Search

This article analyzes the consensus of first-order multiagent systems under the network topology with a directed spanning tree. A distributed PID controller with time delay is designed. D-parameterization approach is used and the crossing set consisting of frequencies such that at least one characteristic root is on the imaginary axis is identified. It is proven that the rightward crossings of the characteristic roots are always guaranteed. The exact delay margin is then determined. Numerical simulation is proposed to demonstrate the theoretical analysis. [ABSTRACT FROM AUTHOR]

This article investigates the output feedback setpoint regulation control of a reaction–diffusion equation by means of boundary control. The considered reaction–diffusion plant may be open-loop unstable. The proposed control strategy consists of the coupling of a finite-dimensional observer and a PI controller in order to achieve the boundary setpoint regulation control of various system outputs such as the Dirichlet and Neumann traces. In this context, it is shown that the order of the finite-dimensional observer can always be selected large enough, with an explicit criterion, to achieve both the stabilization of the plant and the setpoint regulation of the system output. [ABSTRACT FROM AUTHOR]

The document "Stability analysis and design of a nonlinear system with PI controllers" presents an analysis and design of a nonlinear system using PI controllers. The objective is to guarantee the stability of the system and obtain a design that offers good performance. An approach is used to maximize the performance of the nonlinear control system, using two different nonlinearities. The method is shown to be effective through simulations. The document was not submitted for evaluation by academic peers. [Extracted from the article]

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. [ABSTRACT FROM AUTHOR]

In this article, we study the digital implementation of derivative-dependent control for consensus of stochastic multiagent systems. The consensus controllers that depend on the output and its derivatives are approximated as delayed sampled-data controllers. First, we consider the $n$ th-order stochastic multiagent systems. Second, we consider PID control of the second-order stochastic multiagent systems. For the consensus analysis, we propose novel Lyapunov functionals to derive linear matrix inequalities that allow us to find an admissible sampling period. The efficiency of the presented approach is illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

Proportional-integral (PI) control/loop has been widely used in numerous industrial processes. This article focuses on integrating uncertainty estimator into PI controller for better robustness and transient performance against uncertain nonlinear coupling dynamics and time-varying disturbances. First, the descriptions for the sizes of three kinds of uncertainties in a class of multi-input–multi-output nonlinear systems are discussed. Then, the tuning laws of the typical uncertainty estimator, i.e., extended state observer (ESO), are quantitatively presented to ensure the stability of closed-loop systems. More importantly, it is shown that the desired transient performance of tracking error can be ensured by tuning the bandwidth of ESO. In addition, it is proven that much stronger disturbance rejection at low frequency can be achieved by integrating the uncertainty estimator module. The simulation results for calibration-free robotic eye-hand coordination system show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The article deals with the output feedback regulation of exponentially stable systems by an integral controller. We propose appropriate Lyapunov functionals to prove exponential stability of the closed-loop system. An example of parabolic partial differential equation (PDE) systems and an example of hyperbolic systems are worked out to show how exponentially stabilizing integral controllers are designed. The proof is based on a novel Lyapunov functional construction that employs the forwarding techniques. [ABSTRACT FROM AUTHOR]

• Unlike the existing results in the literature, the effects of quantization, strongly interconnection and unmeasurable states are simultaneously investigated in the nonlinear system. This brings more complexity and difficulty to the analysis and synthesis. • Compared with [22] and [23], in this paper, the proposed control method is simpler in structure. • A decentralized input-driven filter is designed and an output feedback controller is developed, which is more applicable in practice. • One adaptive parameter needs only to be regulated for each subsystem, which has no connection with the number of neural network nodes. Hence, the computational overhead is greatly reduced. In this paper, the problem of adaptive decentralized proportional-integral (PI) tracking control is investigated for a class of interconnected nonlinear systems with input quantization and unknown functions, where the interconnection terms are bounded by completely unknown functions. By designing an input-driven filter, the unknown states are estimated and then an adaptive decentralized output feedback PI tracking controller is constructed via the backstepping method and neural network technique. The stability of the closed-loop system is addressed based on the Lyapunov function technique plus graph theory, and all the signals in the closed-loop system are uniformly ultimately bounded. Finally, simulation results are utilized to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to provide a generalization of the so-called Simultaneous Long–Short (SLS) stock-trading result in the feedback control literature. The significance of the SLS strategy is that it guarantees a “win” in expected value of profits. Whereas previous work involves use of static linear feedback to establish this robust positive expectation property of the gain–loss function, here we obtain the same result for the more general case of PI control. In this SLS setting, robustness is assured with respect to stock prices governed by a Geometric Brownian Motion whose drift and volatility parameters are unknown to the trader. This technical note also includes numerical simulations. [ABSTRACT FROM AUTHOR]

