Analysis of singular systems using Taylor series approach

The Taylor series approach to the analysis of singular systems is considered. An example is given to demonstrate the use of this method.     

Torque optimization schemes for kinematically redundant manipulators

One of the important applications for the resolution of redundant manipulators is torque optimization, due to the fact that the actuators used for driving a manipulator have finite power ratings. Nevertheless, not many algorithms have been proposed to accomplish this objective. A survey of the existing local torque optimization control schemes is given in this article. It will be shown that all of them either encounter instability problems for long trajectories or fail in certain cases. For remedying these problems, the authors present the Minimum Velocity Norm (MVN) method, which is the most common approach for kinematic redundancy resolution and has never been adopted for torque optimization by other researchers. Simulation results show that the simple MVN method is moderate for short movements and is stable for long movements. Also, the MVN method can be applied to cases that may not be accomplished by some other approaches. Therefore, the MVN method is better than the other existing approaches for torque optimization. © 1994 John Wiley & Sons, Inc.     

Window-shaped obstacle avoidance for a redundant manipulator

The window-shaped obstacle avoidance problem is studied in this paper. Several research papers regarding obstacle avoidance including the method proposed by Zghal et al., which we believe is the most suitable for three-dimensional (3-D) window-shaped obstacle avoidance are studied. Consequently, several shortcomings of the Zghal's method are discovered. The Zghal's method will produce chattering solution sequences in joint rates due to its deficiency in determining the shortest distance between the manipulator links and the window edges. This paper proposes a new scheme to determine the shortest distance. This new scheme will remedy the chattering problem. Moreover, the nearest link (NL) method is developed for further improvement. Because the NL method only considers the nearest link in the performance criterion, the on-line weighting assignment problem of the Zghal's method is removed, also, less redundancy is required to accomplish the goal for obstacle avoidance. Therefore, the NL method will allow more redundancy to be useful for the other goals under multiple-goal application environments.     

Adaptive Harmonic Control in PWM Inverters with Fluctuating Input Voltage

New techniques of harmonic reduction and voltage regulation in PWM inverters with fluctuating input voltage are described. A novel selective harmonic reduction technique is also developed for three-phase full-bridge inverters to reduce the number of switchings per output cycle. For keeping the fundamental load voltage at the present value and suppressing the generation of low-order harmonics when the input voltage fluctuates, the conventional sinusoidal reference of the triangulation method is replaced by a quasi-sinewave whose magnitude varies inversely with the input voltage to keep the product of the reference voltage and the input voltage sinusoidal. Harmonic analysis of the W-type modulation and M-type modulation is given to show that the load voltage spectra of the output waveforms generated with the proposed methods are insensitive to the source voltage fluctuation and load variation. Experimental results confirm the theoretical analysis.     

Taylor series approach to functional approximation for inversion of Laplace transforms

The letter is devoted to a functional approximation for inversion of the Laplace transform. The function is approximated by a truncated Taylor series, which is expanded about t0=0. Utilising a special transformation, each Laplace transform is converted into a set of simultaneous linear algebraic equations which are then easily computed to give the coefficients of the basis function. Two examples with satisfactory results are given.     

Stability margins of singular perturbation systems via state-feedback control

The gain and phase margins of singular perturbation systems are analysed under unmodelled high-frequency dynamics control, composite control, and the original full-order linear quadratic (LQ) control. The analysis is on the basis that there is a good relation between the minimum singular value of return difference transfer matrix and the stability margins. We begin with the examination of stability margins of subsystems and then show that state-feedback control design of subsystems could preserve gain and phase margins for the original full-order singularly perturbed system if the singular perturbation parameter epsiv; is sufficiently small. The effectiveness of ε on stability margins is formulated and determined. It is found that the effectiveness can be evaluated by a simple method. Two examples are exploited to illustrate the analytic results.     

Robustness of dynamic output feedback control for singular perturbation systems

The problem of the robustness of dynamic output feedback control for singular perturbation systems is investigated. The solution to this problem is reduced to the simultaneous design of static output feedback controllers for the fast subsystem and the so-called auxiliary system of the slow subsystem. Some conditions are proposed to ensure the robustness of the actual closed-loop system. The exact upper bound of the parasitic parameter for the controlled system is also determined. Finally, an actual model which failed in dynamic output feedback control in [4] is reexamined successfully here.