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Online ISSN 1751-8652 Print ISSN 1751-8644

IET Control Theory & Applications

Volume 5, Issue 15, 13 October 2011

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Volume 5, Issue 15

13 October 2011

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  • Regular Papers

    • H∞ filter design for delta operator formulated systems with low sensitivity to filter coefficient variations
      • Author(s): X.-G. Guo  and  G.-H. Yang
      • Source: IET Control Theory & Applications, Volume 5, Issue 15, p. 1677 –1688
      • DOI:  10.1049/iet-cta.2010.0500
      • Type: Article
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      • p. 1677 –1688 (12)
        The problem of designing H∞ filters for delta operator formulated systems with low sensitivity to filter coefficient variations is investigated. The delta operator provides a theoretically unified formulation of continuous-time and discrete-time systems and also has the advantage of better numerical properties at high sampling rates. In addition to the standard H∞ criterion, the H∞ norm of the sensitivity function is introduced in order to improve the designed filter's insensitivity to the filter coefficient variations. Finsler's Lemma is used to derive novel sufficient conditions which are adapted to treat this multiplicative objective optimisation problem in a potentially less conservative framework. Linear matrix inequality conditions are obtained for the existence of admissible filters with respect to additive/multiplicative coefficient variations based on two different types of sensitivity measures. Finally, the effectiveness of the proposed method is illustrated by a numerical example. It is shown that the delta operator approach offers better coefficient sensitivity than the traditional shift operator approach when the sampling rate is high.
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      Stability analysis of polynomial fuzzy-model-based control systems under perfect/imperfect premise matching
      • Author(s): H.K. Lam  and  L.D. Seneviratne
      • Source: IET Control Theory & Applications, Volume 5, Issue 15, p. 1689 –1697
      • DOI:  10.1049/iet-cta.2010.0619
      • Type: Article
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      • p. 1689 –1697 (9)
        This study presents an improved sum-of-squares (SOS)-based stability analysis result for the polynomial fuzzy-model-based control system, formed by a polynomial fuzzy model and a polynomial fuzzy controller connected in a closed loop. Two cases, namely perfect and imperfect premise matching, are considered. Under the perfect premise matching, the polynomial fuzzy model and polynomial fuzzy controller share the same premise membership functions. While different sets of membership functions are employed, it falls into the case of imperfect premise matching. Based on the Lyapunov stability theory, improved SOS-based stability conditions are derived to determine the system stability and facilitate the controller synthesis. Simulation examples are given to verify the stability analysis results and demonstrate the effectiveness of the proposed approach.
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      H∞ Control for stochastic stability and disturbance attenuation in a class of networked hybrid systems
      • Author(s): J. Yao ; F. Lin ; B. Liu
      • Source: IET Control Theory & Applications, Volume 5, Issue 15, p. 1698 –1708
      • DOI:  10.1049/iet-cta.2010.0499
      • Type: Article
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      • p. 1698 –1708 (11)
        The authors study H∞ control for stochastic stability and disturbance attenuation (SSDA) in a class of networked hybrid systems (NHS). A hybrid system has both continuous variables and discrete events. A NHS consists of a set of subsystems that are coupled together. Both continuous dynamics and coupling among subsystems change as events occur. When an event occurs stochastically, the continuous state variables may jump from one value to another. Using the stochastic Lyapunov functional approach, sufficient conditions on the existence of an H∞ state-feedback controller that ensures stochastic stability and H∞ disturbance attenuation for NHS with and without time delays are obtained. The derived conditions are expressed in terms of solutions of appropriate algebraic inequalities. A new approach to the design of such a controller is then presented. An illustrative example of a unified chaotic network with randomly jumping parameters is used to demonstrate the satisfactory control performance.
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      Generalised minimum variance control state-space design
      • Author(s): A.S. Silveira  and  A.A.R. Coelho
      • Source: IET Control Theory & Applications, Volume 5, Issue 15, p. 1709 –1715
      • DOI:  10.1049/iet-cta.2011.0099
      • Type: Article
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      • p. 1709 –1715 (7)
        The main goal of this study is to propose a state-space design technique for the generalised minimum variance control. In this sense, the same results achieved in the transfer function design framework are granted by the state-space method. It simplifies the design procedure while avoiding the solution of the Diophantine equation. Instead, the minimum variance predictor is obtained by the direct feed-through of an estimated state vector using a Kalman filter designed directly from the state-space model and without the need to solve an algebraic Riccati difference equation. In this way, even when dealing with systems with long time delays, the design procedure requires only a small amount of work as compared to the classical Diophantine-dependent technique. The proof of equality between the transfer function and state-space methods is easily verified by simple linear algebra, showing that the Diophantine equation results are intrinsically embedded in the gains of the state-space predictor derived, which means that resultant polynomials of the Diophantine equation can also be obtained by construction with the new design method. Two simulation examples are given to demonstrate the proposed technique.
