Elsevier

Journal of Process Control

Volume 14, Issue 6, September 2004, Pages 603-615
Journal of Process Control

Indirect approach to continuous time system identification of food extruder

https://doi.org/10.1016/j.jprocont.2004.01.004Get rights and content

Abstract

A three-stage approach to system identification in the continuous time is presented which is appropriate for day-to-day application by plant engineers in the process industry. The three stages are: data acquisition using relay feedback; non-parametric identification of the system step response; and parametric model fitting of the identified step response. The method is evaluated on a pilot-scale food-cooking extruder.

Introduction

The food-cooking extruder is an important processing unit within the food manufacturing industry. However, product quality control is often open loop and thus significant improvements to food quality and throughput can be expected by the use of closed-loop quality control. It has been shown previously that model-based predictive control can be successfully applied to this problem (for example [1]). It is known that to design such a control system, a suitable model of the food-cooking extruder is required. Unfortunately, because the extrusion cooking process has strong interactions between mass, energy and momentum transfer, coupled with complex physico-chemical transformations, it is hard to derive a mathematical model from first principles. Moreover, such models can be overly complex for the purposes of model-based predictive control. For these reasons, the use of system identification to deduce a suitable model from input–output data is a more practical approach to building mathematical models of the food-cooking extruder suitable for model-based predictive control.

It is our experience that whilst process engineers in the food industry have a good intuitive grasp of the processes based on their engineering knowledge and experience, they have little experience of system identification techniques. For this reason, system identification will only be accepted in the process industries if each stage has a transparent result that relates directly to the knowledge and experience of industrial process engineers. This paper presents a three stage approach to system identification and demonstrates that each stage is both simple to apply and transparent in its results. The three stages are:

  • Data acquisition using relay feedback: An automated technique for experimental data acquisition based on the relay feedback approach of Astrom and Hagglund [2], but with modified periodic oscillations [3].

  • Step response using frequency-sampling filters: Identification of the system step response from the experimental data using the frequency-sampling filter (FSF) approach of Wang and Cluett [4].

  • Continuous-time transfer-function identification: Identification of a (continuous time) transfer function from the identified step response.


Each stage is automated, yet the output of each stage is readily understandable and can be examined by the process engineer before proceeding to the next stage. Thus the first stage yields data corresponding to square waves at the correct frequency to yield useful information and the process engineer can adjust input and output amplitudes according to his knowledge of process behaviour. The second stage gives a step response which is much `cleaner' (in terms of noise and disturbance) than that obtained by a simple step response experiment and therefore can be matched to the experience and intuition of the engineer. The third stage yields a transfer function approximation to the step; the order of the transfer function can be chosen by the process engineer to trade off accuracy against complexity whilst yielding numerical values for steady-state gains, time constants, natural frequencies and damping.

One of the essential ideas behind the proposed approach is associated with the idea of `data compression' in which the process experimental data using binary input signals are compressed into step responses. During this compression process well-established system identification tools and methods in discrete systems can be applied to obtain high quality step response models. High quality step response models with little noise will lead to the estimation of continuous time transfer function models with high accuracy (as demonstrated in this paper). In addition, the number of data points contained in a step response model is far less than the number of data points in a set of process experimental data using a binary input signal, which is inevitably advantageous in numerical computation of a continuous time transfer function model. It is worthwhile to point out that use of state-variable filters in the estimation of a continuous time transfer function model is essential for overcoming the well-known lack of excitation problem [7] when a step input signal is used.

There was an attempt to identify a continuous time transfer function model of food extruder directly from input and output data using state-variable filter approach [1]. However, because of the high noise level existed in the measurement of food extruder, it was numerically sensitive for the estimation of the pole locations in the continuous time model, as well as for the choice of state variable filters, even though a large number of experimental data were used. In contrast, in the proposed approach as the continuous time system estimation is set on the second stage of the estimation problem, it is anticipated that higher quality continuous time models will be obtained when there is little noise in the step response data.

Although none of these stages proposed in the paper are novel, the contribution of the paper is to combine them in a novel way and to verify the approach in an industrial application context. Section 2 considers the first stage; Section 3 considers the second stage and Section 4 considers the third stage. Section 5 contains the experimental evaluation of the procedure and Section 6 draws some conclusions.

Section snippets

Data acquisition using relay feedback

A simple relay is a nonlinear element that switches between the levels −a and +a based on the error signal e and generates a square wave input signal u to the process. In the extruder case, the process outputs are corrupted with noise, hysteresis is added to the relay to reduce the effect of the noise (see Fig. 1). Adding hysteresis to the relay produces a dead-zone to prevent the relay signal from switching due to the noise. It is well known that if the width of the hysteresis ϵ equals zero,

Step response estimation using frequency-sampling filters

The step response of a system is a standard non-parametric representation, which reflects system time delay, gain and response time in an intuitive way. It is called non-parametric (in contrast to parametric) in the sense that the process dynamics is captured by a set of response coefficients, instead of description of process poles and zeros. Step response representation is invariant between system descriptions in continuous time and discrete time at the sampling instant. It can be derived

Continuous-time transfer-function identification

As discussed in Section 3 stage two of the three-stage approach yields the system step response in non-parametric form. As discussed in Section 3, and illustrated in Section 5, the estimated step response is relatively noise-free compared to an actual step response test and thus can be intuitively judged by the process engineer. Whilst early versions of model-based predictive control were based on step-response models, modern model-based predictive control requires a parametric model. In

Experimental evaluation

Extrusion is a continuous process in which a rotating screw is used to force the food material through the barrel of the machine and out through a narrow die opening. In this process the material is simultaneously transported, mixed, shaped, stretched and sheared under elevated temperature and pressure. Fig. 4 shows the block diagram of a twin screw food extruder. The extruder in the study is an APV-MPF40 co-rotating twin-screw extruder. The extruder has the following specifications:

  • Throughput:

Conclusions

This paper has presented a three-stage approach to system identification in the continuous time which is appropriate for day-to-day application by plant engineers in the process industry. The three stages are: data acquisition using relay feedback; non-parametric identification of the system step response; and parametric model fitting of the identified step-response. One of the contributions of the paper is to combine them in a novel way to provide an indirect continuous time identification

References (16)

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