Fang-Bo Yeh

Generalized guidance law for homing missiles

The concept of a generalized guidance law is presented, and the closed-form solution for a homing missile pursuing a maneuvering target according to generalized guidance laws is given. It is shown that the guidance laws appearing in the literature are merely special cases of the one proposed by the authors. The derived generalized forms of capture area, missile acceleration, and homing time duration that are derived provide insight into the performance of the guidance laws being considered and lead to the discovery of new ones. The problem of finding a nonlinear optimal guidance law for a homing missile with controlled acceleration, applied so as to capture a maneuvering target with a predetermined trajectory while minimizing a weighted linear combination of time of capture and energy expenditures, is solved in closed form. The derived optimal control law is equal to the LOS (line of sight) rate multiplied by a trigonometric function of the aspect angle. Numerical simulation shows that the resulting guidance law appears to yield a significant advantage over true proportional navigation. >

A new algorithm for the minimal balanced realization of a transfer function matrix

Abstract A new algorithm is proposed here to obtain a minimal balanced realization directly from the transfer function matrix (TFM). This method which employs the singular-value decomposition (SVD) of an infinite block-Hankel matrix requires neither an initial minimal realization nor the solution of a Lyapunov matrix equation. The formulation is solely in terms of the coefficients of the transfer function matrix.

Synthesis of robust-performance controllers using matrix experiments and analysis of variance

The integration of robust control and quality control is introduced. Experimental design using orthogonal arrays is an effective approach to directly considering and achieving time domain specifications, which is difficult for approaches based on frequency domain synthesis such as norm-bounded optimization schemes. In addition, by exploiting the analysis of variance (ANOVA), the interrelation between specification and each design parameter can be clearly studied. The proposed approach is shown to provide controllers with the performance-robustness property which is exactly the design goal of synthesis. Systematic procedures for this quality-oriented control design are outlined. A practical example of satellite attitude control is demonstrated to show that the experiment-aided methodology can help to find the parameters of controllers to meet robust-stability and robustperformance requirements.

A computational algorithm for the super-optimal solution of the model matching problem

Abstract In this paper, we develop a computational algorithm to implement the strengthened minimization technique [1] in the model matching problem which arises in robust controller design and weighted sensitivity minimization. A general algorithm is proposed for constructing unitary matrices and the extremal functions for the H ∞ -optimization problem are diagonalized using the constructed unitary matrices. We impose stronger minimization conditions to force the solution of the optimization problem to be unique and explain their physical significance.

On modeling root-locus behavior

The purpose of this paper is to establish a mathematical model precisely describing the force interaction within root loci. The concept of generalized root loci is introduced, and its relation with potential flows, such as streamline in fluids and current in electric fields, is revealed. With the help of complex variable theory, the authors derive formula to compute the force applied on root loci and to predict the quantitative variation of applied force when adding a pole or a zero to a root locus or removing one from it. Root sensitivity and root robustness can also be quantitatively measured by using this mathematical model for root loci.<<ETX>>

Optimal sensitivity bound estimation and controller design

An explicit computational form is given for the estimation of the smallest upper bound on the sensitivity function over an operating band for a given stability margin in a single right half-plane (RHP) zero scalar system. A stable minimum-phase weighting function is constructed to meet such an infimum and the given stability margin with the H∞ criterion. A numerical example is presented to demonstrate the optimal sensitivity estimation, weighting function construction and controller design.