ADAPTIVE CONTROL APPLICATIONS FOR INDUSTRIAL PROCESSES

By Bill Gough, Universal Dynamics Limited, Richmond, BC
John Kay, Universal Dynamics Technologies Inc., Richmond, BC

INTRODUCTION

Adaptive control is a general term which has been applied to control schemes which automatically adjust their control characteristics under various operating conditions in order to maintain control of a process. The adaptive mechanism used and the degree to which the control scheme adapts to the process result in a wide spectrum of adaptive process controllers.

This is a general introduction to adaptive control and an overview of some of Process Automation Systems's field application results with a new, unique adaptive controller called the Universal Adaptive Controller (UAC).

PROPORTIONAL-INTEGRAL-DERIVATIVE CONTROL

Proportional-Integral-Derivative or PID control has been the major control scheme to date in industry. The controller works by examining the instantaneous error between the process value and the set point. The Proportional term causes a larger control action to be taken for a larger error. The Integral term adds to the control action if the error has persisted for some time and the Derivative term supplements the control action if the error is changing rapidly with time.

The values of the P-I-D terms depend on characteristics of the process and must be tuned accordingly to yield satisfactory control. Properly tuned and maintained PID controllers provide adequate control for a large portion of industrial applications.

However, there are many processes with time-variant or non-linear characteristics that are difficult to control with fixed parameter PID controllers. Often it is these processes which are the most critical to the operation of the plant. To cope with these problems, PID controllers have evolved to include adaptive features such as gain scheduling and self-tuning.

Gain scheduling involves experimentation to determine optimal PID parameter values under a variety of operating conditions. The PID parameter values are stored and later recalled for use in the controller according to prevailing ambient factors via a custom scheduling scheme.

Self-tuning PID controllers use a variety of techniques to automatically determine the optimal values for the PID tuning parameters such as the Ultimate Sensitivity method developed by Ziegler and Nichols, the Reaction Curve method, or model fitting algorithms. These techniques typically require the introduction of a disturbance and subsequent analysis of the process reaction. Often the disturbance cannot be tolerated while in production or difficulty arises trying to identify the process response due to other load disturbances. Some self-tuning PID controllers are capable of continuous self-tuning on-line while others only perform the self-tuning function on demand.

In addition to processes which have time varying or non-linear characteristics, processes which have a significant dead time also pose a problem for PID controllers. The Smith Linear Predictor scheme has been applied to the PID controller to compensate for dead time. This scheme relies on a predetermined process model which is difficult to accurately obtain and automatically update on-line as operating conditions change. Modeling errors inhibit the success of this approach. When significant dead times are present, PID controllers are typically tuned with smaller proportional gain and longer integral action than is actually required. This attempt to prevent process cycling results in poor response to load disturbances.

While these adaptive features offer some improvements for PID control of difficult processes, often the process still cannot be controlled within desired tolerances. The underlying problem with PID based control schemes is that the control action is based on instantaneous error between the process variable and the set point without anticipation of the long term effects of the present control action or of the effects of previous control actions to which the process has not yet responded.

ADAPTIVE CONTROL

As mentioned in the introduction, many types of control schemes can be classified as adaptive. However, adaptive control schemes developed to date can be divided into two general categories:

Compensator-based Designs

These designs are based on the automatic tuning of a controller which compensates for the gain and frequency response characteristics of the process. Self-tuning and gain scheduling PID controllers are examples of compensator-based designs. These designs regulate an error signal (typically set point minus process value) to generate a control input to the plant which is compensated for the plant dynamics so that the process remains stable and can respond to load and set point changes quickly and with minimal overshoot.

Process Model-based Designs

These controller designs are based on the automatic adjustment of a mathematical model of the process which is used to calculate the actual control action required to obtain a desired process response. Commercially produced controllers of this type have commonly been called "true" adaptive controllers or "polynomial" adaptive controllers to emphasize the differences in control philosophy compared to the common Compensator-type controllers.

For simplicity, Process Model-based adaptive controllers will be referred to as "Adaptive Controllers" and the Compensator-based adaptive controllers will be referred to as "Self-Tuning PID Controllers" in this document.

