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Control Theory & Applications, IET

Issue 10 • Date October 2010

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Displaying Results 1 - 25 of 36
  • Stabilisation and performance synthesis for switched stochastic systems

    Page(s): 1877 - 1888
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (382 KB)  

    This study is concerned with the stability and performance analysis, stabilisation and H control problems for continuous-time switched stochastic systems. By applying the average dwell time method and the piecewise Lyapunov function technique, a sufficient condition is first proposed to guarantee the mean-square exponential stability for the unforced switched stochastic system. Also, a condition on a weighted H performance is proposed. The stabilisation and H control including both state feedback control and dynamic output feedback control are considered. Numerical examples are provided to illustrate the effectiveness of the proposed theories. View full abstract»

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  • New controller design method for continuous-time systems with state saturation

    Page(s): 1889 - 1897
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (241 KB)  

    This article studies the problems of stability analysis and controllers design for continuous-time linear systems with the consideration of full state saturation as well as partial state saturation. Owing to the difficulty and complexity in the controller design under state saturation, a new and tractable system is constructed, and it is shown that the constructed system is with the same domain of attraction as the original system. Based on this property, an linear matrix inequality (LMI) based method is presented for estimating the attraction domain of the origin for the new constructed system with state saturation. In addition, an algorithm is developed for designing dynamic output-feedback controllers, which guarantee that the attraction domain of the origin for the closed-loop system is as `large` as possible. An example is given to illustrate the effectiveness of the design method. View full abstract»

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  • Path following of a class of non-holonomic mobile robot with underactuated vehicle body

    Page(s): 1898 - 1904
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (411 KB)  

    A new dynamic model for a class of two-wheeled mobile robot (2WMR), whose mass centre locates below its wheel axis, is presented. The dynamic model considered as the motion of an underactuated vehicle body can represent the time-varying horizontal distance of the mass centre with respect to the configuration centre. This model can describe the dynamic behaviours of the robot more accurately. By the computed torque approach, a sliding mode controller based on the adaptive gain to overcome the disturbances of the system is proposed. Integrating with the velocity controller, the whole control system is made up of two closed-loop structures. The control algorithm efficiency is confirmed through simulation in the MATLAB environment. View full abstract»

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  • Adaptive stabilisation for a class of non-linear state time-varying delay systems with unknown time-delay bound

    Page(s): 1905 - 1913
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (230 KB)  

    In this study, the authors address the problem of adaptive backstepping control for a class of single-input and single-output (SISO) non-linear time-delay systems in triangular structure. Both the parameters of the system to be controlled and the upper bounds of the time delays and their derivatives are assumed to be unknown. A direct adaptive controller for this class of uncertain non-linear systems is proposed. The assumption on delay-related non-linearities is further relaxed. An appropriate Lyapunov-Krasovskii functional is constructed, and the backstepping technique is used. It is shown that all the closed-loop signals are bounded, while the plant states converge to zero asymptotically. A simulation example is provided to demonstrate the design procedure and performance of the proposed method. View full abstract»

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  • Closed-form solution to the non-homogeneous generalised sylvester matrix equation

    Page(s): 1914 - 1921
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (163 KB)  

    A closed-form solution to the non-homogeneous generalised Sylvester matrix equation AV + BW = EVF + R, with the matrix F being in an arbitrary form, is proposed. The solution is expressed in terms of R-controllability matrices and observability matrices, and can provide all the degrees of freedom represented by a free parameter matrix. The proposed approach allows the matrices F and R to be set undetermined, and this feature may give great convenience and advantages in many applications of control systems design. A numerical example is given to illustrate the effect of the proposed approach. View full abstract»

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  • Model predictive control of non-linear discrete time systems: a linear matrix inequality approach

    Page(s): 1922 - 1932
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (448 KB)  