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      Design of control strategies for robust dynamic routing in traffic networks
      • Author(s): M.S. Mahmoud
      • Source: IET Control Theory & Applications, Volume 5, Issue 15, p. 1716 –1728
      • DOI:  10.1049/iet-cta.2010.0578
      • Type: Article
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      • p. 1716 –1728 (13)
        In this study, improved centralised and decentralised routing control strategies are developed based on minimisation of the worst-case queuing length. The centralised routing problem is formulated as an ℋ∞ optimal control problem to achieve a robust routing performance in the presence of unknown fast time-varying network delays. Then a decentralised routing problem is reformulated by treating every node as a single subsystem thereby yielding an algorithm that obtains the fastest route. In both cases, unconstrained solution is derived to design a delay-dependent ℋ∞ controller and expressed in terms of the feasibility of linear matrix inequality (LMI). Subsequently, physical constraints are imposed and added as LMIs. Salient features of the developed routing methodology including the increase of robustness against multiple unknown time-varying delays, and the enhancement of the scalability of the algorithm to large-scale traffic networks are delineated. Simulation results are presented to demonstrate the effectiveness and capabilities of the developed dynamic routing strategies.
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      Game approach to distributed model predictive control
      • Author(s): L. Giovanini
      • Source: IET Control Theory & Applications, Volume 5, Issue 15, p. 1729 –1739
      • DOI:  10.1049/iet-cta.2010.0634
      • Type: Article
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      • p. 1729 –1739 (11)
        This study introduces a framework for distributed model predictive control (MPC) based on dynamic games, where centralised and decentralised control algorithms can be viewed as dynamical games with coupled control sets. The original optimisation problem is decomposed into smaller coupled optimisation problems in a distributed structure, which is solved iteratively. Then, the resulting dynamic game is analysed using the theory of potential games to derive the properties of the resulting algorithms. This sheds new light on the properties of existing MPC algorithms and allows us to establish a unified framework to analyse them. The control problem of a heat-exchanger network (HEN) is used to illustrate the effectiveness, practicality and limitations of the proposed framework.
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      Effect of vibration control on the frequencies of a cantilever beam with non-collocated piezo sensor and actuator
      • Author(s): C. Spier ; J.C. Bruch ; J.M. Sloss ; I.S. Sadek ; S. Adali
      • Source: IET Control Theory & Applications, Volume 5, Issue 15, p. 1740 –1747
      • DOI:  10.1049/iet-cta.2010.0674
      • Type: Article
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      • p. 1740 –1747 (8)
        Displacement feedback control of a cantilever beam is studied using non-collocated piezoelectric patch sensors and actuators. The solution to the problem is obtained using two different methods, one analytical and another numerical. The analytical method involves an integral equation formulation of the problem where the eigensolutions of the integral equation are shown to be the eigensolutions of the governing differential equation of motion of the smart beam. This approach eliminates the difficulties associated with discontinuities caused by patch sensors and actuators which introduce Heaviside functions and derivatives of the Heaviside functions into the differential equation formulation. The numerical method of solution uses a finite-element model of the controlled beam with modified beam element mass and stiffness matrices to account for the piezo patches and the control effect. The control circuit consists of a piezoceramic and polyvinylidene fluoride sensor patch and a lead zirconium titanate actuator patch. The mass and stiffness of the piezoceramic actuator patch are taken into account in the mass and stiffness calculations. Numerical examples with non-collocated sensor and actuator patches are presented and the first three natural frequencies are given using the integral equation and the finite-element methods. The results of these methods match very closely which provides a verification of the results.
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      Subspace algorithms for identifying separable-in-denominator two-dimensional systems with deterministic inputs
      • Author(s): J.A. Ramos ; A. Alenany ; H. Shang ; P.J.L. dos Santos
      • Source: IET Control Theory & Applications, Volume 5, Issue 15, p. 1748 –1765
      • DOI:  10.1049/iet-cta.2010.0302
      • Type: Article
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      • p. 1748 –1765 (18)
