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IEE Proceedings - Control Theory and Applications

Volume 150, Issue 6, November 2003

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Volume 150, Issue 6

November 2003

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  • General articles

    • Reliable H∞ control of uncertain descriptor systems with multiple time delays
      • Author(s): D. Yue ; J. Lam ; D.W.C. Ho
      • Source: IEE Proceedings - Control Theory and Applications, Volume 150, Issue 6, p. 557 –564
      • DOI:  10.1049/ip-cta:20030597
      • Type: Article
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      • p. 557 –564 (8)
        The reliable H∞ controller design problem for uncertain descriptor systems with actuator failures and multiple time delays is investigated. Sufficient conditions to guarantee that the unforced system is regular, impulse-free and exponentially stable are derived. The derived conditions are expressed in terms of a set of linear matrix inequalities, which can be effectively solved by using well known algorithms. Then, based on these results, a reliable H∞ controller is proposed such that, for all admissible uncertainties and actuator failures occurring among the prescribed subset of faulty actuators, the resulting closed-loop system is regular, impulse-free and exponentially stable with an H∞ norm bound constraint. The effectiveness of the proposed method is demonstrated by a numerical example.
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      Control of linear systems using piecewise continuous systems
      • Author(s): V. Koncar  and  C. Vasseur
      • Source: IEE Proceedings - Control Theory and Applications, Volume 150, Issue 6, p. 565 –576
      • DOI:  10.1049/ip-cta:20030964
      • Type: Article
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      • p. 565 –576 (12)
        A control method is presented based on the use of piecewise continuous systems (PCS) as a control vector generator over sampling periods. The PCS has two inputs and one output which is equivalent to the control vector. Each input is corresponding to one specific time space, the first to the discrete time space defined by S = {tk, k = 0,1,2, … } and the second to the continuous time space t ∈ ℑ − S with ℑ = { t ∈ [0,∞ [ }. The control is generated in the time space ℑ. The architecture involving the PCS contains two feedback loops, based on the concept of double time and input spaces. These inputs are computed using two transformation maps Ψ and Φ defined in functions of the control strategy adopted to achieve the desired control properties. The control law depends on the PCS properties and on the method used to generate PCS controller inputs. Two examples are given: in the first the PCS controller is working in open-loop configuration during a sample period, therefore ripple is possible during sampling period. This limited control strategy assures imposed trajectory tracking only at sampling instants. In the second example the PCS is generating the control that satisfies the antiripple control strategy. The plant state is observed in continuous time and the imposed state trajectory must be compared with the plant state continuously. The PCS controller initial state is generated according to ‘optimal control’ law that minimises the quadratic criterion concerning the error-control compromise. This method appears to have several advantages over dynamic controllers: it provides control system designers with more freedom, and it requires an important computation only at the beginning of control process. Examples are given.
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      Missile longitudinal autopilot design using a new suboptimal nonlinear control method
      • Author(s): M. Xin  and  S.N. Balakrishnan
      • Source: IEE Proceedings - Control Theory and Applications, Volume 150, Issue 6, p. 577 –584
      • DOI:  10.1049/ip-cta:20030966
      • Type: Article
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      • p. 577 –584 (8)
        A missile longitudinal autopilot is designed using a new nonlinear control synthesis technique called the θ – D approximation. The particular θ – D methodology used is referred to as the θ – DH2 design. The technique can achieve suboptimal closed-form solutions to a class of nonlinear optimal control problems in the sense that it solves the Hamilton–Jacobi–Bellman equation approximately by adding perturbations to the cost function. An interesting feature of this method is that the expansion terms in the expression for suboptimal control are nothing but solutions to the state-dependent Riccati equations associated with this class of problems. The θ– DH2 design has the same structure as that of the linear H2 formulation except that the two Riccati equations are state dependent. Numerical simulations are presented that demonstrate the potential of this technique for use in an autopilot design. These results are compared with the recently popular SDRE H2 method.
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      Pretuning and adaptation of PI controllers
      • Author(s): D.W. Clarke
      • Source: IEE Proceedings - Control Theory and Applications, Volume 150, Issue 6, p. 585 –598
      • DOI:  10.1049/ip-cta:20030853
      • Type: Article
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      • p. 585 –598 (14)
