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Online ISSN 1751-8652 Print ISSN 1751-8644

IET Control Theory & Applications

Volume 4, Issue 7, July 2010

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Volume 4, Issue 7

July 2010

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  • Regular Papers

    • New study of controller design for networked control systems
      • Author(s): T.C. Yang ; C. Peng ; D. Yue ; M.R. Fei
      • Source: IET Control Theory & Applications, Volume 4, Issue 7, p. 1109 –1121
      • DOI:  10.1049/iet-cta.2008.0571
      • Type: Article
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      • p. 1109 –1121 (13)
        Recently there is a great research interest in networked control systems (NCSs). The intended contributions of this study, in the order of they are presented, are (a) to point out a major limitation of current studies on NCSs: many theoretical results – although important and have some significant technical merit – cannot be applied to distributed control systems and therefore have little application value; (b) in contrast to that simple numerical examples – often linear systems – are widely used to demonstrate some theoretical results. The authors study the NCS controller design for a non-linear unstable system, which has been historically used for the study of large-scale system control; (c) application of a new design approach: it is suggested that the NCS controller design problem, where data packet time delay, loss or out-of-order need to be addressed, is equivalent to a design problem where the system is point-to-point connected but has delayed and unreliable measurement subsystems; (d) a theorem for the asymptotic stability of a class of non-linear time-delay systems and (e) the stability theorem and the proposed new design approach are applied to the controller design for a model of a network-connected non-linear unstable system stated in (b). Extensive simulation results presented here have demonstrated the effectiveness of the proposed new design approach and the stability theorem.
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      Delay-dependent robust H∞ control of time-delay systems
      • Author(s): M. Sun  and  Y. Jia
      • Source: IET Control Theory & Applications, Volume 4, Issue 7, p. 1122 –1130
      • DOI:  10.1049/iet-cta.2008.0415
      • Type: Article
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      • p. 1122 –1130 (9)
        In this study, a delay-dependent H∞ performance criterion that possess decoupling structure is derived for a class of time-delay systems. It is then extended to H∞ state-feedback synthesis for time-delay systems with polytopic uncertainty and multichannel H∞ dynamic output-feedback synthesis for time-delay systems. All the conditions are given in terms of the linear matrix inequalities. In some previous descriptor methods, the products of controller matrices and Lyapunov matrices are completely separated in performance analysis, whereas it is not the case in controller synthesis. However, with the method in the paper, the weakness is eliminated. Numerical examples illustrate the effectiveness of our solutions as compared to results obtained by other methods.
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      Sampled-data fuzzy-model-based control systems: stability analysis with consideration of analogue-to-digital converter and digital-to-analogue converter
      • Author(s): H.K. Lam
      • Source: IET Control Theory & Applications, Volume 4, Issue 7, p. 1131 –1144
      • DOI:  10.1049/iet-cta.2008.0599
      • Type: Article
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      • p. 1131 –1144 (14)
        This study investigates the system stability of sampled-data fuzzy-model-based control systems. To conduct the stability analysis, Takagi–Sugeno (T-S) fuzzy model is employed to represent the continuous-time non-linear plant. Based on the fuzzy model, a sampled-data fuzzy controller is proposed to perform the control task. By using a digital computer or microcomputer, the sampled-data fuzzy controller can be realised at low implementation cost. However, the following difficulties are needed to be addressed to put the sampled-data fuzzy controller into practice. First, as the zero-order-hold unit keeps the system states and control signal constant during the sampling period, the immediate system states cannot be accessed to compute the required control signal as what the continuous-time fuzzy control does. Second, the analogue-to-digital and digital-to-analogue converters introduce quantisation error to the control process, which is a source of instability. Third, the sampling activity introduces discontinuity to complicate the system dynamics, which makes the stability analysis difficult. Furthermore, it is due to the sampling activity and zero-order-hold unit, the nice property of continuous-time fuzzy-model-based control system for stability analysis vanishes which leads to conservative stability analysis results. In this study, these difficulties are addressed and the system stability is investigated based on the Lyapunov stability theorem. Membership function conditions are developed to facilitate the stability analysis. An application example is presented to illustrate the effectiveness of the proposed approach.
