A Design Method for 2-Degree-of-Freedom Repetitive Control Systems

This paper presents a method for designing a controller that achieves the best positioning performance while maximizing the energy efficiency of a redundantly actuated hybrid feed drive. A two-degree-of-freedom controller, consisting of a feedforward (FF) controller for tracking and a feedback (FB) controller for regulation, is assumed. It is shown that the ideal FF controller, which achieves perfect tracking with maximum efficiency, is not always stable. Therefore, a method for designing a stable FF controller that achieves perfect tracking with near optimal efficiency is proposed. Furthermore, the optimal relationship between FB control inputs, which guarantees maximum efficiency for any specified regulation performance, is derived. Two approaches for using the derived optimal relationship to synthesize a FB controller that achieves the best positioning performance while maximizing efficiency are proposed. Simulations and machining experiments are conducted to demonstrate the effectiveness of the proposed energy-efficient FF and FB controller design methods. Significant improvements in energy efficiency (without sacrificing positioning performance) are reported.

This paper shows that design of a robustly stable repetitive control system is equivalent to that of a feedback control system for an uncertain linear time-invariant system satisfying the well-known robust performance condition. Once a feedback controller is designed to satisfy the robust performance condition, the feedback controller and the repetitive controller using the performance weighting function robustly stabilizes the repetitive control system. It is also shown that we can obtain a steady-state tracking error described in a simple form without time-delay element if the robust stability condition is satisfied for the repetitive control system. Moreover, using this result, a sufficient condition is provided, which ensures that the least upper bound of the steady-state tracking error generated by the repetitive control system is less than or equal to the least upper bound of the steady-state tracking error only by the feedback system

Dynamics of the mechanical system is described by the matrix-second-order differential equation, and the coefficient matrices in the equation have some special properties such as symmetry and positivity. These properties should be reflected to the design method of controllers for mechanical systems. In this paper we discuss control problems of mechanical systems in the matrix-second-order differential equation model by paying attention to their potential and kinetic energy. First we introduce a concept called generalized energy function and then by using this new concept we discuss observability and controllability and propose a design method of feedback controllers of the mechanical systems.

This paper presents a novel design method for discrete-time repetitive control systems (RCS) based on two-dimensional (2D) discrete-time model. Firstly, the 2D model of an RCS is established by considering both the control action and the learning action in RCS. Then, through constructing a 2D state feedback controller, the design problem of the RCS is converted to the design problem of a 2D system. Then, using 2D system theory and linear matrix inequality (LMI) method, stability criterion is derived for the system without and with uncertainties, respectively. Parameters of the system can be determined by solving the LMI of the stability criterion. Finally, numerical simulations validate the effectiveness of the proposed method.

This paper is concerned with the method of impulsive controller design for linear systems with multiple-packet transmission. First, the mathematic model of respond closed-loop is built in terms of linear impulsive systems description. Second, on the basis of guaranteeing closed loop systems stability, the design method of the impulsive feedback controller and the design procedure are given. Finally, numerical simulation is provided to demonstrate that asymptotically stability of close-loop linear uncertainly impulsive system with multiple-packet transmission is guaranteed by using the impulsive controller.

Robust guaranteed cost control of uncertain fuzzy systems under time-varying sampling

The cerebellum has been hypothesized to form a crucial part of the speech motor control network. Evidence for this comes from patients with cerebellar damage, who exhibit a variety of speech deficits, as well as imaging studies showing cerebellar activation during speech production in healthy individuals. To date, the precise role of the cerebellum in speech motor control remains unclear, as it has been implicated in both anticipatory (feedforward) and reactive (feedback) control. Here, we assess both anticipatory and reactive aspects of speech motor control, comparing the performance of patients with cerebellar degeneration and matched controls. Experiment 1 tested feedforward control by examining speech adaptation across trials in response to a consistent perturbation of auditory feedback. Experiment 2 tested feedback control, examining online corrections in response to inconsistent perturbations of auditory feedback. Both male and female patients and controls were tested. The patients were impaired in adapting their feedforward control system relative to controls, exhibiting an attenuated anticipatory response to the perturbation. In contrast, the patients produced even larger compensatory responses than controls, suggesting an increased reliance on sensory feedback to guide speech articulation in this population. Together, these results suggest that the cerebellum is crucial for maintaining accurate feedforward control of speech, but relatively uninvolved in feedback control.SIGNIFICANCE STATEMENT Speech motor control is a complex activity that is thought to rely on both predictive, feedforward control as well as reactive, feedback control. While the cerebellum has been shown to be part of the speech motor control network, its functional contribution to feedback and feedforward control remains controversial. Here, we use real-time auditory perturbations of speech to show that patients with cerebellar degeneration are impaired in adapting feedforward control of speech but retain the ability to make online feedback corrections; indeed, the patients show an increased sensitivity to feedback. These results indicate that the cerebellum forms a crucial part of the feedforward control system for speech but is not essential for online, feedback control.

