(150d) An Novel Algorithm For Enhanced Convergence Of The Iterative Feedback Tuning Method

Optimal process control requires a controller synthesis based on a performance criterion. In order to minimize the criterion, a model for the process is normally required. Iterative Feedback Tuning is a methodology to tune controller parameters given a performance criterion, with penalty on the controlled variable deviations from a desired trajectory and penalty on the control variable itself or it's increment. Iterative Feedback Tuning does not rely on a model of the process. The methodology has been extended and tested for a number of applications since first published in 1994 [1,2]. The method minimizes the performance criterion using a gradient based search method. The gradient is estimated through three closed loop experiments, designed to give a consistent estimate. The first experiment provides input/output information of the system and the two remaining experiments are used to form an estimate of the gradients of the input and output with respect to the controller parameters. Using closed loop data is an advantage, not only with respect to the operation of the process, but it is also desired from a control design point of view, since it is the loop performance that is subject to optimization. The advantage of the Iterative Feedback Tuning relies on the ability to achieve the desired performance in few iterations. Plant experiments are costly and product produced under an experiment may have a reduced quality since the process is perturbed from it's normal point of operation. Tuning controllers for step changes in the operation with Iterative Feedback Tuning is effective since the step in the reference ensures data with a high information content. In tuning for noise rejection only, a slow convergence of the method may be observed since the noise is the only perturbation of the process. In this paper it is proposed to use designed input perturbations of the reference signal to the first of the three experiments in the Iterative feedback Tuning algorithm. That will increase the information content in the data collected from the experiments and lead to a faster decrease of the cost function, hence a reduced number of iterations and experiments. The input design problem will include constraints on the predicted cost or on other critical variables for that particular experiment in order to guarantee maximal information in the data subject to constrains on the operation. In order to solve the design problem for input perturbation in each iteration of the Iterative Feedback Tuning method, a model estimate of the process or the loop is necessary in order to minimize the use of further plant experiments. Given a plant model estimate, nominal stability of any new controller from the Iterative Feedback Tuning iterations can be insured before implementation. Further more a process model estimate can be utilized in a line search algorithm in the controller parameter update to yield even faster convergence. Iterative Feedback Tuning as a data driven optimization method for control loop performance with optimal input perturbations and a line search optimization based on a model estimate, is proposed as an efficient methodology for controller tuning. Since nominal stability is insured in each iteration the method can be implemented online in order to conduct a scheduled tuning of the loop. The convergence and applicability of the proposed algorithm containing extensions to classic Iterative Feedback Tuning method is illustrated through simulations.

References:

1. Håkan Hjalmarsson, Svante Gunnarsson, and Michel Gevers. A convergent iterative restricted complexity control design scheme. In Proceedings of the 33rd IEEE Conference on Decision and Control, volume 2, 1735 --1740, 1994.

2. Håkan Hjalmarsson. Iterative feedback tuning - an overview. International journal of adaptive control and signal processing, 16:373--395, 2002.