        A method is proposed for the closed-loop tuning of a PI controller in cascade with a plant having an unknown transfer function, based on adding a variable-frequency sinewave to the loop's set-point. It applies design-point methodology in the Nyquist diagram to a phase–frequency adaptor coupled with gain estimators that monitor the closed-loop signals. The approach is shown to give good results over a wide range of cases, using test transfer functions taken from the literature that represent typical process dynamics. By comparing its step responses with those of loops tuned by standard Ziegler–Nichols and Cohen–Coon rules (as applied by many autotuners), the approach is seen to give consistent transients that are characterised by a user-specified damping factor. Adaptive tuning can be attained, ‘quietly in the background’ during normal PI control of a slowly varying plant, as convergence and tracking are obtained even if the output signal:noise ratio is less than one.
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      Control of self-oscillating systems
      • Author(s): Al. Pourhiet ; M. Corrège ; D. Caruana
      • Source: IEE Proceedings - Control Theory and Applications, Volume 150, Issue 6, p. 599 –610
      • DOI:  10.1049/ip-cta:20030696
      • Type: Article
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      • p. 599 –610 (12)
        In order to obtain a mathematical model of a self-sustained oscillation, a Van der Pol oscillator can be enhanced upstream and downstream with transfer functions identified from measurements. Using a specific engineering control technique, the above model has been used to define a control law aimed at suppressing the oscillation. The method has been applied to a two-dimensional buffet observed on an airfoil in a wind tunnel. The results obtained by applying this law confirmed the authors theory, thus, validating the principles of this type of modelling and design. The same method was successfully applied to the Greitzer model of a compressor surge.
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      Sliding-mode observer for speed-sensorless induction motor drives
      • Author(s): S. Xepapas ; A. Kaletsanos ; F. Xepapas ; S. Manias
      • Source: IEE Proceedings - Control Theory and Applications, Volume 150, Issue 6, p. 611 –617
      • DOI:  10.1049/ip-cta:20030882
      • Type: Article
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      • p. 611 –617 (7)
        A sliding-mode observer for the speed-sensorless direct torque vector control of induction motors is proposed. The observer estimates the motor speed, the rotor flux, the angular position of the rotor flux and the motor torque from measured terminal voltages and currents. The use of the nonlinear sliding-mode technique provides very good performance for both low- and high-speed motor operation and robustness in motor losses and load variations. The proposed observer does not uses a PI controller and complicated observer gains and that establishes an easy setup for any type of motor. Also, the convergence of the proposed observer is examined using the Lyapunov theory. Experimental results using a TMS320F240 digital signal processor are presented for low–speed operation (5 Hz), full speed operation (50 Hz), and forward to reverse operation. Finally, the proposed observer is compared with other recently reported model-reference adaptive system techniques.
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      Using circle criteria for verifying asymptotic stability in PI-like fuzzy control systems: application to the milling process
      • Author(s): R.E. Haber Guerra ; G. Schmitt-Braess ; R.H. Haber ; A. Alique ; J.R. Alique
      • Source: IEE Proceedings - Control Theory and Applications, Volume 150, Issue 6, p. 619 –627
      • DOI:  10.1049/ip-cta:20030795
      • Type: Article
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      • p. 619 –627 (9)
        A fuzzy controller that is suitable for regulating the milling process and ensuring absolute stability with a finite domain (i.e. local asymptotic stability) is presented. The stability analysis is performed on the basis of two versions of the circle criterion: (i) the extended circle criterion reducing the problem to the scalar case; and (ii) the multiple-input multiple-output circle criterion, here stated using a linear matrix inequality in order to profit from the advantages of convex optimisation. In order to verify the robust stability of the fuzzy control system, the plant gain is considered to be uncertain, and the allowed range for this uncertainty is maximised. Simulations based on the linearised plant model demonstrate how the improvement of robust stability affects the dynamics of the control loop. The robust stability improvement turns out to also yield a better fuzzy controller performance. A real-time application proves both stability and dynamic performance in an industrial environment.
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      Output feedback sliding mode control for the flying height of a pickup head in near-field optical disk drives
      H∞ model reduction for singular systems: continuous-time case
      • Author(s): S. Xu ; J. Lam ; W. Liu ; Q. Zhang
      • Source: IEE Proceedings - Control Theory and Applications, Volume 150, Issue 6, p. 637 –641
      • DOI:  10.1049/ip-cta:20030815
      • Type: Article
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      • p. 637 –641 (5)
        The problem of H∞ model reduction for linear singular systems in the continuous-time case is considered. The objective is to find a reduced-order system such that the associated error system is admissible and satisfies a prescribed H∞ norm bound constraint. Necessary and sufficient conditions for the solvability of this problem are obtained in terms of linear matrix inequalities (LMIs) and a coupling non-convex rank constraint set. An explicit parametrisation of all reduced-order systems is presented for the case when the related LMIs are feasible. A simple LMI condition without rank constraint is derived for the zeroth-order H∞ approximation problem. All these results are obtained without decomposing the original system, which makes the design procedure simple and direct.
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