Leang S. Shieh

A novel approach to linear model simplification

New techniques for the model simplification problem are presented. If the given system is expressed by a high-order transfer function, the technique is to expand the function into a continued fraction and then ignore some quotients. If the system is in the state equations form, the method is realized by partitioning the matrix and discarding some parts. The new approach not only offers a simple procedure and a good approximation but also gives a unified viewpoint of the general analysis of linear systems.

Interval Kalman filtering

The classical Kalman filtering technique is extended to interval linear systems with the same statistical assumptions on noise, for which the classical technique is no longer applicable. Necessary interval analysis, particularly the notion of interval expectation, is reviewed and introduced. The interval Kalman filter (IKF) is then derived, which has the same structure as the classical algorithm, using no additional analysis or computation from such as H/sup /spl infin//-mathematics. A suboptimal IKF is suggested next, for the purpose of real-time implementation. Finally, computer simulations are shown to compare the new interval Kalman filtering algorithm with the classical Kalman filtering scheme and some other existing robust Kalman filtering methods.

Linear quadratic regulators with eigenvalue placement in a vertical strip

A computational method is presented for finding the linear quadratic regulator such that the optimal closed-loop system has eigenvalues lying within a vertical strip in the complex plane. The proposed method is suitable for the two-stage optimal design of two-time scale systems.

A mixed method for multivariable system reduction

A mixed method which combines dominant-eigenvalue concept and matrix-continued-fraction approach is proposed to obtain a stable reduced model from a stable high degree multivariable system.

Solution of state-space equations via block-pulse functions

A recursive algorithm is developed for the piecewise-constant solution of dynamic equations via block-pulse functions φj(t),where j=1,2,...,m. For 1≤j≤m (where j and m are integers) and final timeT, each block-pulse function φj(t) is defined by φj(t)=1 for (j−1)T/m≤t<j T/m and φj(t)=1otherwise. Compared with Walsh function approaches, the proposed method is simpler to compute, is more suitable for computer programming, and provides the same accuracy. Also, a discrete-time solution is derived for a zero-input state equation.

An algebraic method for control systems design

A computer-oriented algebraic method for the design of duplicator class control systems is established. To involves four steps: (1) Equation fitting, (2) parameter assuming, (3) system simplifying and (4) quotient matching. The power and simplicity of the method are demonstrated by several examples.

Stability of the second-order matrix polynomial

This note summarizes some existing stability and instability conditions of the second-order matrix polynomial which arises in the formulation of classical mechanics, aerodynamics, and robotic systems. Also, some sufficient conditions for stability or instability of the second-order matrix polynomial are newly developed via the relevant linear matrix equation obtained from the Lyapunov theory.

Design of PAM and PWM digital controllers for cascaded analog systems

Abstract This paper discusses the relationship among various recently developed constant state-feedback digital redesign methods. Then, for a unity-output feedback system with an analog plant in cascade with an analog controller, the best and simple Chebyshev quadrature digital redesign method is utilized to find new pulse-amplitude-modulated (PAM) and pulse-width-modulated (PWM) digital controllers for effective digital control of the analog plant. The digital controllers are determined from existing or pre-designed analog controllers as in the case of PID controllers for industrial control processes and robotics, phase lead-lag compensators for servo-mechanisms and regulator systems and guidance-autopilots for aircraft and missiles etc. The proposed method provides an alternative methodology for indirect digital design of a continuous-time unity-output feedback system and enables us to accurately and effectively implement an existing or pre-designed cascaded analog controller via a digital controller.

Transformations of a class of multivariable control systems to block companion forms

Similarity block transformations are developed to transform a class of linear time-invariant MIMO state equations in arbitrary coordinates into block companion forms so that the classical lines of thought for SISO systems can be extended to MIMO systems.

Fast and stable algorithms for computing the principal nth root of a complex matrix and the matrix sector function

This paper presents rapidly convergent and more stable recursive algorithms for finding the principal nth root of a complex matrix and the associated matrix sector function. The developed algorithms significantly improve the computational aspects of finding the principal nth root of a matrix and the matrix sector function. Thus, the developed algorithms will enhance the capabilities of the existing computational algorithms such as the principal nth root algorithm, the matrix sign algorithm and the matrix sector algorithm for developing applications to control system problems.