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Control Theory and Applications, IEE Proceedings -

Issue 1 • Date Jan. 2003

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Displaying Results 1 - 14 of 14
  • Robust stability of singularly perturbed systems with state delays

    Page(s): 2 - 6
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (307 KB)  

    The stability of a linear two-time-scale system with state delays is studied. A delay-dependent sufficient condition for the stability bound ε* is given, such that the stability of the full-order model can be inferred from the analysis of its reduced-order model in separate time scales. The stability robustness problem of the same system is also discussed, where both the system matrices and time delays may be uncertain. Finally, an example is illustrated to show the applications of the results derived. View full abstract»

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  • Control of conditional output probability density functions for general nonlinear and non-Gaussian dynamic stochastic systems

    Page(s): 55 - 60
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (425 KB)  

    A method to control the shape of the conditional output probability density function for general nonlinear-dynamic stochastic systems represented by a nonlinear ARMAX model is presented. The system is subjected to an arbitrary and bounded random input. Under the assumption that all the variables are uniformly bounded, a mathematical relationship is formulated among the conditional output probability density function, the system nonlinear structure and the characteristics of the random input. This leads to the establishment of a recursive formula for the evolution of the conditional output probability density functions for the system. An optimal control has thus been developed by embedding the system dynamics into the recursive formula and by minimising the difference between the conditional output probability density function and a target probability density function. It has been shown that the obtained control input is of an output feedback type, where the on-line measurements of the conditional output probability density functions are not required. An illustrative example is utilised to demonstrate the use of the control algorithm, some satisfactory results have been obtained. View full abstract»

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  • Reliable control design using a two-stage linear quadratic reliable control

    Page(s): 77 - 82
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (432 KB)  

    Two-step linear quadratic optimal control update equations and a sequential gain updating scheme are used to design a reliable guaranteed cost discrete-control system called two-stage linear quadratic reliable control (TSLQRC). Using this method reliable linear quadratic design results for continuous-time systems can be easily extended to discrete-time systems. The stability and performance gain margins of the TSLQRC are evaluated to show the connections between the continuous-time and the discrete-time designs. View full abstract»

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  • Asymptotically optimal stabilising quadratic control of an inverted pendulum

    Page(s): 7 - 16
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (526 KB)  

    A method for the design and synthesis of near-optimal, nonlinear control laws is examined, based on a generalisation of linear quadratic optimal control theory and which effectively provides a near-optimal gain schedule. The method is simple to apply and affords greater design flexibility (via state-dependent weighting) than conventional approaches. The resulting regulator can, in principle, be implemented in real time owing to the causal nature of the required computations. However, the need to solve an algebraic Riccati equation at every time point is burdensome, and a number of algorithms that would permit parallel computation are discussed. The problem of stabilising an inverted pendulum is used to illustrate the method and proves an exacting task that highlights a number of issues. View full abstract»

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  • Guaranteed-cost control of a linear uncertain system with multiple time-varying delays: an LMI approach

    Page(s): 17 - 22
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (373 KB)  

    The guaranteed-cost control program via memoryless state feedback controllers is studied for a class of linear time varying delay systems with norm-bounded time varying parametric uncertainty and a given quadratic cost function. The time varying delays considered are assumed bounded but no information to be available. Sufficient conditions for the existence of guaranteed-cost controllers are given in terms of linear matrix inequalities (LMIs). A convex optimisation problem with LMI constraints is formulated to design the optimal guaranteed-cost controller which minimises the guaranteed cost of the closed-loop uncertain system. View full abstract»

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  • Constructing sparse realisations of finite-precision digital controllers based on a closed-loop stability related measure

    Page(s): 61 - 68
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (537 KB)  

    The authors present a study of the finite word length (FWL) implementation for digital controller structures with sparseness consideration. A closed-loop stability related measure is derived, taking into account the number of trivial elements in a controller realisation. A practical design procedure is presented, which first obtains a controller realisation that maximises a lower bound of the proposed measure, and then uses a stepwise algorithm to make the realisation sparse. Simulation results show that the proposed design procedure yields computationally efficient controller realisations with an enhanced FWL closed-loop stability performance. View full abstract»

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  • Feedback of passive systems: synthesis and analysis of linear robust control systems

    Page(s): 83 - 91
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (609 KB)  

    The feedback interconnection of passive systems always leads to a stable control loop. This fact can be used for synthesis and analysis of linear robust control systems in a uniform framework. In the case of slowly varying uncertainties the plant can be represented by a linear time-invariant (LTI) multimodel. Rendering this multimodel passive and using a strong strictly passive controller ensures robust stability of the closed loop. The paper refines this idea to the design of robust observer-based controllers using parametric controller design. The new method allows the inclusion of a very extensive multimodel. Based on the well-accepted concept of pole assignment, the procedure yields robust controllers whose orders do not exceed the order of the plant. For rapidly varying uncertainties the plant must be modelled as a linear time-variant (LTV) system. To obtain an uncertain control loop that can also be analysed with the feedback theorem the LTV-components must be separated from the LTI system. It is shown that this can be done by establishing an affine relation between time varying parameters and the state-space matrices. The resulting closed-loop structure allows the application of the multivariable circle criterion which is used here in LMI form. View full abstract»

