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.

Repetitive Control for an Electrostatic Microbridge Actuator

2005 ◽  
Author(s):  
Haiyu Zhao ◽  
Christopher D. Rahn ◽  
Huseyin Canbolat
Keyword(s):  
Control Algorithm ◽  
Repetitive Control ◽  
Squeeze Film ◽  
Transverse Displacement ◽  
Residual Vibration ◽  
Rf Switches ◽  
Squeeze Film Damping ◽  
High Bandwidth ◽  
Offline Processing ◽  
Measured Response

Electrostatic microactuators are used extensively in MEMS sensors, RF switches, and microfluidic pumps. Due to high bandwidth operation, however, reduction of residual vibration using feedback control is diffcult to implement. This paper designs, proves stability, and simulates a feedforward repetitive controller for an electrostatic microbridge. Squeeze film damping ensures boundedness of the distributed transverse displacement. Offline processing using repetitive control algorithm updates a waveform generator’s parameters based on measured response to reduce errors between the desired and actual displacement distribution. Simulations show a 36% reduction in midspan overshoot.

An Optimality-Based Repetitive Control Algorithm for Discrete-Time Systems

2008 ◽  
Vol 55 (1) ◽  
pp. 412-423 ◽  
Author(s):  
C.T. Freeman ◽  
P.L. Lewin ◽  
E. Rogers ◽  
D.H. Owens ◽  
J. Hatonen
Keyword(s):  
Discrete Time ◽  
Control Algorithm ◽  
Repetitive Control ◽  
Discrete Time Systems ◽  
Time Systems

ADJOINT MULTIVARIABLE REPETITIVE CONTROL ALGORITHM FOR ACTIVE CONTROL OF VIBRATION

2007 ◽  
Vol 40 (14) ◽  
pp. 228-233
Author(s):  
J. Hätönen ◽  
F. Zhang ◽  
S. Daley ◽  
D.H. Owens
Keyword(s):  
Active Control ◽  
Control Algorithm ◽  
Repetitive Control

The Simulation Research of the Five Level Photovoltaic Grid-Connected Inverter Based on Repetitive and PI Control

2012 ◽  
Vol 608-609 ◽  
pp. 34-37
Author(s):  
Jie Liu ◽  
Song Zhen Yuan
Keyword(s):  
Control Algorithm ◽  
Repetitive Control ◽  
Harmonic Distortion ◽  
Pi Control ◽  
Simulation Research ◽  
Compound Control ◽  
Control Scheme ◽  
Switch Type ◽  
Real Time Tracking ◽  
Grid Connected Inverter

Introducing a kind of bidirectional switch type five level inverter, and put forward the compound control scheme which repetitive control and PI adjustment are combined. And a detailed analysis of the repetitive control algorithm. Through the Matlab/simulink to simulate under different control modes. The results show that, the five-livel inverter which using repetitive PI control, its output grid-connected current waveform stability, harmonic distortion rate is small, and can real-time tracking the network voltage.

Functional Persistence of Excitation and Observability for Learning Control Systems

1992 ◽  
Vol 114 (3) ◽  
pp. 500-507 ◽  
Author(s):  
J. B. Moore ◽  
R. Horowitz ◽  
W. Messner
Keyword(s):  
Integral Operator ◽  
Control Systems ◽  
Learning Process ◽  
Influence Function ◽  
Adaptive Systems ◽  
Control Algorithm ◽  
Repetitive Control ◽  
Natural Generalization ◽  
Function Learning ◽  
Finite Dimensional

Adaptive systems involving function learning can be formulated in terms of integral equations of the first kind, possibly with separable, finite-dimensional kernels. The learning process involves estimating the influence functions (Messner et al., 1989). To achieve convergence of the influence function estimates and exponentially stability, it is important to have persistence of excitation in the training tasks. This paper develops the concept of functional persistence of excitation (PE), and the associated concept of functional uniform complete observability (UCO). Relevant PE and UCO properties for linear systems are developed. For example, a key result is that uniform complete observability in this context is maintained under bounded integral operator output injection—a natural generalization of the corresponding finite dimensional result. This paper also demonstrates the application of the theory to linear error equations associated with a repetitive control algorithm.

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