        The class of subspace system identification algorithms is used here to derive new identification algorithms for 2-D causal, recursive, and separable-in-denominator (CRSD) state space systems in the Roesser form. The algorithms take a known deterministic input-output pair of 2-D signals and compute the system order (n) and system parameter matrices {A,B,C,D}. Since the CRSD model can be treated as two 1-D systems, the proposed algorithms first separate the vertical component from the state and output equations and then formulate a set of 1-D horizontal subspace equations. The solution to the horizontal subproblem contains all the information necessary to compute (n) and {A,B,C,D}. Four algorithms are presented for the identification of CRSD models directly from input-output data: an intersection algorithm, (N4SID), (MOESP), and (CCA). The intersection algorithm is distinguished from the rest in that it computes the state sequences, as well as the system parameters, whereas N4SID, MOESP, and CCA differ primarily in the way they compute the system parameter matrices {A1,C1}. The advantage of the intersection algorithm is that the identified model is in balanced coordinates, thus ideally suited for 2-D model reduction. However, it is computationally more expensive than the other algorithms. A comparison of all algorithms is presented.
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      Hierarchical platoon control with heterogeneous information feedback
      • Author(s): G. Guo  and  W. Yue
      • Source: IET Control Theory & Applications, Volume 5, Issue 15, p. 1766 –1781
      • DOI:  10.1049/iet-cta.2010.0765
      • Type: Article
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      • p. 1766 –1781 (16)
        The problem of autonomous platoon control via wireless communication network is studied in this study. Firstly, a novel hybrid model is established for the platoon's longitudinal movement, where disturbances of lead vehicle acceleration and wind gust, parameter uncertainties and intermediate uncertainties induced by communication network (e.g. time delay, quantisation and packet dropout) are given full considerations and involved in the model for the first time. Then, the authors establish a hierarchical platoon controller design framework comprising a feedback linearisation controller at the first layer and a guaranteed cost H∞ controller at the second layer. By reducing the non-linear system to a linear model using the top layer feedback linearisation controller, a robust H∞ controller, the kernel controller, is designed utilising novel techniques in robust control of time-delay systems. For the general objective of disturbance attenuation, string stability and robust platoon control to be achieved simultaneously, the robust H∞ controller is complemented by additional conditions established for guaranteeing string stability and zero steady-state spacing errors. Simulations are given to show the efficiency of the proposed results.
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      Robust adaptive neural control for a class of uncertain non-linear time-delay systems with unknown dead-zone non-linearity
      • Author(s): J. Wang  and  J. Hu
      • Source: IET Control Theory & Applications, Volume 5, Issue 15, p. 1782 –1795
      • DOI:  10.1049/iet-cta.2010.0633
      • Type: Article
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      • p. 1782 –1795 (14)
        A robust adaptive neural network controller is proposed for a class of uncertain non-linear time-delay systems in strict feedback form with both completely unknown control gains and unknown non-symmetric dead-zone non-linearity based on backstepping design. The proposed design approach does not require a priori knowledge of the signs of the unknown control gains. The unknown time delays are compensated for constructing appropriate Lyapunov–Krasovskii functionals. By utilising integral Lyapunov design and sliding-mode control strategy, the controller singularity problem and the effect of dead-zone input non-linearity are avoided perfectly. From Lyapunov stability theorem, it is proved that the proposed design approach is able to guarantee semi-globally uniformly ultimately boundedness of all the signals in the closed-loop system, and the tracking error of the system is proven to be converged to a small neighbourhood of the origin. The simulation results demonstrate the effectiveness of the proposed approach.
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      Supervisory adaptive tracking control of robot manipulators using interval type-2 TSK fuzzy logic system
      • Author(s): C.-S. Chen
      • Source: IET Control Theory & Applications, Volume 5, Issue 15, p. 1796 –1807
      • DOI:  10.1049/iet-cta.2010.0703
      • Type: Article
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      • p. 1796 –1807 (12)
        This study proposes an interval type-2 Tagaki–Sugeno–Kang fuzzy logic system (IT2TSKFLS) for the supervisory adaptive tracking control of robot manipulators to confront uncertainties in the robot dynamics. The IT2TSKFLS that combines interval type-2 fuzzy sets and TSK fuzzy reasoning is used to approximate unknown non-linear functions in the robot dynamics. Based on IT2TSKFLS, a supervisory controller comprises a weighed combination of the adaptive IT2TSKFLS control and the sliding-mode control (SMC) to suppress the effects of uncertainties and approximation errors. The main idea of this supervisory structure is to exploit their advantages of the IT2TSKFLS with online learning ability and the SMC with robust characteristics. Projection-type adaptive algorithms of IT2TSKFLS parameters derived from the Lyapunov synthesis approach guarantee the stability and robustness of the overall control system. The proposed approach needs no prior system information and offline learning phase. Experiments performed on a two-link robot manipulator demonstrate the effectiveness of the proposed control methodology.
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