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This paper introduces a closed-loop frequency analysis tool for reset control systems. To begin with sufficient conditions for the existence of the steady-state response for a closed-loop system with a reset element and driven by periodic references are provided. It is then shown that, under specific conditions, such a steady-state response for periodic inputs is periodic with the same period as the input. Furthermore, a framework to obtain the steady-state response and to define a notion of closed-loop frequency response, including high order harmonics, is presented. Finally, pseudo-sensitivities for reset control systems are defined. These simplify the analysis of this class of systems and allow a direct software implementation of the analysis tool. To show the effectiveness of the proposed analysis method the position control problem for a precision positioning stage is studied. In particular, comparison with the results achieved using methods based on the Describing Function shows that the proposed method achieves superior closed-loop performance.
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This paper is concerned with a bilinear control problem for enhancing convection-cooling via an incompressible velocity field. Both optimal open-loop control and closed-loop feedback control designs are addressed. First and second order optimality conditions for characterizing the optimal solution are discussed. In particular, the method of instantaneous control is applied to establish the feedback laws. Moreover, the construction of feedback laws is also investigated by directly utilizing the optimality system with appropriate numerical discretization schemes. Computationally, it is much easier to implement the closed-loop feedback control than the optimal open-loop control, as the latter requires to solve the state equations forward in time, coupled with the adjoint equations backward in time together with a nonlinear optimality condition. Rigorous analysis and numerical experiments are presented to demonstrate our ideas and validate the efficacy of the control designs.
In order to deal with issues caused by the increasing penetration of renewable resources in power systems, this paper proposes a novel distributed frequency control algorithm for each generating unit and controllable load in a transmission network to replace the conventional automatic generation control (AGC). The targets of the proposed control algorithm are twofold. First, it is to restore the nominal frequency and scheduled net inter-area power exchanges after an active power mismatch between generation and demand. Second, it is to optimally coordinate the active powers of all controllable units in a distributed manner. The designed controller only relies on local information, computation, and peer-to-peer communication between cyber-connected buses, and it is also robust against uncertain system parameters. Asymptotic stability of the closed-loop system under the designed algorithm is analysed by using a nonlinear structure-preserving model including the first-order turbine-governor dynamics. Finally, case studies validate the effectiveness of the proposed method.
The analysis and proper documentation of the properties of closed-loop control software presents many distinct aspects from the analysis of the same software running open-loop. Issues of physical system representations arise, and it is desired that such representations remain independent from the representations of the control program. For that purpose, a concurrent program representation of the plant and the control processes is proposed, although the closed-loop system is sufficiently serialized to enable a sequential analysis. While dealing with closed-loop system properties, it is also shown by means of examples how special treatment of nonlinearities extends from the analysis of control specifications to code analysis.
This paper investigates bilateral control of teleoperators with closed architecture and subjected to arbitrary bounded time-varying delay. A prominent challenge for bilateral control of such teleoperators lies in the closed architecture, especially in the context not involving interaction force/torque measurement. This yields the long-standing situation that most bilateral control rigorously developed in the literature is hard to be justified as applied to teleoperators with closed architecture. With a new class of dynamic feedback, we propose kinematic and adaptive dynamic controllers for teleoperators with closed architecture, and we show that the proposed kinematic and dynamic controllers are robust with respect to arbitrary bounded time-varying delay. In addition, by exploiting the input-output properties of an inverted form of the dynamics of robot manipulators with closed architecture, we remove the assumption of uniform exponential stability of a linear time-varying system due to the adaptation to the gains of the inner controller in demonstrating stability of the presented adaptive dynamic control. The application of the proposed approach is illustrated by the experimental results using a Phantom Omni and a UR10 robot.
The ongoing energy transition challenges the stability of the electrical power system. Stable operation of the electrical power grid requires both the voltage (amplitude) and the frequency to stay within operational bounds. While much research has focused on frequency dynamics and stability, the voltage dynamics has been neglected. Here, we study frequency and voltage stability in the case of the simplest network (two nodes) and an extended all-to-all network via linear stability and bulk analysis. In particular, our linear stability analysis of the network shows that the frequency secondary control guarantees the stability of a particular electric network. Even more interesting, while we only consider secondary frequency control, we observe a stabilizing effect on the voltage dynamics, especially in our numerical bulk analysis.
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