Minor loop feedback

Abstract: In this design of a feedback system it is desirable to make experimental measurements of the loop gain as a function of frequency to ensure that the physical system operates as analytically predicted or, if not, to supply information upon which a design correction can be based In high loop-gain systems it is desirable that the loop-gain measurement be made without opening the loop This paper discusses practical methods of measuring and interpreting the results for loop gain of the closed-loop system by a voltage injection or a current-injection technique ; extension to the case in which the measurement can be made even though the system is unstable ; and extension to the case in which neither the voltage nor current-injection technique alone is adequate, but in which a combination of both permits the true loop gain to be derived These techniques have been found useful not only in linear feedback systems but also in describing-function analysis of switching-mode converters and regulators

Abstract: For a general class of robots with elastic joints, we introduce an inversion algorithm for the synthesis of a dynamic feedback control law that gives input-output decoupling and full state linearization. Control design is performed directly on the second-order robot dynamic equations. The linearizing control law is expressed in terms of the original model components and of their time derivatives, allowing an efficient organization of computations. A tight upper bound for the dimension of the needed dynamic compensator is also obtained.

Abstract: It is shown that, for any linear time-invariant multivariable system which is both completely controllable and completely observable, almost all output feedback laws can be used to make the closed-loop system have distinct poles; i.e., the set of output feedback laws which fails to achieve this goal is either an empty set or a hypersurface in the parameter space. It is also shown that almost any output feedback law will make the closed-loop system's poles be disjoint from any given finite set of points on the complex plane. It is then shown that any controllable observable system can be made controllable and observable with respect to any nontrivial input and output by applying almost all output feedback laws about the original system. These results have immediate application in pole assignment, in the controllability of parallel-connected systems, and in the identification problem. In addition, it is shown that, for any linear system and for almost all state feedback laws, the closed-loop system has the property that all modes of the system, except possibly those corresponding to the uncontrollable-unobservable part of the system, are observed in the output.

Abstract: In this paper a novel approach to the Cartesian impedance control problem for robots with flexible joints is presented. The proposed controller structure is based on simple physical considerations, which are motivating the extension of classical position feedback by an additional feedback of the joint torques. The torque feedback action can be interpreted as a scaling of the apparent motor inertia. Furthermore the problem of gravity compensation is addressed. Finally, it is shown that the closed loop system can be seen as a feedback interconnection of passive systems. Based on this passivity property a proof of asymptotic stability is presented.