    Using a non-linear model in model predictive control (MPC) changes the control problem from a convex quadratic programme to a non-convex non-linear problem, which is much more challenging to solve. In this study, we introduce an MPC algorithm for non-linear discrete-time systems. The systems are composed of a linear constant part perturbed by an additive state-dependent non-linear term. The control objective is to design a state-feedback control law that minimises an infinite horizon cost function within the framework of linear matrix inequalities. In particular, it is shown that the solution of the optimisation problem can stabilise the non-linear plants. Three extensions, namely, application to systems with input delay, non-linear output tracking and using output-feedback, are followed naturally from the proposed formulation. The performance and effectiveness of the proposed controller is illustrated with numerical examples. View full abstract»

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  • Robustness in fractional proportionalߝintegralߝderivative-based closed-loop systems

    Page(s): 1933 - 1944
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (344 KB)  

    Robustness of a fractional proportional-integral-derivative (PID)-based control system is investigated. At first the largest pathwise connected region subset of a box in three-dimensional space of the parameters of the model is determined such that the closed-loop system is bounded-input bounded-output stable for any point inside it. Then a value that represents the size (in a specified sense) of the calculated region in the first stage and can be considered as a margin for the robustness of the closed-loop system is computed. Furthermore, lower and upper frequency bounds required in depiction of boundaries of the region and computing the mentioned margin are provided. Some special cases in two-dimensional space of the model parameters are investigated as well. To illustrate the results, a numerical example is presented. View full abstract»

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  • Adaptive optimisation of timeout policy for dynamic power management based on semi-Markov control processes

    Page(s): 1945 - 1958
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (590 KB)  

    Timeout policy is an industry standard for dynamic power management (DPM), and thus is easy and safe to implement in many power-managed systems. The optimisation of timeout policy suffered from the lack of effective analytical model and fell in heuristic previously. This study presents an adaptive optimisation method for timeout DPM policy. First, a semi-Markov control processes model is introduced to formulate the DPM problem of finding timeout policies that minimise power consumption under performance constraints. Under this framework, the equivalence of timeout and stochastic policies on power-performance tradeoff is revealed, and the equivalent relation between these two types of DPM policy is derived. Then, a reinforcement learning algorithm that combines policy gradient estimate and stochastic approximation is proposed for optimising timeout policy online. This algorithm does not depend on any prior knowledge of system parameters, and can achieve a global optimum with less computational cost. Simulation results demonstrate the analytical results and the effectiveness of the proposed algorithm. View full abstract»

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  • Delay-dependent robust stability and stabilisation of uncertain two-dimensional discrete systems with time-varying delays

    Page(s): 1959 - 1971
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (608 KB)  

    The problems of delay-dependent robust stability and stabilisation for a class of uncertain two-dimensional (2-D) discrete systems with time-varying delays described by the second Fornasini-Marchesini local state space (FM LSS) model are investigated in this study. By employing improved free-weighting matrix approach, delay-dependent stability criterion for the nominal 2-D state-delayed system is first obtained and formulated in terms of linear matrix inequalities (LMIs); and then, a stabilisation design criterion using static state feedback controller is derived based on the stability result. Since the design criterion is not expressed strictly in terms of LMI, an improved cone complementary linearisation algorithm is employed to solve the non-convex feasibility problem. Furthermore, the stability and stabilisation results are extended to robust stability and stabilisation of the uncertain 2-D state-delayed system. Numerical examples are provided to demonstrate the effectiveness and advantage of the proposed method. View full abstract»

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  • Decentralised L1 adaptive control for large-scale non-linear systems with interconnected unmodelled dynamics

    Page(s): 1972 - 1988
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (643 KB)  

    In this study, the authors investigate a decentralised ℒ1 adaptive controller design for a class of large-scale non-linear systems, with stable linear part and with interconnected non-linearities and unmodelled dynamics. The decentralised adaptive identifiers are presented to design the decentralised ℒ1 adaptive control scheme. The local ℒ1 adaptive controller for each subsystem ensures uniformly bounded transient tracking for subsystem's input and output, simultaneously. The controlled closed-loop decentralised adaptive system can recover the performance of the closed-loop large-scale centralised reference system by increasing the adaptation rates of local controllers. Simulation results for two inverted pendulums on carts are presented to show the effectiveness of the proposed control scheme. View full abstract»

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  • Sensorless induction motor adaptive observer-backstepping controller: experimental robustness tests on low frequencies benchmark

