scholarly journals Linear Optimal Multi-periodic Repetitive Control - A Low Order Controller Scheme

2011 ◽  
Vol 2 (1) ◽  
pp. 1-16
Author(s):  
Youde HAN ◽  
David H. OWENS ◽  
Bing CHU
Keyword(s):  
Closed Loop ◽  
Repetitive Control ◽  
Reference Signal ◽  
Experimental Tests ◽  
Closed Loop System ◽  
Computational Problem ◽  
Mass Damper ◽  
Periodic Components ◽  
Time Linear ◽  
Repetitive Controller

This article proposes a new method for treating the computational problem in discrete time linear multi-periodic repetitive control systems, where the reference signal includes several periodic components with already known periods.  As periods get large, the computational problem becomes prominent. This work thus investigates the frequency contents of reference signals, where the order of original repetitive controller is lowered by considering only a reduced number of poles, namely, the most important contributors to the total energy of the multi-periodic reference signal. A lower order multi-periodic repetitive controller is designed which assures BIBO stability of the closed-loop system, and approximate tracking is achieved. Finally, experimental tests on a non-minimum phase spring mass damper system demonstrate the effectiveness of this new controller.

Positive Finite-Time Stabilization for Discrete-Time Linear Systems

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
Wenping Xue ◽  
Kangji Li
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Finite Time ◽  
State Feedback ◽  
Closed Loop ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Initial State ◽  
Finite Time Stability ◽  
Time Linear

In this paper, a new finite-time stability (FTS) concept, which is defined as positive FTS (PFTS), is introduced into discrete-time linear systems. Differently from previous FTS-related papers, the initial state as well as the state trajectory is required to be in the non-negative orthant of the Euclidean space. Some test criteria are established for the PFTS of the unforced system. Then, a sufficient condition is proposed for the design of a state feedback controller such that the closed-loop system is positively finite-time stable. This condition is provided in terms of a series of linear matrix inequalities (LMIs) with some equality constraints. Moreover, the requirement of non-negativity of the controller is considered. Finally, two examples are presented to illustrate the developed theory.

Repetitive Control for Rejection of Periodic Multiplicative Disturbances and Adaptive Identification of the Unknown Period

2004 ◽  
Author(s):  
Sandipan Mishra ◽  
Manabu Yamada ◽  
Masayoshi Tomizuka
Keyword(s):  
Control Algorithm ◽  
Closed Loop ◽  
Design Method ◽  
Repetitive Control ◽  
Adaptive Controller ◽  
Least Mean Square ◽  
Closed Loop System ◽  
Internal Model Principle ◽  
Periodic Disturbances ◽  
The Stability

Repetitive control has been used extensively for rejection of periodic disturbances, in systems that have to follow periodic trajectories. To date, most repetitive controllers have focused on rejection of additive periodic disturbances. This paper suggests the use of a repetitive control algorithm for rejection of periodic multiplicative disturbances. The first result is a simple design method of a new controller to reject the multiplicative disturbance effectively, provided that the period of the disturbance is known. This controller is based on the internal model principle and the design method consists of a simple norm condition. It is shown that this repetitive-type controller can reject the disturbance. The second result is an extension of the first one to the case that the period of the disturbance is unknown. A period estimator is added to the control system to identify the period of the multiplicative disturbance. The algorithm, consisting of an adaptive recursive least mean square method, is simple. It is shown that this adaptive controller can reject the disturbance with an uncertain period and guarantee the stability of the adaptive closed-loop system including the period estimator.

