Svante Gunnarsson

Iterative feedback tuning: theory and applications

We have examined an optimization approach to iterative control design. The important ingredient is that the gradient of the design criterion is computed from measured closed loop data. The approach is thus not model-based. The scheme converges to a stationary point of the design criterion under the assumption of boundedness of the signals in the loop. From a practical viewpoint, the scheme offers several advantages. It is straightforward to apply. It is possible to control the rate of change of the controller in each iteration. The objective can be manipulated between iterations in order to tighten or loosen performance requirements. Certain frequency regions can be emphasized if desired. This direct optimal tuning algorithm is particularly well suited for the tuning of the basic control loops in the process industry, which are typically PID loops. These primary loops are often very badly tuned, making the application of more advanced (for example, multivariable) techniques rather useless. A first requirement in the successful application of advanced control techniques is that the primary loops be tuned properly. This new technique appears to be a very practical way of doing this, with an almost automatic procedure.

Adaptation and tracking in system identification—a survey

To track the time-varying dynamics of a system or the time-varying properties of a signal is a fundamental problem in control and signal processing. Many approaches to derive such adaptation algorithms and to analyse their behaviour have been taken. This article gives a survey of basic techniques to derive and analyse algorithms for tracking time-varying systems. Special attention is paid to the study of how different assumptions about the true systems variations affect the algorithm. Several explicit and semi-explicit expressions for the mean square error are derived, which clearly demonstrate the character of the trade-off between tracking ability and noise rejection.

A convergent iterative restricted complexity control design scheme

In this contribution we propose an optimization approach to the design of a restricted complexity controller. The design criterion is of LQG type containing two terms. The first term is the quadratic norm of the error between the output of the true closed loop and a desired response. The second term is the quadratic norm of the input signal. It is shown that the minimization of this criterion does not require a model of the system. Closed loop experimental data can be used instead. The result is an iterative scheme of closed loop experiments and controller updates which converges to a local minimum of the design criterion under the condition of bounded signals.<<ETX>>

Brief On the design of ILC algorithms using optimization

Iterative learning control (ILC) based on minimization of a quadratic criterion in the control error and the input signal is considered. The focus is on the frequency domain properties of the algorithm, and how it is able to handle non-minimum phase systems. Experiments carried out on a commercial industrial robot are also presented.

Time and frequency domain convergence properties in iterative learning control

The convergence properties of iterative learning control (ILC) algorithms are considered. The analysis is carried out in a framework using linear iterative systems, which enables several results from the theory of linear systems to be applied. This makes it possible to analyse both first-order and high-order ILC algorithms in both the time and frequency domains. The time and frequency domain results can also be tied together in a clear way. Results are also given for the iterationvariant case, i.e. when the dynamics of the system to be controlled or the ILC algorithm itself changes from iteration to iteration.

Closed-Loop Identification of an Industrial Robot Containing Flexibilities

Closed-loop identification of an industrial robot of the type ABB IRB 1400 is considered. Data are collected when the robot is subject to feedback control and moving around axis one. Both black-box and physically parameterized models are identified. A main purpose is to model the mechanical flexibilities. It is found that a model consisting of three-masses connected by springs and dampers gives a good description of the dynamics of the robot.

Experimental comparison of some classical iterative learning control algorithms

This paper gives an overview of classical iterative learning control algorithms. The presented algorithms are also evaluated on a commercial industrial robot from ABB. The paper covers implicit to explicit model-based algorithms. The result from the evaluation of the algorithms is that performance can be achieved by having more system knowledge.

Model Free Tuning of a Robust Regulator for a Flexible Transmission System

Recently, a data-driven model-free iterative control design method has been proposed [Hjalmarsson et al., Proc. 33rd IEEE CDC, Orlando, FL, 1994, 1735–1740]. This design method works directly with closed loop data from the plant and iteratively improves the pelformance. This contribution reports a simulation study of this method when applied to a flexible transmission system. The system is characterised by load dependent dynamics and certain performance specifications have to be satisfied for three different load cases. These specifications cannot be translated into a specific control criterion a priori. However, by adaptively changing the design criterion it is shown that it is possible to tune the criterion so as to eventually obtain the desired closed loop performance for all three load cases with the same controller. The new concepts of synthetic noise and time delays are shown to be valuable tools when tuning the criterion.

Frequency domain tracking characteristics of adaptive algorithms

The problem of tracking time-varying linear systems is discussed. The focus is on the model quality in terms of the mean square error (MSE) between the true (momentary) transfer function and the estimated one. This MSE is thus a function of frequency. The exact expression for the MSE is complicated, but simple expressions that are asymptotic in the model order are developed for model structures of finite impulse response (FIR) character. Simulations verify that these simple expressions are quite reliable and insightful even for moderate model orders. Expressions are developed for three basic adaptation algorithms (recursive identification algorithms), viz. the least-mean-squares algorithm, the recursive least-squares algorithm with exponential forgetting, and a tracking algorithm based on the Kalman filter. The results apply both to slowly time-varying systems and to the model recovery after an abrupt change in the system dynamics. >

Disturbance Aspects of Iterative Learning Control

Disturbance aspects of iterative learning control (ILC) are considered. By using a linear framework it is possible to investigate the influence of the disturbances in the frequency domain. The effects of the design filters in the ILC algorithm on the disturbance properties can then be analyzed. The analysis is supported by simulations and experiments.