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      Network-based predictive control of multirate systems
      • Author(s): Y. Zou ; T. Chen ; S. Li
      • Source: IET Control Theory & Applications, Volume 4, Issue 7, p. 1145 –1156
      • DOI:  10.1049/iet-cta.2008.0577
      • Type: Article
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      • p. 1145 –1156 (12)
        This study investigates the problem of model predictive control (MPC) for networked multirate control systems (NMCSs) with the output sampling period several times larger than the input updating period. Both sensor-to-controller and controller-to-actuator network-induced delays are considered and are assumed to be upperbounded by one output sampling period. Firstly, using a modified multirate MPC scheme, where the future control sequence is used to compensate for the network-induced time delays, the closed-loop NMCSs are described as switched systems. Sufficient stability conditions are established via a switched Lyapunov function approach. Then, a controller design method for stabilising NMCSs is proposed based on a finite input and state horizon cost with a finite terminal weighting matrix. The feedback gain matrix dependent of every sampling output can be obtained by solving linear matrix inequalities (LMIs). Finally, examples are provided to show the effectiveness of the proposed method.
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      NARX model selection based on simulation error minimisation and LASSO
      • Author(s): M. Bonin ; V. Seghezza ; L. Piroddi
      • Source: IET Control Theory & Applications, Volume 4, Issue 7, p. 1157 –1168
      • DOI:  10.1049/iet-cta.2009.0217
      • Type: Article
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      • p. 1157 –1168 (12)
        The simulation error minimisation (SEM) approach is very effective for polynomial non-linear autoregressive with exogenous variables (NARX) model selection, but is typically limited to the exploration of candidate regressor sets of limited size because of the computational cost involved in model simulation and the complexity of the empirical structure selection process over large candidate regressor sets. This study investigates the combination of a SEM algorithm for model selection, known as simulation error minimisation with pruning (SEMP), with the least absolute shrinkage and selection operator, which operates a regularisation that balances model accuracy with size in parameter estimation. The combined approach can greatly reduce the computational effort of the SEMP, without significantly affecting its accuracy, and sometimes improve the model selection quality with respect to the plain SEMP.
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      Robust transfer function identification via an enhanced magnitude vector fitting algorithm
      • Author(s): L. De Tommasi ; B. Gustavsen ; T. Dhaene
      • Source: IET Control Theory & Applications, Volume 4, Issue 7, p. 1169 –1178
      • DOI:  10.1049/iet-cta.2009.0025
      • Type: Article
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      • p. 1169 –1178 (10)
        The study introduces an enhanced version of the magnitude vector fitting (magVF) algorithm, a robust procedure for the identification of a transfer function from magnitude frequency domain data. The approach is based on the rational approximation of the magnitude square function with enforcement of symmetric poles and zeros, followed by the elimination of poles and zeros located in the right half-plane. The obtained transfer function is stable and of minimum-phase shift type. Robustness and accuracy of the basic magVF algorithm are enhanced by enforcing that the magnitude square rational function is non-negative definite and by introducing a new method to remove purely imaginary conjugate poles from the approximation. Practical application of the proposed approach is demonstrated for measured transformer responses and transmission line propagation functions.
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      Stability and instability conditions using polyhedral Lyapunov functions
      • Author(s): R. Ambrosino ; M. Ariola ; F. Amato
      • Source: IET Control Theory & Applications, Volume 4, Issue 7, p. 1179 –1187
      • DOI:  10.1049/iet-cta.2008.0603
      • Type: Article
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      • p. 1179 –1187 (9)
        In this article, the authors study the robustness analysis problem for linear continuous-time systems subject to parametric time-varying uncertainties making use of piecewise linear (polyhedral) Lyapunov functions. A given class of Lyapunov functions is said to be ‘universal’ for the uncertain system under consideration if the search of a Lyapunov function that proves the robust stability of the system can be restricted, without conservatism, to the elements of the class. In the literature, it has been shown that the class of polyhedral functions is universal, while, for instance, the class of quadratic Lyapunov functions is not. This fact justifies the effort of developing efficient algorithms for the construction of optimal polyhedral Lyapunov functions. In this context, the authors provide a novel procedure that enables to construct, in the general n-dimensional case, a polyhedral Lyapunov function to prove the robust stability of a given system. Some numerical examples are included, where the authors show the effectiveness of the proposed approach comparing it with other approaches proposed in the literature.