    Page(s): 1989?? - 2002
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (929 KB)  

    In this study, experimental tests for an observer-based controller scheme are given to drive a sensorless Induction Motor (IM) even for the low frequencies case. Combining the advantages of a field oriented controller with the backstepping control method, a new robust controller is designed to track low frequencies trajectories. The static errors are eliminated using an integral backstepping technique, improving the robustness properties of the controller in spite of the uncertainties and the perturbations. An adaptive interconnected observer is designed for estimating fluxes, speed, load torque and the stator resistance in order to implement the controller. The knowledge of the stator parameter is crucial for sensorless control in particular to track low-speed trajectories when the observability property is lost. Practical stability based on Lyapunov theory has been proved to guarantee the strongly uniformly practical stability of the closed-loop system using the proposed observer-controller scheme. The tests are completed thanks to the reference trajectories of a specific sensorless IM benchmark where the robustness properties are validated under parameter variations and in presence of disturbances even for the low frequencies case. View full abstract»

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  • H stabilisation of non-linear stochastic active fault-tolerant control systems: fuzzy-interpolation approach

    Page(s): 2003 - 2017
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (408 KB)  

    This study addresses the H control design problem systematically for a class of non-linear stochastic active fault-tolerant control systems with Markovian parameters. A sufficient condition for the non-linear stochastic fault-tolerant H control u1(x(t), ηt) is given in terms of a set of coupled Hamilton-Jacobi inequalities (HJIs). Then, a fuzzy-interpolation approach is developed to conquer the difficulty in solving the coupled HJIs, which sustains a fault-tolerant H fuzzy control u2(x(t), ηt) by solving linear matrix inequalities, instead of HJIs. A simulation example is presented to illustrate the effectiveness of the proposed design method. View full abstract»

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  • Stability analysis of genetic regulatory network with time delays and parameter uncertainties

    Page(s): 2018 - 2028
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (338 KB)  

    The effect of parameter uncertainties on stability of delayed genetic regulatory networks is investigated. With the presence of parameter uncertainties, the delayed coupled genetic regulatory network is a parameter-dependent non-linear system, in which not only the dynamics are indefinite but also its equilibrium point is unknown. The authors first derive a sufficient condition to guarantee robust stability of uncertain genetic regulatory networks by introducing convergence region. Then, the estimation of convergence region bound is obtained by using Lyapunov stability theory and linear matrix inequality. It is worth noting that these results are derived in the case that the equilibrium point of parameter-dependent non-linear system is unknown. Finally, two examples are given to illustrate the effectiveness of the proposed results. View full abstract»

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  • Optimal design and testing of a digital dual-stage actuator servo system

    Page(s): 2029 - 2040
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (1253 KB)  

    This study addresses an optimal dual-stage actuator (DSA) servo design in a discrete-time domain. Maximising the cooperation of a voice coil motor and a microactuator (MA), the authors design a discrete-time fixed-order DSA control system. The controller is applied to a disk drive with DSAs, and experimental results demonstrate remarkable improvements in track seek in the MA range as well as in track follow. It is shown that the optimal control system, with the interaction between the two actuators being minimised, delivers exemplary responses in a disk drive test, despite its minimum controller order. View full abstract»

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  • State-feedback with memory for controlled positivity with application to congestion control

    Page(s): 2041 - 2048
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (230 KB)  

    The problem of designing controllers for systems with delays, such that the closed-loop system is positive, stable and fulfils bounds on the system variables, is studied. In order to design this type of controller, a technique is provided, which is based on solving linear programming problems, as this allows the controllers that fulfil these properties to be easily characterised even in the presence of uncertainty in the plant description. Thus, these controllers ensure that the states are kept non-negative and that they fulfil limitations on the control and states. The work is completed with numerical simulations of the application of the methodology for router congestion control in computer networks, based on the synthesis of an active queue management system, thus demonstrating the usefulness of the proposed technique for practical problems. View full abstract»

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  • Passivity-based control of a wound-rotor synchronous motor

    Page(s): 2049 - 2057
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (361 KB)  

