First coursework ELEC6240: networked control systems reading assignment 1 Introduction A networked control system (NCS in the following) is a distributed system con- sisting of a set of plants, a set of controllers, sensors, and actuators, commu- nicating among themselves through a shared digital communication network of limited bandwidth. Such a configuration has considerable advantages over traditional control systems in which dedicated independent connections exist between controllers and plant: the reduction in the amount of wiring brings about increased reliability, lower maintenance costs, and easier reconfigurability and troubleshooting. The implementation of such a system is a straightforward matter for current technology given the wide availability of low-cost processing power and reliable, standardized (possibly wireless) communication channels and protocols. For these reasons NCSs are currently used in a broad range of applications: mobile sensor networks, manufacturing control systems, robotics, and many others. From the theoretical point of view, control scientists face several challenges when considering the design, analysis and control of NCSs and consequent prob- lems of stabilization and design for performance: limited bandwidth, sampling and quantization issues, information delay and loss, and communication fail- ures, to name but a few. Many of such issues are specific to NCSs or exhibit special features, so that traditional control techniques and paradigms cannot provide adequate solutions. A good introduction to NCSs, including an historical overview, is given in the survey paper [1]. It would do you good to read this paper, to understand the context in which the need for NCSs arises and some of the many challenges facing control theorists and engineers. 2 Aims The aims of this reading assignment are: • to introduce you to one of the frameworks used to analyse and control NCSs, the Model-Based approach (MB-NCS in the following); • to have you read in depth one research paper about MB-NCSs; 1 • for you to get a hands-on experience in assessing the performance of a MB-NCS system by implementing via Matlab a simple simulation. What is required of you in this assignment is: • elementary knowledge about linear systems and stability (that obtained through attending a standard module on continuous-time state-space mod- els); • elementary knowledge of Matlab (see the help command). 3 Reading Please download through the University of Southampton Library website the paper [2]. Read carefully sections 1 and 2 at least, and if possible the whole paper. 4 Questions Answer the following questions, justifying your answers as much as possible. Question 1: Consider the plant dynamics ddtx = Ax+Bu with A = [ 0.14 1.25 0 0.08 ] and B = [ 0 1.07 ] . Assume that C = I2, i.e. that the state is all available for measurement. Is this a BIBO-stable system? (3 marks) Question 2: Define K by K := [−0.2 −0.9] ; is the closed-loop system ddtx = (A+BK)x+Bu, y = x BIBO-stable? (3 marks) Question 3: Consider the scheme described in sect. 2 of [2], with the model described by  := [ 0 1 0 0 ] and B̂ := [ 0 1 ] . Compute the matrix Λ defined on p. 1838 of [2] before Prop. 1. (1 mark) Question 4: Using Matlab for your computations if necessary, give an analyt- ical expression for the matrix M(h) defined in Th. 1 p. 1839 of [2]. (6 marks) 2 Question 5: Using Matlab, plot the evolution of max{|λi(M(h))|, i = 1, . . . , 4}, where λi(M(h)) is the i-th eigenvalue of M(h) as h varies between 0 and 20. Include the plot in your answer. (4 marks) Question 6: Using the result of Th. 1 of [2] and the plot obtained answering Question 5, determine for which values of h the MB-NCS is stable. (3 marks) Question 7: Using Matlab and the MB-NCS dynamics defined in equation (1) of [2], plot the response of the system (y1 = x1 and y2 = x2) of the system for h = 1, h = 5, and h = 18, respectively, when the initial conditions of the plant are x(0) = [ 1 −1 ] and those of the model are x̂(0) = [ 0 0 ] . (3 marks) References [1] J. Baillieul and Antsaklis, P.J., “Control and Communication Challenges in Networked Real-Time Systems,” in Proceedings of the IEEE, vol.95, no.1, pp.9-28, Jan. 2007. [2] L.A. Montestruque and Antsaklis, P.J., “On the model-based control of networked systems”, Automatica, Vol. 39, No. 10, October 2003, pp. 1837- 1843. 3
