Stabilization and Control of Mechanical Systems with Backlash

Stabilization and Control of Mechanical Systems with Backlash

Ahmad Taher Azar, Fernando E. Serrano
DOI: 10.4018/978-1-4666-7248-2.ch001
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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. In this chapter, three different control approaches are derived to stabilize mechanical systems in which this phenomenon is present in the actuators of the system. First, an independent joint control approach when backlash is found in the actuators is derived; then a PI loop shaping control design implementing a describing function to find the limit cycle oscillations and the appropriate control gain is developed. Finally, an optimal controller for mechanical systems with backlash is derived, obtaining the optimal control law and oscillations frequency when this nonlinearity is found implementing a describing function to model the backlash effects.
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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 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 book chapter 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.

Key Terms in this Chapter

Independent Joint Control: A control approach implemented for the stabilization and control of robotics and other mechanical systems in which the control of each joint is designed independently.

Mechanical Systems: A kind of system which consists or can be represented by a series of mechanical parts.

Multivariable Control: A control strategy for multivariable systems generally represented by a state space model.

Robotics: A science field that deals with informatics, mechanical engineering, electrical engineering and industrial engineering to develop and design mechanisms to substitute operators or persons in many industrial and other dangerous operations.

H8: Control: A control technique which consists in obtaining a controller minimizing the H 8 norm of the system.

Optimal Control: A control technique which consist in find the optimal controller input among all admissible control functions while minimizing a performance criteria.

Limit Cycles: A self-excited self-sustaining periodic oscillation.

Backlash: A nonlinearity found in many mechanical, hydraulic and other kinds of systems; due to the interconnections of elements such as gears and other elements in which there is an imperfect contact between two mating elements.

Nonlinearities: Different phenomena found in many kinds of systems which introduce a nonlinear behavior to the model.

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