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      Belief propagation as a dynamical system: the linear case and open problems
      • Author(s): B.S. Rüffer ; C.M. Kellett ; P.M. Dower ; S.R. Weller
      • Source: IET Control Theory & Applications, Volume 4, Issue 7, p. 1188 –1200
      • DOI:  10.1049/iet-cta.2009.0233
      • Type: Article
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      • p. 1188 –1200 (13)
        Systems and control theory have found wide application in the analysis and design of numerical algorithms. The authors present an equivalent discrete-time dynamical system interpretation of an algorithm commonly used in information theory called belief propagation (BP). BP is one instance of the so-called sum–product algorithm and arises, for example, in the context of iterative decoding of low-density parity-check codes. The authors review a few known results from information theory in the language of dynamical systems and show that the typically very high-dimensional, non-linear dynamical system corresponding to BP has interesting structural properties. For the linear case, they completely characterise the behaviour of this dynamical system in terms of its asymptotic input–output map. Finally, the authors state some of the open problems concerning BP in terms of the dynamical system presented.
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      Switched affine systems control design with application to DC–DC converters
      • Author(s): G.S. Deaecto ; J.C. Geromel ; F.S. Garcia ; J.A. Pomilio
      • Source: IET Control Theory & Applications, Volume 4, Issue 7, p. 1201 –1210
      • DOI:  10.1049/iet-cta.2009.0246
      • Type: Article
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      • p. 1201 –1210 (10)
        This study presents a novel procedure for switched affine systems control design specially developed to deal with switched converters where the main goal is to attain a set of equilibrium points. The main contribution is on the determination of a switching function, which assures global stability and minimises a guaranteed quadratic cost. The implementation of the switching function taking into account only partial information is analysed and discussed with particular interest. The theoretical results are applied to buck, boost and buck–boost converters control design. Several simulations show the usefulness of the methodology and its favourable impact in a class of real-world control design problems.
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      Linear matrix inequality approach to static output-feedback stabilisation of discrete-time networked control systems
      • Author(s): F. Hao  and  X. Zhao
      • Source: IET Control Theory & Applications, Volume 4, Issue 7, p. 1211 –1221
      • DOI:  10.1049/iet-cta.2009.0164
      • Type: Article
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      • p. 1211 –1221 (11)
        This study is concerned with the static output-feedback stabilisation problem of discrete-time networked control systems. If the controlled plant is a discrete-time system, the networked control system with time-varying network-induced delays and data packet dropouts in the transmission is modelled as a discrete-time system with time-varying delays in the state. The network-induced delays are assumed to have both an upper bound and a lower bound. Next, an asymptotic stability condition for the networked control systems is established, which depends on the upper and lower bounds of delay times. Then, three approaches to the static output-feedback controller are proposed, where the effect of both network-induced delays and data packet dropouts has been considered. Furthermore, the robust stability condition and controller design method for such networked control systems with structured uncertainties are presented. All the results are formulated in the terms of linear matrix inequalities (LMIs), which are numerically very efficiently solved via LMI toolbox in the Matlab. Finally, three examples are worked out to illustrate the feasibility and effectiveness of the proposed method.
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      Non-linear robust filter design for satellite attitude determination
      • Author(s): K. Xiong ; L. Liu ; Y. Liu
      • Source: IET Control Theory & Applications, Volume 4, Issue 7, p. 1222 –1234
      • DOI:  10.1049/iet-cta.2009.0076
      • Type: Article
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      • p. 1222 –1234 (13)
        In this study, a non-linear robust filter (NRF) is proposed for a satellite attitude determination system. The system under consideration is subject to both the model parameter uncertainties and the linearisation errors. The proposed NRF is derived to guarantee an optimised upper bound on the estimation error covariance. The characteristics of the filter are analysed using some standard results from stochastic stability theory. It is specified that the stability of the proposed algorithm can be guaranteed independent of the model uncertainties as well as the linearisation errors. In addition, the efficiency of the NRF is demonstrated with the telemetry data from a satellite. The algorithm is developed in general such that it can be applied to stochastic uncertain non-linear systems other than satellite attitude determination.
