Abstract: This chapter presents a design method and stability analysis for discrete time pole placement adaptive control systems with input rate saturation constraints. It is shown that with appropriate design, the robust adaptive control system is stable for a class of uncertain stable minimum phase plants in the sense that all the signals in the loop remain bounded in the presence of modeling uncertainties and disturbances. If the plant is free from modeling uncertainties and disturbances and the control input rate remains unsaturated for a period of time, then the closed loop adaptive control system will be asymptotically characterized by the desired closed loop poles.

Abstract: Integration of controllers with smart structural systems require the controllers to consume less power and to be small in hardware size. These requirements pose as limits on the control input and the order of the controllers. Use of reduced order model of the plant in the controller design can cause spill over problems in the closed-loop system due to possible excitation of the unmodeled dynamics. In this paper, we present a method to design output feedback robust controllers for smart structures in the presence of control input limits considering unmodeled dynamics as additive uncertainty in the design. The performance requirements for the design are specified as regional pole placement constraints on the closed-loop poles. The controller design problem requires the maximization of damping ratio in the presence of additive uncertainty and control input limits. The resulting optimization problem for the controller design is formulated as a generalized eigenvalue problem involving linear matrix inequality (LMI) constraints. The proposed controller is designed and implemented on a multiinput-multioutput 3-mass smart structural test article. The tradeoffs involved in the controller design are analyzed and the performance and robustness specifications are verified experimentally.

Abstract: The paper describes a new composite control method combining a neural network estimator with a conventional pole-placement based adaptive controller. The neural network estimation technique presented by Hussain (2000) is particularly effective when there is no complete plant information, or when considering a controlled plant as a 'black box'. In the proposed composite controller, the neural network estimator weights are adapted online to minimise the identification error, and these weights are fed into a robust self-tuning PID controller which provides an adaptive mechanism to ensure that the closed loop poles are placed at the desired positions. Simulation results show that the proposed method applies to general linear or nonlinear control systems.

Abstract: We consider indirect frequency domain non-parametric transfer function plant estimators in closed-loop. We make the assumption that the real and imaginary parts of the corresponding closed-loop system transfer function estimate at each frequency have Gaussian distribution, but do not necessarily have equal variance, nor are they necessarily independent. We characterise the probability density function of the plant transfer function estimate, and show it to have a unique minimum, and at most two maxima.

Abstract: The starting point for filters and group delay equalisers design is the appropriate solution of the approximation problem. Through the presented technique is possible to design a transfer function standard even no standard filters with respect to their poles and zeros quality and group delay responses. The technique was also used for transfer function design of group delay equaliser. In this case there were prescribed requirements on group delay response and quality of poles and zeros as well. To solve these large constraint problems, modifying Differential Evolution (DE) is used, as an effective way for penalty function minimisation.

Abstract: We propose a congestion control algorithm and design a state feedback controller for regulating the congestion of available bit rate (ABR) traffic in asynchronous transfer mode (ATM) networks. ABR service is specified as the rate-based feedback mechanism for congestion control and provides a control signal to throttled sources from a bottleneck node in order to adjust the throttled source rates based on available capacity. Our main purposes are as follows: (1) to design a state feedback controller; (2) to place the closed-loop poles in any desired regions based on a pole placement constraint; (3) to use the LMI (linear matrix inequalities) approach for finding the optimal state feedback gain K. The simulation results show that, under pole placement and LMI approaches, our state feedback congestion controller for ABR traffic in ATM networks can possibly guarantee the system stability, provide no buffer overflow, determine the optimal source traffic rates and place the closed-loop poles in any desired regions as well.

Abstract: We present here the sensitivity of classical filter transfer functions that are polynomial approximations to the ideal brick-wall magnitude response. The transfer function is decomposed into the part corresponding to the passband ripple parameter and the approximating polynomial. It is shown that the sensitivity has a complementary transfer function response. With these sensitivity relations, it is possible to relate filter parameter variations to any part of the circuit implementing the transfer function. Examples are submitted and discussed to show the usefulness of these new results in providing a more thorough assessment of filter performance potential and limitations.

