Second-order Sliding Mode Control For Linear Systems With Time-delay

Variable sliding mode control had been developed to an important branch of the modern control theory. Variable sliding mode control structure is widely used due to its attractive characteristics the sliding mode are robustness to uncertainties and perturbations. Unfortunately, high frequency control switching may also cause the dangerous chattering effect. This chattering phenomenon of the variable sliding mode control will increased the difficult in practical engineering. The second order sliding mode control as not only maintains the advantages of the first order sliding mode, and effectively reduce the chattering. The second-order sliding mode control is received extensive attention mainly due to limiting the chattering phenomenon, improving the controlling accuracy and preserving the main advantages of the original sliding mode approach.Time-delays and uncertain are often present in the objective world and the engineering technology. They appear in different forms such as communication, electronic systems, transportation, chemical systems, economical. Compared with the systems without delays, the presence of delay in dynamical systems is often the cause of instability and poor performance, and at the same time it is also increase the special difficulties of the design in the theory analysis and engineer applications. Therefore, it is necessary to investigate the second order sliding mode control method with the character of invariance and descend order, and this problem is a true challenge and has received considerable attention.In this paper, we proposed the second order sliding mode algorithm to design the controllers for the system with input time delay and state time delay respectively. The main contents are summarized as follows:1. The problem of designing second order sliding mode control for the linear system with input time delay is considered. The linear system with input time-delay is transformed into the equivalent non-delayed system, and then based on transformation, a simple and easily variable structure controller is designed by introducing optical algorithm and super twisting algorithm. At the same time the asymptotic stability of sliding mode is proved by constructing reasonable Lyapunov function.2. When investigating variable structure control of the system with state time delay, a novel second-order sliding mode control law is designed depending on the traditional sliding mode control law and second-order sliding mode algorithm. And then a sufficient condition for asymptotic stability of sliding mode is described in terms of linear matrix inequality, the tendency law and Lyapunov functional method. The obtained results are illustrated by an example.3. Two novel BLDC motor speed controllers are studied based on the second order sliding mode control algorithm for the remote control system with input and state time delay. At the end some simulations confirm the effectiveness and correctness of the designed controller.