© ApICS ® LLC 2000

Abstract

In this tutorial a frequency response based adaptive control scheme with robust frequency domain specifications for industrial center-driven web winders is presented. The adaptive control scheme consists of:

1. A self-tuning initialization.
2. An adaptive controller, with robust design specifications, based on a transfer function estimation of the controlled plant from frequency response data taken from the plant.
3. Supervisory monitoring and controls.

In the tutorial, the modeling of the plant is first investigated and then the adaptive scheme is described. The simulation results are described along with discussions of pertinent implementation issues.

A web transport system (WTS), which handles a continuous strip or web, can be found in many industries such as steel mills, paper mills, plastic and textile industries. A WTS usually consists of n+1 rollers with n tension zones. A winder, the last roll of a WTS, is often a limiting factor [1] to the overall effectiveness of the system control structure whose control performance will directly affect the quality of final product. A popular method of regulating winder tension is accomplished with various control logic and feed-forward approaches [5]. A typical feed-forward closed loop web tension hybrid regulator winder control system is shown in Fig. 1. Here the tension regulator is usually implemented with a PI controller using a distributed control system (DCS) or a programmable logic controller (PLC). In some applications the tension loop is cascaded with an intermediate speed loop. For the controller structure presented in this tutorial, the intermediate speed loop is not used.

The controlled web tension plant including the dynamics of a drive, motor, gearbox, roller, and the web tension can be described adequately from first principles [2], [6]. However unknown and time varying parameters make the implementation of a conventional analytical tuning algorithm a difficult task [4]. The tuning is usually based on worst case operating conditions and as a result of this, the control performance is inadequate. The controller is essentially de-tuned for most common operating conditions. Even so it is not uncommon for the regulator to become unstable during normal operation and re-tuning of the PI will be required.

Fig. 1. Simulated Winder System

Many self-tuning and adaptive control approaches have been proposed but few has been applied to winder tension control applications. The reason for this is that the proposed algorithms are either not suitable for the application or too complex for the hardware and software that is currently used in DCS and PLC platforms.

In recent years, frequency response technique based adaptive controls have been proposed [4, 7-14]. Adaptive methods described in these approaches can be classified into several categories. The experimental method represented by the relay feedback tuning approach used extensively in process controls applications [7, 9] is popular. Using this method, a quick and stable tuning without apriori knowledge of the system can be obtained. This method yields useful information about the ultimate closed loop gain of the tuned controller, thus it has been suggested that it may be used to initialize an adaptive control system [8]. Another elegant method that has been implemented using system identification techniques in the frequency domain estimates the system transfer functions at a predetermined set of frequencies. Loop shaping techniques are then applied to identify a controller with the desired frequency domain specifications [4]. Other approaches simply use filters to estimate the transfer functions at a few specified frequencies [9, 10], but experience has shown that these methods do not easily yield reliable estimations of the plant.

In this tutorial, a frequency response based adaptive control algorithm with an easy-to-implement scheme and robust frequency domain performance specifications for the regulation of web tension in a center driven winder application is presented. The algorithm, utilizing derived general structure knowledge of the plant model, consists of:

1. Self-tuning initialization,
2. An adaptive control with robust frequency-domain specifications based on a transfer function estimation from the frequency response of the system.
3. Supervisory monitoring and controls.

In the self-tuning initialization stage, the relay feedback [7] method, whose usual application use is to identify the loop ultimate gain and 1^st order response frequency, is used to identify the dominant 2^nd order natural frequency and damping of the plant. In the adaptive control stage, a probing signal at the identified specified frequency is used to stimulate the plant. Signals to and from the plant are then retrieved through band-pass filters as described in [9,10]. Using the information obtained from these signals, the dominant 2^nd order natural frequency and damping of the plant is estimated on-line. Based on the estimated transfer function of the plant, a controller structure is determined and tuned to yield a robust closed loop regulator design. In the supervisory monitoring and control mode, a set of system operating conditions is monitored, from these measurements the dynamic closed loop performance of the system is estimated, and based on these observations a decision defining when to re-initiate the adaptation process will be determined. A novel feature in this task is to monitor the dynamic control performance of the closed loop system by estimating the frequency response at the specified crossover frequency.

This tutorial is organized as follows. The system model will be investigated in section 2. The control algorithm will be presented in section 3. The simulation results will be discussed and implementation issues will be addressed in section 4. The conclusions will be given in section 5.

4. Implementation Issues

When implementing the proposed algorithm, the following issues need to be addressed. Firstly web winder control systems are commonly implemented using DCS or PLC hardware/software packages. These systems network the sensors and drives, thus transport lags are present in all feedback and reference signal paths. If the transport delay time is large enough such that the filter estimation algorithm -90 degree phase detection frequency is shifted by the delay time, then no useful information identifying the plant natural frequency can be obtained. The effect of transport delays can be negated if all signals that are fed into the estimator are equally delayed, such that the time stamps of signal stimuli and responses are synchronized.

Secondly, probing stimulus signals are required to execute the identification scheme. If frequent adaptive control is required, the stimulus required to perform the estimation, and performance tests, will itself add a disturbance to the system. This may not be practical in certain applications, such as strain-sensitive polymer and photo-mask lines, as these applications require precise regulation of tension and cannot tolerate the addition of tension disturbances. This is true even though very small stimulus signals may be added, the magnitude of such signals in these applications would be too insignificant to yield satisfactory estimations, and would therefore be unreliable.

Finally the identification process needs to be executed in a finite period of time. In the practical implementation on the test line, and in simulation, it was found that a period of at least 5 sec was required to obtain a reasonable estimation. This method is therefore not applicable to systems where fast adaptation is required.

5. Conslusion

In this tutorial a frequency response based adaptive control scheme for center-driven web winders is proposed. Given the ease of implementation, and resulting stable control and monitoring algorithms, and extensive simulation results, the control algorithm has shown the promise for not just the described application, but any of industrial web winder control systems with different configurations, and many other industrial process control systems.