Zheng-Hua Luo

Shear force feedback control of a single-link flexible robot with a revolute joint

In this paper we present a shear force feedback control method for a single-link flexible robot arm with a revolute joint for which it has been shown that direct bending strain feedback can suppress its vibration. Our primary concern is the stability analysis of the closed-loop equation which has not appeared in the literature. We show the existence of a unique solution and the exponential stability of this solution by doing spectral analysis and estimating the norm of the resolvent operator associated with this equation. Some experiments are also conducted to verify these theoretical developments.

Shear force feedback control of flexible robot arms

For flexible robots with rotational joints it has been shown previously by Luo (1993), that direct strain feedback can damp out vibrations very satisfactorily. In this paper, a simple sensor-based output feedback control law, called shear force feedback, is newly proposed to control vibrations arising from structural flexibility of robots of Cartesian or SCARA types. Closed-loop exponential stability of such shear force feedback system is proved. Experimental results on set point control and trajectory tracking control are reported. It is found that the simple PI+shear force feedback can yield good performance for both robot motion and vibration suppression. >

Further theoretical results on direct strain feedback control of flexible robot arms

This paper is concerned with stability analyses for some nonstandard second-order partial differential equations arising from direct strain feedback control of flexible robot arms. Exponential stability issues are addressed for three types of differential equations, one of which is in general abstract evolution equation form and the other two are in partial differential equation form. The obtained results are of especially theoretical interest because they reveal the essence of direct strain feedback control and demonstrate its power in control of flexible arms. >

Stability Analysis of a Hybrid System Arising from Feedback Control of Flexible Robots

This paper presents stability analysis for a hybrid system consisting of a coupled partial differential equation and an ordinary differential equation arising from shear force feedback control of flexible robots. Conditions on the uniformly exponential decay of solutions of the entire system have not been obtained by using the conventional method such as the Liapunov function method. These conditions are made clear in this paper by reformulating the problem and by doing spectral analysis. It is shown that if the feedback gains are properly chosen then the entire hybrid system is uniformly exponentially stable, which is very useful in practical applications.

On the exponential stability of an initial-boundary equation arising from strain feedback control of flexible robot arms with rigid offset

This paper is concerned with an initial-boundary value equation arising from direct strain feedback control of flexible robot arms with a revolute joint and rigid offset. By analyzing the spectrum and by estimating the norm of the resolvent of the system operator associated with the equation, it is verified that the equation admits a unique solution and, furthermore, the solution is exponentially stable, no matter how long is the rigid offset.

Stability of C0-Semigroups

Stability analysis and feedback stabilization are issues of great importance in control system design. In this chapter, we study the stability of the following abstract Cauchy problem on a Danach space X:

Static Sensor Feedback Stabilization of Euler-Bernoulli Beam Equations

\left\{ {\begin{array}{*{20}{c}} {\frac{{du(t)}}{{dt}} = Au(t).} \\ {u(0) = x \in X.} \end{array}} \right.

Stability and Stabilization of Infinite Dimensional Systems with Applications

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