Contents
7.1 Conclusions . . . . 139 7.2 Scope for future work . . . . 140
7.1 Conclusions
7.1 Conclusions
This thesis attempts to design sliding mode controllers for uncertain systems having both matched and mismatched types of uncertainty. In conventional first order sliding mode controllers, chattering in the control input is the major disadvantage. Of late, second and higher order sliding mode controllers have evolved promising better chattering mitigation. This thesis attempts to design chattering free sliding mode (SM) controllers to overcome the shortcomings of conventional first order sliding mode controllers. The basic philosophy of the proposed control scheme is that instead of the normal con- trol input, its time derivative is used for designing the controller. The discontinuous sign function is contained in the derivative control and the actual control is obtained by integrating the discontin- uous sign function and hence it is continuous and smooth. This strategy is the core idea which is followed in this thesis to develop sliding mode controllers of different types. Another limitation of the conventional sliding mode controllers is the design prerequisite of knowing the upper bound of the system uncertainty apriori which is practically difficult to realize. The proposed controller attempts to overcome this difficulty by using an adaptive gain tuning methodology.
An adaptive integral sliding mode controller using chattering free sliding mode technique is proposed in this thesis. Reaching phase is totally eliminated in the integral sliding mode and hence the system becomes invariant towards the matching uncertainty right from the beginning. Application of the proposed controller to both stabilization and tracking problems of single input single output (SISO) system demonstrates the efficacy of the proposed control strategy.
An adaptive chattering free sliding mode control scheme is proposed for a class of dynamic systems with matched and mismatched perturbations. The controller is used to stabilize the twin rotor MIMO sys- tem (TRMS) in significant cross-couplings to reach a desired position and accurately track a specified trajectory. The TRMS model is divided into a horizontal and a vertical subsystem. The cross-coupling existing between the two subsystems is considered as the system uncertainty. The major advantage offered by this adaptive sliding mode controller is that advance knowledge about the upper bound of the system uncertainty is not a necessary requirement and the control input is smooth. The problem of controlling of a vertical take-off and landing (VTOL) aircraft system affected by both types of uncertainties, matched and mismatched, is also addressed by applying the proposed control scheme.
A proportional plus integral sliding surface is used in the proposed control technique. An adaptive gain tuning mechanism is used to ensure that the switching gain is not overestimated with respect to
the actual unknown value of the uncertainty.
Experimental studies conducted on the laboratory set-up of 1 degree of freedom VTOL system validate the efficacy of the proposed controller.
An adaptive terminal sliding mode (TSM) controller is proposed where the nonsingular terminal slid- ing manifold guarantees fast and finite time convergence. The proposed adaptive TSM controller is successfully applied for stabilization of a triple integrator system affected by uncertainty. Trajectory tracking of a two-link robotic manipulator which is a nonlinear system with mismatched uncertainty is considered which demonstrates the efficiency of the proposed control strategy.
A nonlinear sliding surface based chattering free adaptive sliding mode controller is proposed to im- prove the transient performance of an uncertain system. The basic philosophy of the proposed scheme is that using a nonlinear sliding surface, the damping ratio of a system can be changed from its initial low value to a final high value. The initial low value of damping ratio results in a quick response and the later high damping avoids overshoot. To improve the transient performance in discrete time uncertain systems, an integral sliding mode is used with composite nonlinear feedback (CNF).
The control strategies developed in this thesis using the chattering free adaptive sliding mode show robust performance even in presence of matched and mismatched uncertainties. The controllers de- veloped ensure high transient performance while preserving the robustness property of conventional sliding mode controllers but successfully overcoming their inherent chattering disadvantage. As such, the proposed control strategies promise high application potential in many important fields like elec- tric drives, robotics, power electronics, servo applications and aerospace where performance needs to be guaranteed consistently despite being challenged by an uncertain environment.
7.2 Scope for future work
Future possible directions of research based on the design methods developed in this thesis are outlined below:
• A natural extension of this work may be to design discrete sliding mode algorithms with adap- tive techniques which will enhance the flexibility in implementation. Now-a-days, a large class of continuous systems are controlled by digital signal processors (DSPs) and high end micro controllers. Hence discrete SM controller will be easier and effective from implementation point of view.
7.2 Scope for future work
• Another possible extension of this work may be the incorporation of an optimal sliding mode controller to optimize the control effort.
• Nonlinear sliding surface based adaptive sliding mode controller may be extended to improve the transient performance of general references, such as sinusoidal and other periodic signals.
• The proposed design method may be extended by using intelligent controllers based on fuzzy logic and neural network to incorporate flexibility and intelligence.
• The extension of these techniques with constraints on system states is also an avenue worth exploring.
• The high performance requirement of many practical applications like electric drives, electro- pneumatics, power system stabilizers and robotics may be addressed by using the proposed techniques.