Abstract: In this paper we will present two techniques to design a dynamic output feedback controller for Linear Parameter Varying (LPV) systems with H 2 constraint. Assuming that the model is polytopic, the first technique allows a direct synthesis of a controller having the same LPV structure as the system. The second technique seeks for an observer based controller, the originality of this controller that both state feedback gain and observer gain are LPV. Assuming that the parameter variation is so slow that the system can be nearly considered as LTI, the controller will satisfy additional constraints on the closed loop pole location.

Abstract: To maximize the bandwidth of dedicated negative feedback amplifiers by passive frequency compensation, the order of the amplifier needs to be known. Here a method is introduced to determine the order of a circuit with negative feedback. It is shown that the slim of poles in the negative feedback loop, i.e. the loop poles, can be used to determine the order of the amplifier. These loop poles, can be found relatively easily from the circuit diagram and thus the order of the circuit is also relatively easily found.

Abstract: The problem of designing the state feedback controllers is studied which guarantee the closed-loop poles within a specifiled disc and steady-state variances to be less than given uppper bounds for linear discrete-time systems with norm-bounded paramdter uncertatainties. Based on the linear matrix inequality approach, existence conditions of rotust variance controllers and derived. A parameterized representation of robust varance controllers in provided in tems of the feasible solutions to a certain linear matrix inequality system. Furthemore, the design problem of the minimum-effect robust variance controller is formulated as a convex optimization problem.

Abstract: Sufficient conditions for the optimality of real or nonmultiple complex-conjugate right-most roots of characteristic polynomials in a maximally stable system are formulated. The problem is solved for cases in which the controlled object is described by a transfer function containing a polynomial of degree greater than zero in the numerator.

Abstract: The author considers stability and robustness of feedback systems, where plant and compensator need not be strictly proper. In his earlier paper (2001) he described a functional R/sub /spl infin// which, when negative, guarantees closed-loop instability as a result of parasitic interactions in the feedback loop. In his main result, Theorem 5, he proves that, when R/sub /spl infin//>0. there exist perturbations of plant and compensator from a narrow class which result in closed-loop stability and convergence. Hence, one may view R/sub /spl infin//>0 as a necessary and sufficient condition for closed-loop robustness in non-strictly-proper feedback loops.

Abstract: Synthesizing a controller frequency response is a common requirement in feedback system design. A method is described for synthesizing a continuous-time minimum-phase frequency response specification. For a discrete set of frequencies, the designer may specify linear inequalities that bound the magnitude and phase of the frequency response. A linear programming problem is formulated using these bounding inequalities, together with constraints that force the frequency response to be minimum-phase and sufficiently smooth so that it can be approximated with a low-order transfer function. The objective for the linear programming problem is to minimize the frequency weighted gain of the controller. The problem solution prescribes both the magnitude and phase of the frequency response specification. A controller that approximates the specification can then be readily designed using existing continuous-time filter approximation methods. A design example is presented to demonstrate the application of the proposed...

Abstract: The limiting zero distribution of a sampled system represented by a FIR model is derived. The continuous time system under study may not have a rational transfer function.

Abstract: A method is proposed to construct a controller for a delayed stable plant that ensures the desired location of the roots of the characteristic equation of a closed-loop system. The design procedure expresses the controller transfer function directly in terms of the coefficients of the plant transfer function.

Abstract: The problem of robust stabilisation of interval plants with a first-order compensator is considered. A first-order compensator can robustly place the closed-loop poles of an interval plant in the shifted left-half plane or a shifted circular region if and only if it can simultaneously place the closed-loop poles of all the vertex plants in the same region.

Abstract: This paper presents a robust control method for uncertain nonminimum phase systems with external disturbances. A systematic design algorithm is developed which links the sliding mode control and the root locus technique. Complete closed-loop pole placement is achieved in addition to the placement of the reduced order equivalent system poles. An integration function is employed in the sliding variable formulation. The output tracking error is guaranteed to vanish. The proposed method was successfully applied to control the angle of attack of a missile attitude control system.