded non-linear couplings, with unknown bounds, hybrid adaptive and impulsive controllers are designed based on adaptive control theory and impulsive control theory. By the generalised Barbalat's lemma, the uncertain complex dynamical network is proved to be locally or globally asymptotically synchronised. Several robust local and global hybrid adaptive and impulsive synchronisation criteria are also established. Two numerical examples are given to demonstrate the effectiveness of the proposed controller design methods.

Reduced-order L 2 -L/ ∞ filtering for a class of nonlinear switched stochastic systems

Abstract: The L 2 -L infin filtering problem for a class of nonlinear switched stochastic systems is dealt with here. The authors attention is focused on the design of full- and reduced-order filters that guarantee the filtering error system to be mean-square exponentially stable with a prescribed weighted L 2 -L infin performance. Sufficient conditions are proposed by applying the average dwell time method and the piecewise Lyapunov function technique. The corresponding full-order filter design is cast into a convex optimisation problem, which can be efficiently handled by using standard numerical algorithms. Moreover, two sharply different approaches are proposed to solve the reduced-order filtering problem: one is the convex linearisation approach and the other is the projection approach. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed approaches.

Evaluation and tuning of robust PID controllers

Abstract: Based on a general controller evaluation method, taking both performance and robustness in different frequency regions into account, an analytical PID design method is presented. It is related to the well known and often used lambda tuning approach, which is based on internal model control (IMC) for a specific second-order non-minimum phase plant model. The analytical method introduced in this paper includes two tuning parameters, one that guarantees a specified stability margin for the given model, and one that is also able to adjust the control activity to a desired level. The suggested method, called robust IMC, gives the user the important freedom to control both mid- and high-frequency robustness. An extended evaluation procedure also illustrates how efficiently PI and PID controllers including a Smith predictor (SP) can control time delayed plants. More specifically, it is shown to be more profitable to provide a PI controller with derivative action than with a SP for plants with long time delays.

Robust attitude synchronisation controllers design for spacecraft formation

Abstract: The attitude synchronisation control problem for spacecraft formation with switching communication topologies and information transmission delays is addressed. Common Lyapunov functions are employed to tackle such a problem. To compensate the adverse effect on an individual spacecraft arising from model uncertainties and external disturbances, parameter estimation variables and nonlinear integral terms are incorporated into the Lyapunov functions. The main result of this research is that one of the presented controllers can render a spacecraft formation consistent to a given trajectory globally with dynamic information exchange graph and non-uniform time-varying delays while coping with the parameter uncertainties and unexpected disturbances. In addition, several corollaries of the main results are provided. By virtue of a corollary of Barbalat's lemma, attractiveness of the proposed controllers for the corresponding closed-loop systems is proven. Numerical simulations are also included to demonstrate the theoretical results.

Stability analysis of T-S fuzzy control systems using parameter-dependent Lyapunov function

Abstract: The system stability of T–S fuzzy-model-based control systems with a parameter-dependent Lyapunov function (PDLF) is investigated. As PDLF approach includes information of the membership function (time derivatives of membership functions), it has been reported that relaxed stability conditions can be achieved compared to the parameter-independent Lyapunov function (PILF). To investigate the system stability, the non-linear plant is represented by a T–S fuzzy model. Various non-parallel distribution compensation (PDC) fuzzy controllers, which can better utilise the characteristic of the PDLF, are proposed to close the feedback loop. To relax the stability conditions, an improved PDLF is employed. Some inequalities are proposed to relate the membership functions and its time derivatives, which allow the introduction of some slack matrices to facilitate the stability analysis. Stability conditions in terms of linear matrix inequalities are derived to aid the design of stable fuzzy-model-based control systems. Simulation examples are given to illustrate the effectiveness of the proposed non-PDC fuzzy control schemes.

Robust fault tolerant tracking control with application to hybrid nonlinear systems

Abstract: A class of nonlinear systems with faults, parametric uncertainties and without full state measurements are considered. A novel observer is designed whose estimation error is not affected by faults, and an observer-based fault tolerant tracking controller is proposed to make the outputs asymptotically track the reference signals while the states are bounded. The proposed fault tolerant control method can help to provide a switching detection scheme and a family of Lyapunov functions for a class of hybrid nonlinear systems with uncontrollable switchings, and to guarantee the global tracking performance. A three-tank system is taken as an example to show the efficiency of the proposed method.