Adaptive control schemes provide the opportunity to achieve improved control performance by basing the control action on a mathematical model of the process, including dead time, so that the control actions made are done in consideration of the effects of past control actions which have not yet appeared in the measurable process variable and the long-term consequences of the action about to be taken.

The mathematical model is adjusted automatically to compensate for changes in the process characteristics so that the controller can maintain control under various operating conditions.

Adaptive controllers are of particular interest for use on complex processes with significant dead times which typically cause difficulty for PID-based controllers. Adaptive controllers also provide a means to incorporate measured process disturbances such as feedforward variables to improve controller performance.

HISTORY OF ADAPTIVE CONTROL

Adaptive controllers were developed in the early 1950's for the avionics industry when difficulties were encountered applying PID controllers to the task of auto-piloting aircraft.

The ability of adaptive control to "adapt" to variations in flight characteristics caused by such factors as air speed, altitude and aircraft load, and the ability to incorporate all these factors into a single mathematical control strategy, made adaptive control the ideal candidate for this task.

To incorporate these factors requires the development of a mathematical model that can be used to represent the responses of the aircraft. This mathematical development, along with the requirement of a fast computer to execute the algorithm, are the major reasons that the potential of adaptive control has taken so long to be realized in conventional industrial applications. Adaptive control has been limited primarily to specialized applications in aerospace and naval auto-pilots.

The cost of computers has dropped dramatically over the past few years and research into adaptive control algorithms has increased. The control improvements possible with adaptive controllers have also become more significant due to increasing economic pressures and environmental concern as better process control can often save money and reduce pollution.

These factors have caused new interest in adaptive control applications for industry.

BASIC STEPS IN ADAPTIVE CONTROL

Numerous adaptive control schemes have been developed to date but they all perform essentially the same basic steps as shown in Figure 1.

1. Process Transfer Function Identification: The process model is adjusted to correct for model errors and to respond to changes in process characteristics by fitting observed process responses to the process model.

2. Control Update: The previous control action and observed process response are incorporated into the model.

3. Control Output: The plant model is used to predict process response and calculate the required controller output to bring the process variable to the desired set point.

The most important step is the model update (identification of the model parameters). The model structure chosen, and the method of fitting the observed process responses to that model, account for a significant portion of the variations found among the different adaptive control schemes. The degree to which the model is able to represent the process and automatically adjust to the process changes determines the accuracy of the calculated control actions and the resulting control performance.

Model Reference Adaptive Systems (MRAS) are one popular adaptive control scheme currently used. These schemes rely on the creation of an exact mathematical model of the process for each application of the controller. It requires a detailed knowledge of the transfer function (plant order, time constants, dead time), usually determined experimentally, before it is possible to make an accurate process model. This requirement limits the ability to transfer a single controller design from process to process.

Until now, commercially available industrial adaptive controllers have been based on general process models which do not always adequately represent the individual process characteristics; they are usually difficult to apply and have had varying degrees of success.

UAC CONTROLLER

The Universal Adaptive Controller (UAC) is a new adaptive controller that Process Automation Systems has been working on for almost six man-years and consists of over 25,000 lines of 'C' code. The advantage of the UAC is that it does not require a predetermined model of the process to be controlled. Only a minimum amount of prior knowledge of the process dynamics is required to apply the controller. The UAC's unique feature is its ability to learn the process transfer function while it is controlling the process. The UAC adapts its control action to changing process dynamics and dead times by building and continuously updating a mathematical model of the process being controlled.

APPLICATION EXAMPLES

CHLORINE PLANT APPLICATION

The UAC controller was tested on the pH loop of a Chlor-Alkali plant. The purpose of the test was to compare the performance of the UAC controller with that of the existing, self-tuning, PID controller.

The loop controls the pH of the combined waste water of the Chlor-Alkali and adjacent Pulp and Paper plant. The waste water enters a neutralizing tank at a high pH (11 to 12) and is buffered down to a pH of about 4 before exiting to a settling pond. A sulfuric acid source with a pH of 2 is used to buffer the waste water.

