Gunnar Hillerström

Adaptive suppression of vibrations - a repetitive control approach

The aim of this paper is to present an adaptive solution to suppression of vibrations. Adaptation is appropriate whenever the fundamental frequency is unknown or drifting, e.g., when the vibration is caused by a rotational machine with unknown rotational speed. The approach presented here has its roots in repetitive control based on models of isolated frequencies rather than the commonly used delay model. The relationship between different modeled frequencies is fixed by the model structure, and the fundamental frequency is obtained by gradient descent or Newtons method. To show the feasibility of this approach, it was used to reduce the vibrations on a lever that were caused by a motor with imbalance in its rotation. As an actuator, a standard loudspeaker was used, and the vibration was sensed by an accelerometer.

Repetitive Control Theory and Applications - A Survey

Abstract The aim of this paper is to present repetitive control, controllers for rejecting periodic disturbances or tracking periodic reference signals, This survey covers both continuous and discrete time theory, together with a number of applications

Rejection of periodic disturbances with unknown period-a frequency domain approach

A self-tuning discrete time repetitive controller comprising a gradient descent disturbance model estimation and a pseudo feedforward controller is investigated. To illustrate the feasibility of the approach considered an example is given for rejecting a periodic disturbance acting on a nonminimum-phase plant.

Repetitive control using low order models

In repetitive control based on the internal model principle of Francis and Wonham (1976) much interest has been focused around the model comprising a time delay with a memoryless positive feedback around it. A definite merit of this model is that, when used in the closed loop, it will generate an arbitrary periodic signal. In discrete-time the model order increases proportionally to the rise in sampling rate, giving a high order model. The input (disturbance or reference) signal may however be concentrated to some frequencies rather than the whole band up to the Nyquist frequency. Then the model is too large in the sense that it models frequencies that are not present in the input. The inactive part of the model can produce oscillations in the closed loop. Oscillations can be reduced by introducing a lowpass filter (or Q-filter) in the feedback path of the model, but thereby the asymptotic zero error property is lost. A lower order model is shown to overcome this problem and feasibility illustrated by a simulation example.

Robustness properties of repetitive controllers

Stability robustness properties of sampled data repetitive control systems are examined. Due to the infinite loop gain at periodic frequencies originating from the included internal model (Internal Model Principle), repetitive systems are, if properly designed, not very sensitive towards possibly time-varying gains. Uncertainty in plant delay is, however, a problem. Controller action timing becomes more or less out of order and may result in severe performance degradation, depending on model type and the number of frequencies included in the design. With a Linear Time-Invariant (LTI) controller comprising the commonly used time delay internal model, the closed loop system is stable for nominal time delay plus/minus at most one sampling interval. A controller based on a reduced order model, perhaps not modelling all harmonics, is utilized to enhance robustness properties. Simulation runs with different controllers show how different models work in the closed loop, and also that synchronization in time is of utmost importance in order to utilize the delay internal model.

On perfect disturbance rejection

A new observer-based approach to perfect disturbance rejection in linear continuous systems is introduced. A technique of continuous deadbeat observation is exploited to estimate the disturbance signal described by a known dynamic model. A realization condition in the form of linear algebraic equations is derived. It is shown that the introduced disturbance rejection scheme can be used in combination with any conventional control technique such as stabilization or servo control.<<ETX>>

Adaptive suppression of vibrations-a repetitive control approach

The aim of this paper is to present an adaptive solution to suppression of vibrations. Adaptation is appropriate whenever the fundamental frequency is unknown or drifting, e.g. when the vibration is caused by a rotational machine with unknown rotational speed. The approach presented here has its roots in repetitive control based on models of isolated frequencies rather than the commonly used delay model. The relationship between different modeled frequencies is fixed by the model structure, and the fundamental frequency is obtained by gradient descent. To show the feasibility of this approach, it was used to reduce vibrations on a lever that were caused by a motor with imbalance in its rotation. As actuator, a standard loudspeaker was used, and the vibration was sensed by an accelerometer.

Adaptive Rejection of Periodic Disturbances With Unknown Period

A disturbance cancellation extension by means of Youla parametrization to a stabilizing nominal controller is investigated. In the case of a known disturbance model, disturbance frequencies or period time, it may be implemented directly as an add-on device to the existing control system. The nominal control system may be designed without consideration of the deterministic disturbances. This way it may suffice with a PID controller. It may also be a more complex one e.g., designed to obtain certain robustness properties. For known relation between the disturbance frequencies (one or more periodic signals) but unknown fundamental frequency, a frequency shaped disturbance model estimation scheme is utilized. This makes it possible to e.g., adapt the disturbance model to minimize the error directly with respect to the output. For periodic disturbances the scheme implements a self-tuning discrete time repetitive controller. To illustrate the feasibility of the approach taken it is used for rejecting a periodic disturbance acting on a nonminimum-phase plant.

Periodic Disturbance Rejection: A Neural Network Approach

A feedback controller comprising a Luenberger observer and a Time-Delay Feedforward Neural Network is shown to possess a periodic disturbance rejection property for linear multivariable dynamic systems. Stability of the resulting closed-loop system is proved and the controller performance is exemplified by a simulation example.

EXTERNAL MODEL CONTROL OF A PERISTALTIC PUMP

Abstract An observer-based approach to perfect disturbance rejection in linear continuous systems with delayed control is presented and exemplified by an application to a peristaltic pump. Disturbance rejection properties of the Smith Predictor are studied. A recently developed technique of continuous deadbeat observation is exploited to predict the disturbance signal which is described by a known dynamic model. It is shown that under certain algebraic conditions a disturbance estimate based control law is able to provide a disturbance-free output signal. The disturbance rejection scheme can be used in combination with any conventional control technique such as stabilizing or servo controller.