Design Of Linear Time-invariant Systems Research Articles

An approximate model matching technique for controller design of linear time-invariant systems using hybrid firefly-based algorithms

In this article, a delta operator based intelligent control scheme is developed with the help of model match approximately using some new firefly-based hybrid metaheuristic algorithms developed by the authors. The design approach is systematic and applies to a wide variety of plant models. The approach depends mainly on an approximate model match and gives rise to rational controllers of a lower order that can be implemented using only output feedback. The plant model, when attached with a PID controller having unknown parameters, is compared with a model considered as a reference using an approximation technique to realize the controller in the unified domain. It can be agreed upon that the estimated controller parameters using the unified delta operator approach are quite similar to those found in the continuous-time domain. Thus, a consolidated approach in the area of controller synthesis is established. Some typical models widely popular in the literature further justify the usefulness of the advocated techniques. A sufficient number of comparison has been carried out to validate the efficacy of the techniques presented. The percentage improvement of the proposed methods over the parent algorithms and other techniques has also been shown for each of the test systems. The selection of a suitable reference model may increase the utility of the new control scheme applicable to various unstable and non-minimum-phase plant models.

Disturbance attenuation in observer design for linear systems – a new parametric approach

In this paper, a new parametric approach is developed for disturbance attenuation in observer design of linear time-invariant systems. First, based on the general solution to a type of generalised Sylvester equations, a complete parametric form of the observer gain matrix is established. Secondly, a new disturbance attenuation index is introduced, and the parameters are further optimised to minimise the index. Under certain conditions, the optimal solution of this optimisation problem is obtained. Finally, the proposed method is used to design the robust observer for the yaw/roll channel attitude control system of a nonrotating missile. It is verified from the simulation results that the proposed method shows a stronger tolerance to disturbances compared with the traditional robust pole assignment method.

On Real Stable Pole Placement for Structured Systems Using Sturm and Sturm-Habicht Sequences

During the last decades, many approaches for controller design of linear time-invariant systems have been developed. However, if a prescribed controller structure is desired, controller design may become more complicated. Typical examples include PID controllers and static output feedback. We propose a method for purely real pole or eigenvalue placement. Our approach is based on the closed-loop characteristic polynomial whose coefficients are polynomials in the controller parameters. We employ quantifier elimination to verify the existing conditions and to compute the controller gain.

Simplified derivations of time-weighted quadratic functionals used in optimal control and filtering applications

In this article, we present simple alternative derivations for efficient evaluation of a matrix integral that has applications in optimal control and filtering, stability, controllability, observability, and controller design of linear time-invariant systems. The quadratic matrix integral (functional) is computed in terms of solutions of a sequence of algebraic Lyapunov equations. We present also a method to efficiently solve the obtained sequence of algebraic Lyapunov equations.

Fault Detection Filter Design With Optimization and Partial Decoupling

For the fault detection filter design of linear time-invariant systems, we propose a novel problem formulation, which not only makes a tradeoff between fault sensitivity and disturbance sensitivity, but also incorporates partial fault decoupling and disturbance decoupling. This formulation compensates the drawbacks of the available frameworks such as ${\cal H}_{-}/{\cal H}_{\infty}$ , ${\cal H}_{2}/{\cal H}_{\infty}$ and ${\cal H}_{\infty}/H_{\infty} $ . One optimal fault detection filter design for this problem framework is derived. It is shown that the faults in a certain space have arbitrary sensitivities, while the faults in the complementary space have bounded and maximized sensitivities with the proposed filter. Both the decoupling and non-decoupling conditions are derived. Moreover, decoupling disturbances is discussed. Finally, an example is given to illustrate the results.

On Switched Control Design of Linear Time-Invariant Systems with Polytopic Uncertainties

This paper proposes a new switched control design method for some classes of linear time-invariant systems with polytopic uncertainties. This method uses a quadratic Lyapunov function to design the feedback controller gains based on linear matrix inequalities (LMIs). The controller gain is chosen by a switching law that returns the smallest value of the time derivative of the Lyapunov function. The proposed methodology offers less conservative alternative than the well-known controller for uncertain systems with only one state feedback gain. The control design of a magnetic levitator illustrates the procedure.

Overlapping Quadratic Optimal Control of Linear Time-Varying Commutative Systems

Overlapping quadratic optimal control of linear time-invariant continuous-time systems by using generalized selection of complementary matrices has been recently developed as a powerful and effective means of decentralized control design of linear time-invariant systems. In this paper, it is shown that similar generalizations exist for linear time-varying systems. The results presented here concern implicit conditions for a general form of the transition matrices and explicit conditions for a commutative class of linear time-varying systems. Several important large classes of complementary matrices are selected to offer computationally attractive results. The effectiveness of this generalized selection scheme is illustrated by a numerical example of overlapping decentralized control design.

Optimal design of partial-band time-varying systems

The design of partial-band linear periodically time-varying systems (PBTV) imitating linear time-invariant (LTI) systems is approached using a relative t/sup 2/ error criterion. This error criterion results from a natural extension of the Chebyshev error criterion for the design of LTI systems. A complete analysis of the error criterion is presented. An algorithm is introduced which finds a locally optimal solution. This algorithm is based on recent results in nonsmooth optimization. The methods introduced allow the designer to compare as well as design PBTV systems in a systematic and meaningful manner.

Design of near-zero sensitivity optimal control systems†

A method for the optimal design of linear time-invariant systems with low sensitivity is proposed. The criterion of optimality is to choose system parameters and the corresponding optimal control so as to obtain zero or near-zero sensitivity of the optimal cost function. The proposed method yields a transient response, not only with faster settling time, but also insensitive to small parameter variations. The procedure is simple and can be extended to the optimal design of multi-parameter systems. It can be easily programmed on a digital computer without excessive increase in computer memory.