13.1 Introduction

The complexity and nonlinear dynamics of motion control systems, along with the high-performance required during operation, require complex, often nonlinear control system design, to fully exploit system capabilities. Basic goals for motion control systems include trajectory tracking, velocity control and control of the force exerted by the system on the environment with torque or force as the control input. The torques or forces are on the other hand the outputs of actuators, often electrical motors, with their own complex nonlinear dynamics. In most approaches to motion control systems, the dynamics of torque or force is neglected and controllers are designed assuming perfect tracking in the torque or force control loop, which is not the case in many systems and such a design procedure may create some difficulties in systems with high demands. Direct application of discontinuous control in motion control systems with torque or force as the input may lead to chattering [1, 2] and some precaution must be taken in order to overcome chattering related problems. One of the ways to accomplish this is by smoothing the control in the ?-vicinity of the sliding mode manifold [1, 2] or in the framework of the discrete-time sliding mode design (due to the fact that in such systems the control action may be continuous [3]). Another solution for avoiding chattering is to augment the description of the system with torque or force dynamics - actuator dynamics.

In this chapter, the main problems in...