We study a sampled-data implementation of linear controllers that depend on the output and its derivatives. First, we consider an LTI system of relative degree $r\geq 2$ that can be stabilized using $r-1$ output derivatives. Then, we consider PID control of a second-order system. In both cases, the Euler approximation is used for the derivatives giving rise to a delayed sampled-data controller. Given a derivative-dependent controller that stabilizes the system, we show how to choose the parameters of the delayed sampled-data controller that preserves the stability under fast enough sampling. The maximum sampling period is obtained from LMIs that are derived using Taylor's expansion of the delayed terms with the remainders compensated by appropriate Lyapunov–Krasovskii functionals. Finally, we introduce the event-triggering mechanism that may reduce the amount of sampled control signals used for stabilization. [ABSTRACT FROM AUTHOR]

For a point mass subject to Coulomb friction in feedback with a PID controller, we consider a model based on a differential inclusion comprising all the possible magnitudes of static friction during the stick phase and having unique solutions. We study the set of all equilibria and we establish its global asymptotic stability using a discontinuous Lyapunov-like function, and a suitable LaSalle's invariance principle. The well-posedness of the proposed model allows to establish useful robustness results, including an ISS property from a suitable input in a perturbed context. Simulation results are also given to illustrate our statements. [ABSTRACT FROM AUTHOR]

This paper considers the tracking control problem for a class of multi-input multi-output nonlinear systems subject to unknown actuation characteristics and external disturbances. Neuroadaptive proportional–integral (PI) control with self-tuning gains is proposed, which is structurally simple and computationally inexpensive. Different from traditional PI control, the proposed one is able to online adjust its PI gains using stability-guaranteed analytic algorithms without involving manual tuning or trial and error process. It is shown that the proposed neuroadaptive PI control is continuous and smooth everywhere and ensures the uniformly ultimately boundedness of all the signals of the closed-loop system. Furthermore, the crucial compact set precondition for a neural network (NN) to function properly is guaranteed with the barrier Lyapunov function, allowing the NN unit to play its learning/approximating role during the entire system operation. The salient feature also lies in its low complexity in computation and effectiveness in dealing with modeling uncertainties and nonlinearities. Both square and nonsquare nonlinear systems are addressed. The benefits and the feasibility of the developed control are also confirmed by simulations. [ABSTRACT FROM PUBLISHER]

It is a long lasting open problem to synthesize a general PI control for nonlinear systems with its gains analytically determined, yet ensuring stability and transient performance. The problem is further complicated if modeling uncertainties and external disturbances as well as actuation failures are involved in the systems. In this note, a generalized PI control with adaptively adjusting gains is presented, which gracefully avoids the adhoc and time-consuming “trial and error” process for determining the gains as involved in traditional PI control; collectively accommodates modeling uncertainties, undetectable disturbances and undetectable actuation failures that might occur in the systems; and dynamically maintains pre-specified transient and steady-state performance. [ABSTRACT FROM PUBLISHER]

The PI control configuration for stabilization and signal tracking of nonlinear systems is investigated. Semiglobal asymptotic stability and semiglobal practical signal tracking of the controlled system are proven using results from the theory of nonlinear singularly perturbed systems. [Copyright &y& Elsevier]