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      Smooth time-varying pure feedback control for chained non-holonomic systems with exponential convergent rate
      • Author(s): H. Yuan  and  Z. Qu
      • Source: IET Control Theory & Applications, Volume 4, Issue 7, p. 1235 –1244
      • DOI:  10.1049/iet-cta.2008.0413
      • Type: Article
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      • p. 1235 –1244 (10)
        The feedback stabilisation problem of non-holonomic chained systems and a novel feedback design scheme is proposed, which renders a smooth, time-varying, aperiodic, pure feedback control with exponential convergence rates. There are three main advantages with the proposed design. (i) In general, time-varying designs are mostly periodic and render asymptotic stability, whereas the proposed approach is aperiodic and have exponential convergent rates. (ii) A novel state scaling transformation is proposed. It shows that even though u1 vanishes in regulation problems, intrinsic controllability of chained systems can be regained by judiciously designing the input u1 and by applying the state scaling transformations. (iii) A class of memory functions is introduced into the control design, the controller dependency on the system's initial conditions in our previous work is removed and the control is a pure feedback. Moreover, the design is shown to be inversely optimal. Simulations and comparisons are conducted to verify the effectiveness of the proposed approach.
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      Numerical solution to linear matrix equation by finite steps iteration
      • Author(s): Z.-Y. Li ; B. Zhou ; Y. Wang ; G.-R. Duan
      • Source: IET Control Theory & Applications, Volume 4, Issue 7, p. 1245 –1253
      • DOI:  10.1049/iet-cta.2009.0015
      • Type: Article
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      • p. 1245 –1253 (9)
        The matrix equation Σli=1AiXBi = C, which contains the well-known Sylvester matrix equation and Lyapunov matrix equation as special cases, has many important applications in control system theory. This study presents an iterative algorithm to solve such linear matrix equation. It is shown that the proposed algorithm converges to the unique solution to the linear matrix equation at finite steps for arbitrary initial condition. Moreover, if the matrix equation is not consistent, the least squares solution can be obtained by alternatively solving a linear matrix equation in the same form, which can also be solved by the proposed iterative algorithm. Numerical example shows the effectiveness of the proposed approach.
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      Sliding-mode adaptive attitude controller design for spacecrafts with thrusters
      • Author(s): F.-K. Yeh
      • Source: IET Control Theory & Applications, Volume 4, Issue 7, p. 1254 –1264
      • DOI:  10.1049/iet-cta.2009.0026
      • Type: Article
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      • p. 1254 –1264 (11)
        In this study, the authors propose two non-linear attitude controllers, mainly consisting of the sliding-mode attitude tracking controller and the sliding-mode adaptive attitude tracking controller, for spacecrafts with thrusters to follow the predetermined trajectory in outer space by use of employing the spacecraft's attitude control. First, the attitude model and non-linear controllers of the attitude control system of a spacecraft are established and derived, considering the external forces suffering from the gradient torque in a gravitational field because of universal gravitation, the optical torque because of solar shining and so on, to utilise the sliding-mode and/or adaptive control theory for designing the non-linear attitude controllers. Also, we consider the variation of moment inertia matrix of a spacecraft during the whole flying course to analyse their influences for the practical controller design as the conditions of limitation and correction. Simultaneously, the authors use both the adaptive control theory and the sliding-mode control to estimate parameters and eliminate disturbances of the attitude control system. Accordingly, the non-linear attitude controllers of a spacecraft are designed while the spacecraft is flying. Finally, the authors employ the Lyapunov stability theory to fulfil the stability analysis of two non-linear controllers for the overall non-linear attitude control system. Extensive simulation results are obtained to validate the effectiveness of the proposed attitude controllers.
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      Robust control for high-speed crafts using QFT and eigenstructure assignment
      • Author(s): R. Muñoz-Mansilla ; J. Aranda ; J.M. Díaz ; D. Chaos
      • Source: IET Control Theory & Applications, Volume 4, Issue 7, p. 1265 –1276
      • DOI:  10.1049/iet-cta.2009.0152
      • Type: Article
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      • p. 1265 –1276 (12)
        In this work, the problem of stabilisation of a high-speed craft with coupled dynamics is addressed. The action of the actuators to control the longitudinal dynamics (heave and pitch modes) produces a coupling in the transversal dynamics (roll mode), and vice versa. A combination of quantitative feedback theory (QFT) robust methodology and eigenstructure assignment (EA) methods is used to control the coupled system on a high-speed craft. The multi-input multi-output (MIMO) problem is firstly handled with the EA technique in order to decouple the dynamics, which results in three single-input single-output (SISO) systems to solve with QFT design. Dynamic responses of roll, pitch and heave modes of the entire fast ferry system are analysed at different sea states and angles of incidence. Time-domain simulations and frequency-domain performance analyses provide satisfactory results. It is shown that the combined EA/QFT technique is a feasible and very suitable robust method that can accomplish decoupling and damped responses and consequently a reduction in the motion sickness.
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