Nan K. Loh

Modeling and Identification of a Class of Servomechanism Systems With Stick-Slip Friction

On tient compte de la friction de broutement dans la modelisation du processus. Lidentification des parametres du systeme est formulee comme un probleme doptimisation non lineaire

Optimal output feedback regulation with frequency-shaped cost functional

The theory of optimal output feedback control is extended to a class of quadratic performance measures whose weighting matrices are functions of frequency. The incorporation of frequency-dependent weighting matrices allows one to emphasise or de-emphasise the importance of the variables being penalised over specific bands of frequencies. Optimization of the frequency-shaped performance measure yields optimal compensators that can be more meaningful for certain minimisation problems. Results are presented for different configurations of frequency-shaping feedback control. An example is presented to illustrate the usefulness of the design technique.

Dynamic model for industrial robots based on a compact Lagrangian formulation

A compact Lagrangian formulation has been developed and discussed to deal with the highly coupled non-linear dynamic equations of robotic manipulators. It bridges the dynamic and kinematic problems of robotics closely together by means of Jacobian and subjacobian matrices. Its numeric computational complexity has been reduced to O(n2) time. When n<6, the number of operations required for computing all joint torques is almost close to that of Newton-Euler approach. Due to its significant insight of the robot behavior, it is concluded that the compact Lagrangian formulation offers a convenient approach to building up a feasible real-time adaptive control strategy for computer-based manipulators. Finally, it has been found that all information required for solving the dynamic equation and the adaptive control problems is concentrated in Hessian matrix of the kinetic energy for a given robotic manipulator.

Observer design for time-varying systems

The state estimation problem is considered for linear time–varying continuous systems with non–lexicographic–fixed observability basis. A two–stage design strategy is presented for constructing observers for this class of systems. At the first stage, by augmenting the given system with an auxiliary system, the original system is transformed to a new augmented model whose observability indices are lexicographic–fixed. A specific augmentation scheme is proposed in order to find this auxiliary system. At the second stage, a design procedure is given to construct minimum–order observers for the augmented system by utilizing the new input and output information. The canonical transformation technique is also employed to simplify the design procedure. Finally, with the help of a simple reverse transformation, solutions to the original problem arc obtained. An example is also given to illustrate the design techniques.

Continuous-time optimal robust servo-controller design with internal model principle

The linear quadratic design of an optimal robust servo–controller for a continuous–time control system is described. It introduces a servo–control performance measure which accommodates the internal model principle. The measure selectively discounts penalties on control effort of desirable frequencies and provides complete flexibility in the selection of weighting matrices. The proposed servo–controller uses plant state feedback, signal state feedforward and a servo–compensator for ensuring robust asymptotic command tracking and disturbance rejection. An informal alternate proof of the internal model principle in the state variable domain is presented using an operator-transformation technique. Where necessary, observers are used to complement the servo-controller. The proposed optimal robust servo–controller yields the expected superior performance in terms of response and error minimization. An illustrative example is given.

Imaginary robot: Concept and application to robotic system modeling

A new dynamic model which represents an exact linearization scheme with a simplified nonlinear feedback is presented in this paper. To realize this model for robotic systems, the output function should be chosen so that a special decomposition of the total inertial matrix is satisfied. The concept of an imaginary robot is introduced to achieve the formulation and to solve the realization problem. Two illustrative examples are given in the paper, one for the Stanford arm and the other for a PUMA type of robots.

Optimal suspension design with microcomputerized parameter optimizing damping

The problem of vibration isolation is investigated from the standpoint of modern control and optimization theory. The proposed suspension design was verified experimentally by means of a micromputerized suspension model. The experimental results are very encouraging and indicate promising potential application of the proposed scheme to real-world systems. This paper describes the modeling and formulation of an optimal suspension design and the implementation aspects of the proposed microcomputerized optimal suspension scheme.

Necessary and sufficient conditions of quadratic stability of uncertain linear systems

The stability of linear systems subject to possibly fast time-varying uncertainties is analyzed. A necessary and sufficient condition for quadratic stability is derived. An uncertainty stability margin coefficient rho is introduced to give a quantitative measure of the stability. It is proposed that the uncertain region be approximated by a convex hyperpolyhedron. In this case, the computation of rho becomes a two-level optimization problem, in which the extremum of the inner level can be reached by one of the corners of the hyperpolyhedron.<<ETX>>

Design of minimal-order state observers for time-varying multivariable systems

Abstract The design of minimal-order state observers is considered for linear time-varying multivariable continuous systems. Employing the observable block companion canonical transformation technique, a simple and straightforward design procedure is given for constructing the minimal-order state observers. This design technique also allows all eigenvalues of the observer to be arbitrarily assigned. Compared with existing observer design techniques for time-varying systems, the method developed has the advantage of being applicable to a more general class of systems and reducing the design complexity in the sense that various observer matrices can be determined as constant matrices. An example is also presented to illustrate the design technique.

Robust optimal parametric LQ control with a guaranteed cost bound and applications

For an optimal parametric linear quadratic (LQ) control problem, a design objective is to determine a controller of constrained structure such that the closed-loop system is asymptotically stable and an associated performance measure is optimized. In the presence of system uncertainty, the system via a parametric LQ design is further required to be robust in terms of maintaining the closed-loop stability with a guaranteed cost bound. This problem is referred to as ‘robust optimal parametric LQ control with a guaranteed cost bound’ and is addressed in this work. A new design method is proposed to find an optimal controller for simultaneously guaranteeing robust stability and performance over a specified range of parameter variations. The results presented generalize some previous work in this area. A versatile numerical algorithm is also given for computing the robust optimal gains. The usefulness of the design method is demonstrated by numerical examples and a design of the robust control of a VTOL helico...