Grinding Process Instability

1969 ◽  
Vol 91 (3) ◽  
pp. 597-606 ◽  
Author(s):  
B. Bartalucci ◽  
G. G. Lisini
Keyword(s):  
Closed Loop ◽  
Experimental Tests ◽  
Grinding Wheel ◽  
Closed Loop System ◽  
Regenerative Effect ◽  
Machine Tool Structure ◽  
Chatter Vibrations ◽  
Grinding Machine ◽  
Theoretical Results ◽  
Good Agreement

The paper describes a theoretical investigation on chatter vibrations of cylindrical plunge grinding. The system grinding machine-grinding wheel-workpiece is represented as a closed loop system with two feedback paths, one due to the machine tool structure, the other to the regenerative effect of the grinding wheel. Theoretical results are in good agreement with the experimental tests.

scholarly journals Robust aperiodic-disturbance rejection in an uncertain modified repetitive-control system

2016 ◽  
Vol 26 (2) ◽  
pp. 285-295 ◽  
Author(s):  
Lan Zhou ◽  
Jinhua She ◽  
Chaoyi Li ◽  
Changzhong Pan
Keyword(s):  
Control System ◽  
Output Feedback ◽  
Disturbance Rejection ◽  
Closed Loop ◽  
Repetitive Control ◽  
Linear Matrix ◽  
Time Varying ◽  
Dimensional Model ◽  
Closed Loop System ◽  
Output Feedback Controller

Abstract This paper concerns the problem of designing an EID-based robust output-feedback modified repetitive-control system (ROFMRCS) that provides satisfactory aperiodic-disturbance rejection performance for a class of plants with time-varying structured uncertainties. An equivalent-input-disturbance (EID) estimator is added to the ROFMRCS that estimates the influences of all types of disturbances and compensates them. A continuous-discrete two-dimensional model is built to describe the EID-based ROFMRCS that accurately presents the features of repetitive control, thereby enabling the control and learning actions to be preferentially adjusted. A robust stability condition for the closed-loop system is given in terms of a linear matrix inequality. It yields the parameters of the repetitive controller, the output-feedback controller, and the EID-estimator. Finally, a numerical example demonstrates the validity of the method.

Iterative Generation of Virtual Reference for a Manipulator

Robotica ◽  
1991 ◽  
Vol 9 (1) ◽  
pp. 71-80 ◽  
Author(s):  
M. Yamakita ◽  
K. Furuta
Keyword(s):  
Functional Analysis ◽  
Closed Loop ◽  
Reference Signal ◽  
Dual System ◽  
Loop System ◽  
Experimental Results ◽  
Closed Loop System ◽  
Virtual Reference ◽  
Local Feedback ◽  
The Difference

SUMMARYVirtual reference is defined as the signal for a closed-loop System so that the response tracks the desired path perfectly. It is proposed to obtain a virtual reference signal suitable for a manipulator to track a predetermined trajectory using repetitive operations. Thus the algorithm ensures that the difference between the desired and the manipulator trajectories will become negligible as the number of operations approaches infinity if the manipulator is compensated for properly by local feedback. This algorithm uses a dual System to recursively improve the reference signal. Such a System has the advantage of being simple to design. The derivation of this algorithm is based on functional analysis. The effectiveness is confirmed by two experimental results.

scholarly journals Padé-Approximation-Based Preview Repetitive Control for Continuous-Time Linear Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Jia-Yu Zhao ◽  
Zhao-Hong Wang ◽  
Jian-De Yan ◽  
Yong-Hong Lan
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Padé Approximation ◽  
Repetitive Control ◽  
State Equation ◽  
The State ◽  
Space Representation ◽  
Pade Approximation ◽  
Time Linear ◽  
Repetitive Controller

This paper concerns a Padé-approximation-based preview repetitive control (PRC) scheme for continuous-time linear systems. Firstly, the state space representation of the repetitive controller is transformed into a nondelayed one by Padé approximation. Then, an augmented dynamic system is constructed by using the nominal state equation with the error system and the state equation of a repetitive controller. Next, by using optimal control theory, a Padé-approximation-based PRC law is obtained. It consists of state feedback, error integral compensation, output integral of repetitive controller, and preview compensation. Finally, the effectiveness of the method is verified by a numerical simulation.

scholarly journals Design of a Backstepping Tracking Controller for a Class of Linear Systems with Actuator Delay

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Yonglong Liao ◽  
Fucheng Liao
Keyword(s):  
Linear Systems ◽  
Tracking Error ◽  
Reference Signal ◽  
Coupled System ◽  
Closed Loop System ◽  
Hyperbolic Pde ◽  
System A ◽  
Input Control ◽  
Tracking Controller ◽  
Time Linear

