Discrete-Time Sliding Mode Control for Networked Control System

In this chapter, brief introduction and literature survey for Networked Control Systems (NCSs) are presented. The chapter includes detailed literature survey for NCS that covers control algorithms, compensation methods for network delay with packet loss and mathematical modelling of network delays and packet loss in continuous-time as well as discrete-time domain.

In this chapter, we introduce the concept of Networked Control System (NCS), the irregularities such as time delay and packet loss that occurs in the NCS. We also discussed the various control methods available for NCS. This chapter also presents the concept of sliding mode control along with the literature survey on SMC for NCS.

In this chapter, a novel approach is presented for designing a discrete-time sliding mode controller. The effect of sensor to controller fractional delay and controller to actuator fractional delay in discrete-time domain is compensated through Thiran’s approximation technique. The forward channel delay is compensated at the actuator side, while feedback channel delay is compensated at the sliding surface. An evolved sliding surface with delay compensation is used to derive SMC law. The stability condition for the closed-loop system with proposed controller is derived using Lyapunov function. The efficacy of the proposed algorithm is shown by simulation results and also validated by the experimental results considering DC servo system in networked environment having matched uncertainties.

In this chapter, the design of discrete-time sliding mode controller using Thiran’s delay approximation is extended for non-switching type algorithm. The effect of sensor to controller delay is compensated using Thiran’s delay approximation technique in the sliding surface. Further, Lyapunov approach is used to determine the stability of closed-loop NCSs with the proposed controller. The efficacy of the control methodology is endowed by simulation and experimental results in the presence of networked delay. The performance of the proposed control algorithm is further validated in the presence of real-time networks such as CAN and Switched Ethernet using true time simulator.

In Networked Control System, the state feedback SMC is the simplest way for designing controller provided all state information is available. However, in many practical situations in network-based control system most of the states are observable but they are immeasurable. So it is essential to design the SMC controller using output information which is always available. This chapter presents the design of multirate output feedback-based discrete-time sliding mode controller in which the control input is computed using the system outputs and past control signals by taking full advantage of network transmission. A Thiran approximation technique is used to compensate the networked-induced delays for designing sliding mode controller (SMC). The stability of the closed-loop NCSs is derived using Lyapunov approach. Simulations results are presented to demonstrate the effectiveness of the proposed approach.

In Networked Control System, the behaviour of network delays generally depends on the characteristics of communication medium as well as occupancy of channel by different elements. When large number of sensors, controllers and actuators share their information through the common communication medium, then the network delays and packet losses are random in nature. In this chapter, a novel approach is presented for designing discrete-time sliding mode controller by treating random fractional delay and packet loss separately. The fractional delay that occurs within sampling period while transmitted from sensor to controller and controller to actuator channel is modelled using Poisson’s distribution function and is approximated using Thiran’s delay approximation technique for designing the discrete-time sliding mode controller. The packet loss that occurs in communication channel between sensor to controller and controller to actuator is treated with Bernoulli’s distribution function and compensated at controller end as well as actuator end. Further, Lyapunov approach is used to determine the stability of closed-loop NCSs with proposed discrete-time SMC controller. The feasibility and efficiency of the proposed control methodology is outlined through simulation and experimental results which shows a significant response even in the presence of random fractional delay, packets loss and matched uncertainties.

The concept of remotely controlling a system through communication network gave birth to Networked Control Systems (NCSs). The NCSs are traditional feedback control loops closed through a real-time communication network. It is evident that the performance of closed-loop system deteriorates due to network delay and information loss in communication channel due to bandwidth limitation or congestion. Hence, it is mandatory to improvise the existing control strategies for NCS. In this chapter, we propose an approach for designing discrete-time sliding mode controller for NCS having random fractional delay and multiple packet loss simultaneously. The fractional delay that occurs within sampling period is modelled using Poisson’s distribution function and is approximated using Thiran’s delay approximation technique. The multiple packet loss that occurs in communication channel between sensor and controller is treated with uniform probability distribution function and compensated at controller end. Based on the proposed approach, a sliding surface is designed and is used to derive discrete-time sliding mode control law that computes the control actions in the presence of random network delay and multiple packet loss. Further, a second-order disturbance estimator is incorporated at the plant side to estimate the disturbance that occurs in the plant. The disturbance estimator guarantees the width of quasi-sliding mode band (QSMB) of order \(O(h^{3})\) with decreasing reaching steps. Hence, the robustness properties of closed-loop NCS are improved. The stability of the closed-loop NCS is also derived using Lyapunov approach that assures the finite-time state convergence in the presence of network non-idealities. The efficacy of the proposed algorithm is examined through simulation results.

In this book, a novel method of designing discrete-time sliding mode controller in the presence of fractional delay along with packet loss occurrence due to network medium is presented. Firstly, the effect of deterministic type fractional delay is compensated using Thiran’s approximation technique and the compensated state information is used for the design of sliding surface. A switching type discrete-time networked sliding mode controller is designed using the compensated sliding surface which computes the control sequences in the presence of matched uncertainty. The condition for stability of the closed-loop system is derived using Lyapunov approach.