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  • Delay dependent stability of neutral systems with time delay: an LMI approach

    Page(s): 23 - 27
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (306 KB)  

    A delay dependent stability problem is addressed for neutral systems with discrete and distributed delays. A new stability criterion, based on the solution of linear matrix inequalities, is proposed. Two examples are given to illustrate that the proposed method is effective and can provide a less conservative result. View full abstract»

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  • Design of a robust controller using only output feedback to solve the servomechanism problem

    Page(s): 28 - 36
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (531 KB)  

    The design of a robust controller using only output feedback to solve the servomechanism problem is considered. A PI control algorithm and a sliding-mode control design are combined to alleviate system uncertainties and to solve the output regulation problem. A reduced-order observer for the transformation matrix is proposed to estimate the system states, and a control law is designed with respect to the estimated signals. Asymptotic regulation is also satisfied by using the estimated states in the controller. A numerical example is presented to demonstrate the applicability of the proposed control scheme. View full abstract»

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  • Modified anti-windup scheme for PID controllers

    Page(s): 49 - 54
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (350 KB)  

    An anti-windup scheme for proportional-integral-derivative controllers is presented. The approach is based on the combined use of back-calculation and conditional integration anti-windup techniques. In this way, the disadvantages that can hinder previously proposed strategies are overcome. Specifically, the method can guarantee a satisfactory performance for processes with different normalised dead times, without the tuning of additional parameters being required. Therefore, considering its simplicity, it is highly suitable for implementation in industrial regulators. View full abstract»

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  • Profile tracking performance of a low ripple hybrid stepping motor servo drive

    Page(s): 69 - 76
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (550 KB)  

    A control strategy to harness the torque ripple of a hybrid stepping motor at low speeds for precision profile tracking is proposed. The strategy uses a model-based control design that controls the phase current based on the direct quadrature transformation of the second-order nonlinear dynamics. An identification procedure based on a least-squares algorithm is applied to estimate the model parameters for calculation of the ripple dynamics. The method produces a more appropriate form of linear regression which avoids the problem of reconstructing important signals such as the rotor speed and the derivatives of the driving current, and rejects additional errors created by the quantisation of the measurements. This paves the way for an integrative process to obtain precise trajectory tracking by combining a reference trajectory, traditional PID control, and dynamic feedback linearising control coupled with feedforward compensation over a broad torque-ripple frequency band. Simulations And experiments are performed with a typical hybrid stepping motor to test its profile tracking accuracy. The results may be used to develop a commercial control scheme for tuning computer-controlled drives. View full abstract»

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  • Nonlinear rule-based controller for missile terminal guidance

    Page(s): 45 - 48
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (316 KB)  

    The design of a rule-based guidance law for homing missiles onto targets is presented. The stability of the missile-target dynamics is proven. Unlike conventional approaches that solve the Hamilton-Jacobi partial differential inequality associated with the missile guidance problem, the proposed guidance law is based on heuristic fuzzy rules. Furthermore, the proposed missile guidance control law guarantees that the missile can reach the impact region and destroy the target. An example is used to illustrate the application of the proposed design method. View full abstract»

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  • Parametric eigenstructure assignment via output feedback based on singular value decompositions

    Page(s): 93 - 100
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (549 KB)  

    Eigenstructure assignment in multivariable linear systems via output feedback is investigated. Three problems are proposed that are related to a type of generalised Sylvester matrix equations. By proposing a general complete parametric solution to this type of generalised Sylvester matrix equations based on singular value decompositions, a general complete parametric approach is presented for the proposed eigenstructure assignment problems. General parametric expressions for both the closed-loop eigenvector matrices and the output feedback gain are established in terms of certain parameter vectors. These parameter vectors provide the design degrees of freedom and can be utilised to achieve desired specifications. Based on the proposed results and the Matlab Optimisation Toolbox, a Matlab file is created, which finds a solution that gives minimum closed-loop eigenvalue sensitivities for the problem of eigenstructure assignment via output feedback. View full abstract»

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  • Q-domain four-blocks l1-optimal control design for SISO plants

    Page(s): 37 - 44
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (575 KB)  

    The multiblock l1-optimal control problem for single-input single-output (SISO) plants is considered. It is shown that it can be converted via polynomial equation techniques to an infinite-dimensional linear programming (LP) problem. Finite dimensional sub/super approximations can be determined by considering two sequences of modified finite-dimensional linear programming problems derived directly from the YJBK parameterisation by exploiting the underlying algebraic structure. This approach induces the application of a consistent truncation strategy that leads to a redundancy-free constraint formulation and, as a consequence, to linear programming problems less affected by degeneracy. Further, more insight on the algebraic structure of the problem and on the achievement of exact rational solutions is provided, allowing the development of a simple and conceptually attractive theory. View full abstract»

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