This paper presents a method for designing a backstepping tracking controller for a class of continuous-time linear systems with actuator delay subject to a reference signal. The actuator delay can be modeled by a first-order hyperbolic PDE, and then a PDE-ODE coupled system is obtained. By applying the backstepping transformation to the coupled system, a feedback controller that includes the state of the system, the integral of the input control, and the integral of the tracking error is derived. We show that the closed-loop system is asymptotically stable at the equilibrium point and achieves complete regulation under the stabilizability assumption. The designs in this paper are illustrated with numerical simulations.

scholarly journals State-Estimator-Based Asynchronous Repetitive Control of Discrete-Time Markovian Switching Systems

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13 ◽  
Author(s):  
Xinghua Liu ◽  
Guoqi Ma ◽  
Prabhakar R. Pagilla ◽  
Shuzhi Sam Ge
Keyword(s):  
Discrete Time ◽  
Closed Loop ◽  
Repetitive Control ◽  
Sufficient Conditions ◽  
Switched System ◽  
Markovian Switching ◽  
Switching Systems ◽  
Mean Square ◽  
Markovian Switching Systems ◽  
Repetitive Controller

This paper investigates the problem of asynchronous repetitive control for a class of discrete-time Markovian switching systems. The control goal is to track a given periodic reference without steady-state error. To achieve this goal, an asynchronous repetitive controller that renders the overall closed-loop switched system mean square stable is proposed. To reflect realistic scenarios, the proposed approach does not assume that the system modes are available synchronously to the controller but instead designs a detector that provides estimated values of the system modes to the controller. Based on a detected-mode-dependent estimator, the plant and asynchronous repetitive controller are formulated as a closed-loop stochastic system. By utilizing tools from stochastic Lyapunov–Krasovskii stability theory, we develop sufficient conditions in terms of linear matrix inequalities (LMIs) such that the closed-loop system is mean square stable and also simultaneously establish a synthesis procedure for obtaining the gain matrices. We provide numerical simulations on an electrical circuit switched system to illustrate the approach.

H ∞ and Passivity Control via Static and Integral Output Feedback for Systems With Input Delay

2011 ◽  
Vol 134 (2) ◽  
Author(s):  
Baozhu Du ◽  
James Lam ◽  
Zhan Shu
Keyword(s):  
Output Feedback ◽  
Closed Loop ◽  
Computational Algorithm ◽  
Input Delay ◽  
Closed Loop System ◽  
Feedback Controllers ◽  
New Approach ◽  
Delay Partitioning ◽  
Monotonic Property ◽  
Time Linear

This paper addresses a new approach on H∞ and passivity control via static and integral output feedback controllers of continuous-time linear systems with input delay. By combining an augmentation approach and the delay partitioning technique, criteria for static and integral output feedback H∞/passivity stabilizability are proposed for the closed-loop system in terms of matrix inequalities. These new characterizations possess a special monotonic property, which underpin the convergence of a linearized iterative computational algorithm. The effectiveness and merits of the proposed approach are illustrated through numerical examples.

A Digital Segmented Repetitive Control Algorithm

1994 ◽  
Vol 116 (4) ◽  
pp. 577-582 ◽  
Author(s):  
Jwusheng Hu ◽  
Masayoshi Tomizuka
Keyword(s):  
Internal Model ◽  
Control Algorithm ◽  
Repetitive Control ◽  
Reference Signal ◽  
Control Law ◽  
Memory Space ◽  
Periodic Disturbance ◽  
Internal Model Principle ◽  
Control Actions ◽  
Repetitive Controller

This paper presents the structure and analysis of the segmented discrete-time repetitive controller. The repetitive controller is designed to reject periodic disturbance and/or track periodic reference signal with known period. Resulted from the Internal Model Principle, the repetitive control law is applied to the entire control path. However, when crucial segments within a control path are of concern, the segmented repetitive control law, which applies control actions only to those segments, can be utilized to save the memory space. It is shown that such a segmented repetitive control system is stable if the original nonsegmented one is stable.

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