This paper concerns the delay margin achievable using PID controllers for linear time-invariant (LTI) systems subject to variable, unknown time delays. The basic issue under investigation addresses the question: What is the largest range of time delay so that there exists a single PID controller to stabilize the delay plants within the entire range' Delay margin is a fundamental measure of robust stabilization against uncertain time delays and poses a fundamental, longstanding problem that remains open except in simple, isolated cases. In this paper we develop explicit expressions of the exact delay margin and its upper bounds achievable by a PID controller for low-order delay systems, notably the first- and second-order unstable systems with unknown constant and possibly time-varying delays. The effect of nonminimum phase zeros is also examined. PID controllers have been extensively used to control and regulate industrial processes which are typically modeled by first- and second-order dynamics. While furnishing the fundamental limits of delay within which a PID controller may robustly stabilize a delay process, our results should also provide useful guidelines i

In this note we study robust consensus problems for continuous-time first-order multi-agent systems (MAS) with time delays. We assume that the agents input is subject to an uncertain constant delay, which may arise due to inter-agent communication or additionally, also by self-delay in the agent dynamics. We consider dynamic feedback control protocol in the form of PD control, and seek to determine the delay consensus margin (DCM) achievable by PD feedback protocols, whereas the DCM is a robustness measure that defines the maximal range of delay within which robust consensus can be achieved despite the uncertainty in the delay. With an undirected graph, we show that the DCM can be determined exactly by solving a unimodal concave optimization problem, which is one of univariate convex optimization and can be solved using convex optimization or gradient-based numerical methods. The results show how unstable agent dynamics and graph connectivity may limit the range of delay tolerable, so that consensus can or cannot be maintained in the presence of delay variations.

This article aims at proposing a regulation anti-disturbance control scheme for switched systems encountered by multiple disturbances, including the measurable disturbance and unmeasurable disturbance, through a multiple Lyapunov functions method. A switched estimator is developed for estimating the unmeasurable disturbance, under which a switched regulator and a switching law are co-designed to regulate the system output, while resisting the influence of the disturbances on the switched systems. Sufficient conditions are provided to ensure the output regulation performance and the disturbance restrain performance for the switched systems, even if all subsystems may not have the performances. These conditions are also appropriate for non-switched systems. By applying the established regulation anti-disturbance control method to the regulation of the speed for an engine model, the validity of the control scheme is displayed.

In this article, we study delay robustness of PID controllers in stabilizing systems containing uncertain delays. We consider second-order systems and seek analytical characterization and exact computation of the PID delay margin, where by PID delay margin we mean the maximal range of delay values within which the system can be robustly stabilized by a PID controller. Our primary contribution is threefold. First, we show that the delay margin achieved by PID control coincides with that by PD controllers. Second, we show that the PID delay margin can be computed efficiently by solving a pseudoconcave unimodal problem, i.e., a univariate optimization problem that admits a unique maximum and, hence, is a convex optimization problem in one variable. Finally, we demonstrate analytically the tradeoff between achieving delay margin and tracking performance, showing that for several canonical performance criteria, integral control reduces the delay margin. These results lend useful insights into the PID control of delay systems, and useful guidelines in the tuning and analytical design of PID controllers.

This paper studies the delay consensus margin and its bounds for second-order multiagent systems to achieve robust consensus with respect to uncertain delays varying within a range. This paper attempts to answer the question: What is the largest delay range within which a control protocol is able to achieve and maintain the consensus? We consider second-order agents with unstable poles, which communicate over an undirected network topology, and derive explicit bounds on the delay consensus margin. The results show that the consensuability robustness of such unstable agents depends on the pole locations of the agents, as well as on the eigenratio of the network graph.

The active fault-tolerant control (FTC) problem for a class of switched nonlinear systems is investigated by using average dwell time method. First, an observer-based fault detection scheme is established. Because only the system output is assumed to be available, the threshold of fault detection only depends on the output error. Moreover, all the signals in the closed-loop system are bounded in fault-free case. After a fault has been detected, the fault estimation and FTC schemes are activated. Due to the existence of faults, unstable subsystems are allowed to exist. The fault-tolerant controllers of subsystems and a class of switching signals with average dwell time are designed such that all the signals in the closed-loop system remain bounded, and the system states can be estimated by the observer. Finally, in order to illustrate the effectiveness of the proposed method, we apply it to the switched RCL circuit system.