Nonlinear Backstepping Control Of A Series DC Motor With Input Dead-zone

The control problem of nonlinear actuators with input dead-zone has been an active research area.The nonsmooth nonlinearity in the motor along with the external disturbances make the plant dynamics nonlinear,the control is very difficult using the traditional linear techniques,as they can only offer local stability.Dead-zone is time-varying and thus in order to design a suitable controller,it is necessary that the parameters in the control desig n must be adapted due to the time-varying nonlinear conditions.In this regard,robust control design dictates to consider the mathematical characteristics of nonlinearities as well as external disturbances,during the control design.However,the bounds o f these terms may change during the system operation and adapting these bounds in order to have a smooth operation requires the combination of robust as well as control theories,which is a highly challenging task.In this thesis,the analysis of stability of the series DC motor is considered.The backstepping control technique is employed.Several cases have been considered.In the first case,the parameters and quantities of the plant are assumed to be perfectly known and a proportional-integral controller is developed.However,since PI control can be somewhat destabilizing,the control development is extended to include a PD term.Such a term helps to reduce the destabilizing effect of the PI term.Due to the nonlinear nature of the system under study,the resulting control is also nonlinear.In the second case,a backstepping controller is employed to compensate dead-zone nonsmooth nonlinearity.The Lyapunov stability theory is applied to all of the cases to prove the stability of the system under the developed control.The results are then verified through MATLAB Simulink.In the third case,the system under study which contains bounded uncertainties is examined.The load torque and armature inductance are assumed to be uncertain,but vary from expected nominal values within a specified range.To handle this situation a robust nonlinear control is designed.The background knowledge on this design includes a discussion of the generalized matching conditions and their importance in developing a control law.