H ∞ control of a class of extended markov jump linear systems

Abstract: A class of extended continuous-time Markov jump linear systems is proposed in this study. The generality lies in that the discrete dynamics of the class of systems is described by a Markov stochastic process, but with only partially known transition probabilities, which relax the traditional assumption in Markov jump systems that all the transition probabilities must be known a priori. Moreover, in contrast with the uncertain transition probabilities studied recently, no structure (polytopic ones), bounds (norm-bounded ones) or ‘nominal’ terms (both) are required for the partially unknown elements in the transition rate matrix. The sufficient conditions for H∞ control are derived via the linear matrix inequality formulation such that the closed-loop system is stochastically stable and has a guaranteed H∞ noise-attenuation performance. A tradeoff can be built using our approach between the difficulties to obtain all the transition probabilities and the systems performance benefits. A numerical example is provided to show the validity and potential of the developed theoretical results.

Hα-filtering and state feedback control for discrete-time switched descriptor systems

Abstract: The problem of H_inf filtering for a class of discrete time switched systems with unknown inputs is investigated. By using a switched Lyapunov function, sufficient conditions for the solution of this problem are obtained in terms of linear matrix inequalities. Filtering is envisaged both with proportional and proportional integral observers. In addition, the results obtained in observer design are transposed to the controller design for switched descriptor systems. The control of a switched uncertain descriptor system is also treated. A numerical example is also given to illustrate the presented results

Non-fragile dynamic output feedback control for linear systems with time-varying delay

Abstract: This paper is devoted to the problems of non-fragile H∞ and L2–L∞ control for a class of linear systems with time-varying state delay. The purpose is to design a dynamic output feedback controller with additive gain variations such that the closed-loop system is asymptotically stable while satisfying a prescribed H∞ (or L2–L∞) performance level. By using linear matrix inequality approach, a delay-dependent stability criterion is obtained by introducing a new type of Lyapunov–Krasovskii functional. Based on the obtained criterion, sufficient conditions for the existence of desired controllers are derived, and the corresponding stabilisation dynamic output feedback controller design algorithm is proposed. Numerical examples are included to illustrate the benefit and effectiveness of the proposed method.

Improved robust H∞ filtering for uncertain discrete-time switched systems

Abstract: This paper is concerned with the robust H∞ filtering problem for uncertain switched linear discrete-time systems. Combining the mode-switching idea with the well-known Finsler's lemma, and further utilising the parameter-dependent result, a new characterisation of the asymptotic stability with an H∞ noise-attenuation level bound for the filtering error system has been addressed. The existence condition of such a filter is formulated in terms of dilated linear matrix inequalities. This directly leads to performance improvement and reduction of conservativeness in the filtering solution. Performance of the presented approach in comparison with that of the existing results is illustrated by a numerical example.

Exponential stability and static output feedback stabilisation of singular time-delay systems with saturating actuators

Abstract: This study deals with the class of continuous-time singular linear systems with time-varying delays. The stability and stabilisation problems of this class of systems are addressed. Delay-range-dependent sufficient conditions such that the system is regular, impulse free and α-stable are developed in the linear matrix inequality (LMI) setting and an estimate of the convergence rate of such stable systems is also presented. An iterative LMI (ILMI) algorithm to compute a static output feedback controller gains is proposed. Some numerical examples are employed to show the usefulness of the proposed results.

On the simultaneous state and unknown input estimation of complex systems via a multiple model strategy

Abstract: This study addresses the analysis and design of unknown input observer in order to provide both state and unknown input estimations of complex systems modelled with the help of a particular class of multiple model. The proposed observer uses the multi-integral strategy successfully employed in the classic linear control theory and known for its robustness properties. The observer design is based on the representation of the system via a particular multiple model, known as ‘decoupled multiple model’. This structure of multiple model allows to use submodels with different number of states and this feature constitutes the main advantage of the proposed observer with respect to the classic multiple model structure where the submodels have the same dimension. It is shown how the gains of the suggested observer can be obtained by solving a linear matrix inequality optimal problem. An academic example is also proposed in order to illustrate the proposed methodology.

Fixed final time optimal control approach for bounded robust controller design using Hamilton-Jacobi-Bellman solution

Abstract: In this study, an optimal control algorithm based on Hamilton-Jacobi-Bellman (HJB) equation, for the bounded robust controller design for finite-time-horizon nonlinear systems, is proposed. The HJB equation formulated using a suitable nonquadratic term in the performance functional to take care of magnitude constraints on the control input. Utilising the direct method of Lyapunov stability, we have proved the optimality of the controller with respect to a cost functional, that includes penalty on the control effort and the maximum bound on system uncertainty. The bounded controller requires the knowledge of the upper bound of system uncertainty. In the proposed algorithm, neural network is used to approximate the time-varying solution of HJB equation using least squares method. Proposed algorithm has been applied on the nonlinear system with matched and unmatched system uncertainties. Necessary theoretical and simulation results are presented to validate proposed algorithm.