    This study presents a new non-linear passivity-based controller for a wound-rotor synchronous machine, acting as a motor drive. The control objectives are stated in the dq-frame, and the port-controlled Hamiltonian model is also obtained. A power flow analysis allows to state the control goals in terms of ohmic losses reduction, and motivates the use of the field current for the reactive power compensation. From the Hamiltonian structure, the simultaneous interconnection and damping assignment technique is used to compute the control action, which results in a controller with a simpler architecture than the standard one for this class of machines, able to cope with both positive and negative external mechanical loads and having thus bidirectional power capabilities. The robustness of the control action is also taken into account in the design procedure. Finally, the computed controller is validated via numerical simulations. View full abstract»

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  • Tracking control of pneumatic artificial muscle actuators based on sliding mode and non-linear disturbance observer

    Page(s): 2058 - 2070
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (978 KB)  

    The dynamic properties and non-linear control of the pneumatic muscle actuator (PMA) were investigated in this study for use in a specially designed hand rehabilitation device. The phenomenological model of PMA was established in the lower pressure range applicable for hand rehabilitation. The experimental results show that PMA's characteristics can be approximated by piecewise functions. In order to improve the performance and robustness of control for accurate trajectory tracking, a sliding mode control based on non-linear disturbance observer (SMCBNDO) was designed. The simulation and experimental results demonstrated that the model and the sliding mode control achieved the desired performance in tracking a desired trajectory within guaranteed accuracy. The work indicates that the model and the non-linear control proposed in this study can be applied in PMA-driven hand function rehabilitation devices requiring lower pressures. View full abstract»

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  • Discrete time integral sliding mode control for overhead crane with uncertainties

    Page(s): 2071 - 2081
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (693 KB)  

    This study firstly addresses an integral sliding mode control method for discrete time systems. The underlying continuous system is affected by both matched and unmatched uncertainties. The past value of the disturbance signal is taken as the estimate of its present value. The sliding mode controller is designed to ensure the existence of sliding mode in the presence of uncertainties. The proportional part is designed based on the analysis of closed-loop stability conditions. The controller design theory above is applied to an overhead crane system in later sections. The overhead crane system, which is a familiar control problem is described by a linear model, the parameters of which are estimated. It is affected by uncertainties such as friction, swing of the load and non-linearities because of changing rope length. Both simulation and experimental results are reported. The efficacy and robustness of the proposed controller are demonstrated. View full abstract»

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  • Discretisation of linear parameter-varying state-space representations

    Page(s): 2082 - 2096
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (416 KB)  

    Discretisation of linear parameter-varying (LPV) systems is a relevant, but insufficiently investigated problem of both LPV control design and system identification. In this contribution, existing results on the discretisation of LPV state-space models with static dependence (without memory) on the scheduling signal are surveyed and new methods are introduced. These approaches are analysed in terms of approximation error, considering ideal zero-order hold actuation and sampling of the input-output signals and scheduling variables of the system. Criteria to choose appropriate sampling periods with respect to the investigated methods are also presented. The application of the considered approaches on state-space representations with dynamic dependence (with memory) on the scheduling is investigated in a higher-order hold sense. View full abstract»

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  • Robust stability testing function and kharitonov-like theorem for fractional order interval systems

    Page(s): 2097 - 2108
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (381 KB)  

    This study deals with the subject of robust bounded-input bounded-output (BIBO)-stability of a family of fractional order interval systems. Employing the idea of `robust stability testing function` and extending it to the case of intended systems, a simple graphical procedure for checking the robust BIBO-stability applicable to both commensurate and incommensurate orders is developed. Moreover, a Kharitonov-like theorem is provided that presents necessary and sufficient conditions for checking the mentioned stability of the fractional order interval systems with commensurate order ` belonging to [1,2), but only sufficient conditions for commensurate order ` in interval (0,1). Besides, lower and upper bounds applicable to both commensurate and incommensurate cases are provided which are useful for simulation purposes. Finally, three numerical examples are given to illustrate the results. View full abstract»

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  • Adaptive tracking control for a class of wheeled mobile robots with unknown skidding and slipping

    Page(s): 2109 - 2119
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (612 KB)  

