The discrete application of a continuous control designed using continuous time model of a plant is common practice. The work in this chapter evaluates new conditions required to be satisfied by the parameters of a sliding mode control so designed, such that the plant response remains bounded under such discrete application of the control. This work is taken forward to propose a generalized reaching law for discrete time sliding mode designs. This generalized reaching law is more flexible in its choice of functions and parameters, enabling it to deal with potentially new problem scenarios. A new problem in which the disturbance affecting the system is bounded by known functions, instead of a constant bound, is solved utilizing this generalized reaching law.

Chapter Contents:

• Abstract
• 3.3.1 Introduction
• 3.3.2 Definition of the bands
• 3.3.3 Digital application of continuous sliding mode control
• 3.3.3.1 Reaching phase and ultimate band
• 3.3.3.2 Stability of sliding mode
• 3.3.4 Simulation example
• 3.3.4.1 Proposed design
• 3.3.4.2 Gao's design
• 3.3.4.3 Instability with classical design
• 3.3.5 The generalized reaching algorithm
• 3.3.5.1 Main analysis with band approach method
• 3.3.5.2 Simulation example
• 3.3.6 Summary
• References

Inspec keywords: control system synthesis; continuous time systems; discrete time systems; variable structure systems

Other keywords: continuous time model; discrete-time control; continuous control; generalized reaching law; sliding mode control design

Subjects: Discrete control systems; Multivariable control systems; Control system analysis and synthesis methods