Repetitive control in the presence of multiple periodic disturbances

1992 ◽  
Author(s):  
EDWARD SOLCZ ◽  
RICHARD LONGMAN
Keyword(s):  
Repetitive Control ◽  
Periodic Disturbances

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.

Prototype Angle Domain Repetitive Control: Design and Robustness

2015 ◽  
Author(s):  
Perry Y. Li
Keyword(s):  
Design Methodology ◽  
Repetitive Control ◽  
Control Design ◽  
Periodic Case ◽  
Periodic Disturbances ◽  
Compensator Design ◽  
The Stability ◽  
Control Methodology ◽  
Time Periodic ◽  
Model Approach

Angle-domain repetitive disturbances refer to disturbances that are periodic in a generic angle variable which is monotonically increasing with time but not uniformly. This paper extends the classical prototype repetitive control methodology for time periodic disturbances to this situation. Instead of using an internal model approach to derive the control, an affine parameterization approach is adopted which reduces the control design methodology to one of estimating and canceling the disturbance. While the resulting control architectures are similar to the classical time-domain periodic case, the stability conditions are different and depend on the choice of signal norms. Compensator design for non-minimum phase plants also need to be modified. Robustness is also considered in the L2 setting and an affine Q-filter concept is introduced to achieve robust stability.

Asymptotic Rejection of Periodic Disturbances With Fixed or Varying Period

2000 ◽  
Vol 123 (3) ◽  
pp. 324-329 ◽  
Author(s):  
Shiang-Hwua Yu ◽  
Jwu-Sheng Hu
Keyword(s):  
Design Method ◽  
Repetitive Control ◽  
Sampling Interval ◽  
Control Law ◽  
Integer Multiple ◽  
Tuning Method ◽  
Periodic Disturbances ◽  
Optimal Delay ◽  
Close Relationship ◽  
Tuning Methods

A constructive derivation of repetitive control is obtained, through attempting to derive a control law for asymptotic rejection of periodic disturbances. This derivation not only reveals a close relationship between iterative operator inversion and repetitive control, but also suggests a unified design method for a learning control algorithm. Also, based on the observation, digital repetitive control can be generalized to reject periodic disturbance whose period is not exactly an integer multiple of the sampling interval. This study introduces a delay filter in the digital repetitive control law, which optimally interpolates the signal between samples, thus effectively reconstructing the signal of the previous period and making the learning process of repetitive control successful. The proposed optimal delay filter can be updated easily according to different signal periods. Thus it is specifically suitable for on-line tuning when the signal period is changing. Compared with the available tuning methods, the proposed tuning method has excellent steady-state performance while maintaining fast transient and system robustness. The simulations on active noise cancellation within a duct confirm the superiority of this tuning method.

Spatially Periodic Disturbance Rejection With Spatially Sampled Robust Repetitive Control

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
Cheng-Lun Chen ◽  
George T.-C. Chiu
Keyword(s):  
Actuator Saturation ◽  
Linear Time ◽  
Angular Displacement ◽  
Repetitive Control ◽  
Optical Encoder ◽  
Input Nonlinearity ◽  
Linear Time Invariant ◽  
Periodic Disturbances ◽  
Reference Signals ◽  
Spatially Periodic

Repetitive controllers have been shown to be effective for tracking periodic reference commands or for rejecting periodic disturbances. Typical repetitive controllers are synthesized in temporal domain where the periods of the reference or disturbance signals are assumed to be known and stationary. For periodic references and disturbances with varying periods, researchers usually resort to adaptive and robust control approaches. For rotational motion systems where the disturbances or reference signals are spatially periodic (i.e., periodic with respect to angular displacement), the temporal period of the disturbance and reference signals will be inversely proportional to the rotational speed and vary accordingly. Motivating by reducing halftone banding for laser printers, we propose a design framework for synthesizing spatially sampled repetitive controller by reformulating a linear time-invariant system subject to spatially periodic disturbances using angular displacement as the independent variable. The resulting nonlinear system can be represented as a quasi-linear parameter-varying (quasi-LPV) system with the angular velocity as one of the varying state-dependent parameters. An LPV self-gain–scheduling controller that includes a spatially sampled repetitive control can be designed to take into consideration bounded model uncertainty and input nonlinearity, such as actuator saturation. Using the signal from an optical encoder pulse as a triggering interrupt, experimental results verified the effectiveness of the proposed approach in rejecting spatially periodic disturbances that cannot be compensated with fixed period temporal repetitive controllers.

Robust Repetitive Control System With On-Line Identification of the Period of Periodic Disturbances

2004 ◽  
Author(s):  
Manabu Yamada ◽  
Masayoshi Tomizuka
Keyword(s):  
Control System ◽  
Tracking Error ◽  
Repetitive Control ◽  
Lower And Upper Bounds ◽  
L1 Norm ◽  
Periodic Disturbances ◽  
Norm Minimization ◽  
Line Identification ◽  
On Line ◽  
Unknown Period

Repetitive control system is a servo system that achieves zero steady-state tracking error for any periodic desired outputs and any periodic disturbance inputs with a known period. This paper deals with a repetitive control problem for the case where the plant has a norm-bounded uncertainty and the period of periodic disturbances is unknown but is within known lower and upper bounds. A new robust repetitive controller is proposed not only to guarantee the robust stability against the uncertainty but also to estimate the unknown period and to reject any periodic disturbances with the period. It is shown that the design problem is reduced to a simple and feasible l1 norm minimization problem. The controller can be obtained easily by solving a simple linear programming problem. Simulation results show the effectiveness of the proposed controller for rejection of periodic disturbances with uncertain periods.

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