    This study presents an adaptive tracking control approach for trajectory tracking of wheeled mobile robots with torque saturation in the presence of unknown skidding and slipping. The robot kinematics and dynamics are induced from the perturbed non-holonomic constraints. The adaptive control system using the kinematics transformed in polar coordinates is developed to compensate unknown skidding and slipping at the dynamic level of mobile robots with the input saturation. All signals of the controlled closed-loop system are uniformly bounded and the point tracking errors converge to an adjustable neighbourhood of the origin regardless of large initial tracking errors, input saturation and unknown skidding and slipping. Simulation results are provided to demonstrate the performance and stability of the proposed control scheme. View full abstract»

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  • Stabilisation of time-delay switched systems with constrained switching signals and its applications in networked control systems

    Page(s): 2120 - 2128
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (250 KB)  

    This study focuses on investigating the asymptotical stabilisability of time-delay switched systems with constrained switching signals and its applications in networked control systems (NCSs). First, based on an important lemma, asymptotical stabilisability criteria are established and stabilising switched output feedback controllers can be designed. Then, for NCSs with dropouts, the dropouts are modelled as the time delay in the control input and the switching signal in controller. Thus, the NCS with dropouts can be equivalently converted into a switched system with constrained switching signals and time delay. The asymptotical stabilisability criteria of such switched system can be applicable to the NCS with dropouts. The maximum allowable dropout bound can be obtained by solving an optimisation problem. Finally, two examples are given to illustrate the authors' main results. View full abstract»

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  • Motion synchronisation of bilateral teleoperation systems with mode-dependent time-varying communication delays

    Page(s): 2129 - 2140
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (457 KB)  

    In this study, motion synchronisation control of bilateral teleoperation system is investigated. Compared with previous passivity framework, the communication delays are assumed to be stochastically time varying. By feedback linearisation, the non-linear dynamics of the teleoperation system is transformed into two linear subsystems: local master-slave position control and delayed motion synchronisation. The authors propose new control strategies based on linear matrix inequalities (LMIs) and Markov jump linear systems, which guarantees ultimate boundedness of the master-slave trajectories. With Lyapunov methods, they show that the master-slave teleoperation system is stochastically stable in mean square under specific LMI conditions. Finally, the simulations are performed to show the effectiveness of the proposed method. View full abstract»

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  • Effect of the order of parameterisation in gradient learning for kernel methods

    Page(s): 2141 - 2151
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (579 KB)  

    Reproducing kernel Hilbert spaces (RKHSs) provide a natural framework for data modelling and have been applied to signal processing, control, machine learning and function approximation. A significant problem with models derived from RKHS is that the estimation scales poorly with the number of data. This is due to the need to invert a matrix of size equal to the number of data. Among the methods proposed to overcome this are gradient-based iterative techniques such as steepest descent and conjugate gradient that avoid direct matrix inversions. In this study the authors explore the use of gradient methods for estimating RKHS models from data. It is possible to apply the gradient iteration in function space and subsequently parameterise the algorithm or, alternatively, apply the gradient iteration directly to a parameterised version of the function approximation problem. The main contribution of this study is to demonstrate that the order in which the model is parameterised affects the rate of convergence of gradient-based iterative solution algorithms. The authors also provide conditions for which parameterisation to use in practise. Criteria for selecting the best approach, functional or parametric, are given and results demonstrating the different convergence rates are presented. View full abstract»

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  • Improved approach to delay-dependent stability analysis of discrete-time systems with time-varying delay [Brief Paper]

    Page(s): 2152 - 2159
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (173 KB)  

    This study focuses on studying the asymptotical stability analysis problem for discrete-time systems with time-varying delay. By utilising the S-procedure and an inequality technique, a novel delay-dependent stability criterion is derived in terms of two linear matrix inequalities. Since no slack variable is introduced, less decision variables are involved in the stability condition and the burden of numerical computation is thus reduced. It is also rigorously proved that the authors' result is less conservative than some recent ones. Furthermore, the developed approach is extended to address the stability analysis problem of delayed discrete-time systems with norm-bounded uncertainties. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed results. View full abstract»

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