Stabilization of Mechanical Systems with Backlash by PI Loop Shaping

Stabilization of Mechanical Systems with Backlash by PI Loop Shaping

Ahmad Taher Azar (Benha University, Egypt) and Fernando E. Serrano (Central American Technical University (UNITEC), Honduras)
DOI: 10.4018/978-1-5225-1759-7.ch097
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Backlash is one of several discontinuities found in different kinds of systems, it can be found in actuators of different types, such as mechanical and hydraulic, giving way to unwanted effects in the system behavior. PI loop shaping control design implementing a describing function to find the limit cycle oscillations and the appropriate control gain is developed. Therefore a frequency domain approach is implemented for the control of nonlinear system of any kind such as robotics, mechatronics, other kind of mechanisms, electrical motors etc. Finally, in order to corroborate the theoretical background explained in this article, the stabilization of a cart-pendulum system with the proposed control strategy is shown.
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1. Introduction

Backlash is a phenomena found in different kinds of actuators such as mechanical and hydraulic, generally it occurs when the contact of two mating gears do not match and this give way to many unwanted effects on the systems provoking problems to the whole mechanical system. Thus some authors have proposed several solutions respect to the control and stability issues of these systems with input nonlinearities; taking in count that is not a trivial task due to the complexity of the model, traditional control strategies fail in most of the cases, and therefore it is necessary to design nonlinear control strategies or implement modified traditional ones. The objective of this article is to explain diverse control strategies for systems with this kind of nonlinearity. The intention is to show some nonlinear control techniques that have been developed and propose different approaches to solve this problem.

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