FeedNetBack-D04.03 - Design of Robust Variable Rate Controllers

A consequence of the execution of control algorithms on digital distributed platforms is inducing delays, jitter and various limitations in sampling rate from different sources in the control loops. These disturbances should be taken into account in the control algorithms design and tuning. Control systems are often cited as examples of "hard real-time systems" where jitter and deadline violations are strictly forbidden. In fact experiments show that this assumption may be false for closed-loop control. Any practical feedback system is designed to obtain some stability margin and robustness w.r. t. the plant parameters uncertainty. This also provides robustness w.r. t. timing uncertainties: closed-loop systems are able to tolerate some amount of sampling period and computing delays deviations, jitter and occasional data loss without loss of stability or integrity. Hence the design of dependable distributed control systems may rely on robust controllers, i.e. controllers which are slightly sensitive to both process model and execution resource uncertainties, or on controllers which are made adaptive w.r. t. the variations of the control intervals and other implementation induced disturbances. Section 2 provides new results concerning the control of systems with delays. A novel analysis of linear systems under asynchronous sampling is provided. This approach is based on the discrete-time Lyapunov Theorem applied to the continuous-time model of the sampled-data systems. Tractable conditions are derived to ensure asymptotic stability and also to obtain an estimate of the exponential rate of the solutions. Examples show the efficiency of the method and the reduction of the conservatism compared to other results from the literature. Moreover the methodology addresses the stability analysis of systems under several sampling periods. We show that a sampled-data system can be stable even if one of the sampling period leads to instability. This has been treated by a continuous-time approach and allows considering uncertain or time-varying systems. An extension of the method includes transmission delays in the control loop. As the variations of the control intervals can be both a consequence of network induced delays and a control variable to manage the CPU and/or network load, robust variable sampling control design is investigated in section 3. Here it is assumed that the control interval is itself a control parameter, e.g. which can be adapted at run-time by a feedback scheduler to cope with operating conditions in a varying environment. The control design is stated using the formulation of Linear Parameters Varying (LPV) systems, where the sampling interval is considered as a varying and measurable parameters of the system. Previous results using a polytopic model of a discretized plant are recalled. A new design using a Linear Fractional Transform (LFT) is developed, where the control interval is considered as a system's uncertainty. This new approach is expected to be more tractable that the polytopic one when the system has several varying parameters. Both designs are assessed and compared using as testbed the control of Autonomous Underwater Vehicles using scheduled ultrasonic sensors for control and navigation. 2