A Design of Repetitive Control Systems – high Accuracy Servomechanisms for Periodic Inputs

Feedforward (FF) control uses a priori knowledge about a given system and its disturbances to influence the system’s behavior in a pre-defined way. However, unlike feedback (FB) control, it does not adjust the control signal (or manipulated variable) in response to how the system actually reacts. In other words, FF control is proactive while FB control is reactive. Model-inversion-based FF (MIBFF) control is a specific type of FF control where the control variable is determined by inverting a model of the system to be controlled. It is very popular for its use in output tracking control problems, where the goal is to force the system’s output to follow a desired trajectory. Output tracking is critical in several different applications, e.g., in manufacturing, robotics, automotive, aerospace, and is typically achieved using a combination of FF and FB control. As motivating examples, consider MIBFF in ultra-precise wafer scanners used in photolithography (see Sidebar S1) and in desktop 3D printing (see Sidebar S2). As these motivating examples illustrate, non-minimum phase (NMP) zeros often arise in practical engineering applications due to non-collocated sensors and actuators, fast sampling, etc. MIBFF for systems with NMP zeros is arguably the most important (and certainly the most researched) issue related to MIBFF.

Interval Criterion of Robust Stability for Nonlinear System and Its Application to Flight Control

This paper discusses the problem of delay-dependent robust control for uncertain singular systems with time-delay. Firstly, based on Jensen inequality formula and Lyapunov stability theory, the sufficient condition is established for delay-dependent singular system with time-delay, which guaranteed the nominal system is regular, impulse free and stable. Secondly, based on the sufficient condition, the design method of robust state feedback controller for delay-dependent uncertain singular systems with time-delay, which guarantees that, for all admissible uncertainties, the resultant closed-loop system is regular, impulse free, and stable. All the obtained results are delay-dependent and formulated by strict LMI involving no decomposition of the system matrices. Finally, numerical examples are given to illustrate the less conservativeness and effectiveness of the method.

Robust observer-based passive control for uncertain singular time-delay systems subject to actuator saturation

Leader–follower output consensus of multiagent systems over finite fields

Many manufacturing machines must execute motions as quickly as possible to achieve profitable high-volume production. Most of them exhibit some flexibility, which makes the settling time longer and controller design difficult. This paper develops a control strategy that combines feedforward and feedback control with command shaping for systems with collocated actuator and sensor. First, a feedback controller is designed to increase damping and eliminate steady-state error. Next, an appropriate reference profile is generated using command-shaping techniques to ensure fast point-to-point motions with minimum residual vibration. Finally, a feedforward controller is designed to speed up the transient response. The proposed proportional-integral-derivative (PID) controller design ensures that two important resonant frequencies nearly match, making the design of the input commands much simpler. The resulting control strategy is successfully demonstrated for a generic dimensionless system that incorporates some modeling errors to assess robustness.

To achieve proper operation of an online static uninterruptible power supply (UPS) system, feedforward and feedback (FF/FB) controls are introduced. Feedforward control is applied to reduce the low order harmonics in the output voltage due to the ripples included in the input DC voltage to the UPS inverter resulting from the controlled rectifier, while feedback control is applied mainly for stabilizing the output voltage. In this paper, a feedforward technique is selected that was found to give free ripple output, and two types of feedback techiques are compared and the most suitable one is considered. The paper gives the modeling and simulation results of the whole system, that compare the performance without and with FF/FB under different steady state and transient conditions.