Adaptive control of time-varying mechanical systems: analysis and experiments

Abstract

Adaptive control of time-varying mechanical systems is considered in this paper. A new adaptive controller for time-varying mechanical systems is proposed based on two assumptions. First, the dynamics of time-varying mechanical systems is derived under the assumption that the generalized constraints on the system do not depend on time but the system parameters such as masses and payloads are time-varying. Second, the time-varying parameters are given by a group of known bounded time functions and unknown constants. It is shown that the proposed adaptive controller results in a stable closed-loop system. Further, if the desired trajectory of the system is periodic, a time-scaling technique of mapping one cycle period of the desired trajectory into a unit interval is proposed to provide robustness to the parameter adaptation algorithm. An experimental platform consisting of a two-link robot with a time-varying payload is developed to test the proposed adaptive controller. The experimental platform mimics robotic pouring and filling operations in industry. Comparative experimental results demonstrate the effectiveness of the proposed design.

The Dynamics of a Vibromachine With Parametric Excitation

“…Besides, this book presents some other designs of mechanical elements with periodically time-varying elasticity. At present, the mechatronics systems o!er other possibilities for practical realization of parametric excitation [13,14].…”

A switching periodic adaptive control approach for time‐varying parameters with unknown periodicity

“…In this paper, we investigate not only the periodic disturbance rejection considered in [25,27] but also the linearly parameterized nonlinear systems with unknown periodic parameters multiplying known nonlinear functions. For example, a two-link robot with a periodic payload [2] in the form of (1) can be handled with the learning control method proposed in this work, whereas the learning scheme proposed in [25] loses its efficacy.…”

“…These variations can exist in the system parameters [1,2], as a disturbance to the system [3][4][5] or as the tracking objective [6,7]. Classical adaptive control, which mainly focuses on the constant parametric uncertainties, cannot produce satisfying performance for periodic variations, even for the slow-varying case [8].…”

Discrete‐time adaptive control for nonlinear systems with periodic parameters: A lifting approach

“…which is the same as (2). By choosing the same initial conditions for (2) and (8), we haveˆ j,k =ˆ k .…”

“…Comparing with the PAC [6], the proposed lifting approach expedites the convergence speed by parallel updating, meanwhile does not increase the time complexity. In fact, the lifting algorithm (4) has the same structure as the PAC algorithm (2). The parameter estimation is updated linearly and iteratively in both algorithms, hence the time complexity remains at the same order for both algorithms.…”