Stability Analysis and Controller Synthesis for Networked Control Systems

Abstract

In recent years, Networked Control Systems (NCSs) are recognized as a new research frontier in the advanced control engineering, theory and applications due to various advantages such as higher reliability, more flexibility, design modularity, and easier deployment and maintenance. An NCS refers to a system controlled remotely by a digital controller over a wired or wireless network. Networks can be either dedicated such as control area network (CAN), or shared such as Internet. In the NCSs, system components such as plant, sensor, controller and actuator are spatially distributed over the networks and each component represents a network node. Several design constraints have also emerged due to insertion of networks and distributed system components. Recently, two research approaches, 1) scheduling algorithms, and 2) control designs, are used to cater for the constraints in the NCSs. The scheduling algorithm approach is used to reduce the effect of network-induced constraints on the system performance, whereas control design approach covers novel control methodologies that compensate for the inherited constraints. In this thesis, control design approach is investigated to improve quality of control in the NCSs. It requires identification and modelling of the constraints before their incorporation in the system designs. Therefore, the potential constraints, induced by a network, are identified with a detailed literature survey and by a comparison of two sampling mechanisms: 1) time triggered (TT), and 2) event triggered (ET). Both mechanisms are compared through qualitative analysis and simulations, and effect of these mechanisms is analyzed on the system performance. The constraints identified in this research include: 1) time delays, 2) packet dropouts, 3) quantization error, and 4) limited bandwidth. Time delays that cause performance degradation and system instability are mostly time varying or random in shared networks. In this thesis, time delays are considered as stochastic processes, which follow a finite state Markov chain. The transitions in the Markov chain take values from a transition probability matrix obtained by performing experiments on a cellular network. Packet dropouts that adversely affect the system performance can be single or successive. This work presents the modelling of single and successive packet dropouts using Bernoulli random distribution and Poisson distribution, respectively. In the NCSs, networks and controllers are digital which require quantization of data before transmission of data from sensor to controller over a network. Quantization process not only adds up quantization error in the system design, but is also useful in the NCSs designs as an information coder. In this thesis, both characteristics of the quantizers are investigated. Firstly, a sector bound approach is used to bound the quantization error and robust state and output feedback controllers are proposed to mitigate its effect. In case of multiple quantizers, errors are bounded by the sector bound approach and are represented as poly-topic uncertainties. Secondly, an adaptive quantizer is proposed to explore its advantages as an information coder. The quantizer adapts its quantization densities according to network load conditions, hence is used to adjust data rate. Since components are directly connected in classic control systems, bandwidth is therefore infinite, whereas components are spatially distributed in the NCSs, bandwidth is therefore limited. To cater for this issue, robust state and output feedback controllers are proposed with a novel congestion control mechanism. In this mechanism, data is transmitted when required which helps in the optimization of bandwidth utilization. In addition to congestion control mechanism, this work also investigates ET sampling mechanism to optimize the bandwidth consumption. Various NCSs frameworks are considered which incorporate one or more constraints. For each framework, the constraints are properly modelled before proposing stability criterion and control design. This thesis proposes detailed Lyapunov-Krasovskii (L-K) functionals to obtain new sufficient conditions for the stability of NCSs. On the basis of stability criteria, state of the art control laws are proposed in terms of bilinear matrix inequalities (BMIs). Furthermore, an iterative cone complementarity algorithm is suggested to convert the BMIs into quasi-convex linear matrix inequalities (LMIs). Numerical values of the proposed controllers are obtained by solving the LMIs with the help of MATLAB based LMI and YALMIP toolboxes. Simulation examples, performed using Simulink and Simulink based toolbox TrueTime, elaborate the effectiveness of the proposed designs. Simulation results are also used to analyze the effects of the NCSs constraint on system stability, H∞ performance, and bandwidth utilization.