This loop is difficult to control for a variety of reasons:

- typical non-linearities associated with an acid-base reaction.
- pH sensor located at the bottom of the tank while effluent discharge and acid addition occur at the top,
- the acid addition control valve is oversized and normally operates in the non-linear 0 to 10% range,
- an undersized tank and agitator.

As the objective of the test was to evaluate the relative performance of the two controllers, these process deficiencies were not corrected. Hence both controllers had to contend with the same physical problems.
The reason for trying to control pH accurately is to minimize chemical costs and optimize plant operation.

Under normal operation, sodium sulfide is added to the sewer water to settle out the mercury in the form of mercury sulfide, an insoluble compound. If the pH is too low, the amount of sodium sulfide added increases, resulting in higher operating costs. If the pH is above 7 a soluble compound, mercury polysulfide, and insoluble forms of polysulfide are created. This allows the mercury to escape the reclaiming process while the insoluble polysulfides plug up the filters designed to reclaim the mercury sulfide. The target pH of the loop is 4, however the optimum pH is between 5 and 6. The target pH is lower than the optimum because the existing self-tuning PID controller cannot control rapid fluctuations in the process. The set point of 4 represents a compromise between the cost of the sodium sulfide and ensuring that the pH does not exceed 7. A block diagram of the test loop is shown in Figure 2.

Steady State Results

The test was conducted over a 22-hour period with control switched between the UAC and the PID controller. The relative performance is shown in Figure 3. The RMS error of the PID controller was 31.9% versus 15.9% for the UAC controller which represents a 50% reduction in process error compared to set point. The UAC output was clamped to a final output range of 0 - 30% during the tests to prevent large output swings. The 30% valve limit was reached during the three major upsets from 15 hours to 16.5 hours, which prevented the UAC from reducing the transient.

Transient Results

Figure 4 shows the response of the UAC and PID controllers to set point changes. The process was initially under manual control until a pH of approximately 8.5 was reached after 30 minutes. The UAC controller was then inserted and cycled through two set point changes. At about 150 minutes a bumpless transfer to the PID controller showed its inability to cope with the changes in gain due to the prevailing pH. This difficulty was also evident at about 250 minutes when the set point was changed to 3.0 pH. Control was switched back to the UAC controller at about 290 minutes with a set point of 5.5 pH.

The Self-Tuning PID controller had a difficult time adapting to different process conditions while the UAC controller had only an initial overshoot before settling down about set point.

INDUSTRIAL IMPLEMENTATION AT A ROTARY LIME KILN

The UAC controller is presently installed at a rotary lime kiln. The goal of this application is to control the level of lime in the cooler at the discharge end of the kiln while maintaining an even temperature distribution in the cooler. Four vibratory feeders located at the bottom of the cooler are adjusted to control the level and temperature distribution of the lime in the cooler (Figure 5).

It is important to have stable level/temperature conditions in the cooler to ensure product consistency. In addition, stable temperatures in the cooler tend to stabilize temperatures in the firing hood and in the kiln.

This process is difficult to control because of the following problems:

- the process dead time between changes in feeder rate and discharge temperature at the feeder varies from 45 minutes to 90 minutes (PID control impossible);
- final control element (feeder) is a vibrating trough with non-linear characteristics;
- interaction of all four feeders with each other.

Prior to installation of the UAC, cooler level was controlled using a single PID controller to regulate all four feeders. Temperature control in each feeder was performed manually using a trim signal added to the output of the cooler level controller. Level control was satisfactory, but the lime discharge temperature control was poor.

The UAC controller was installed to control cooler level and four additional UAC controllers were installed to automatically provide a trim signal to stabilize the temperatures in the four feeders.
Results

A comparison between cooler feeder temperatures under manual control and under UAC control is given in Figure 6. The UAC reduced cooler feeder temperature deviations from 200oF to about 30oF. (Note that there is an intentional 40o offset in temperature between the north and south pairs of feeders.)

The UAC was able to successfully automate the level and temperature control in the cooler. Stabilized cooler conditions have improved product quality and enabled the kiln to produce lime with a more consistent slaking rate.

BLEACH PLANT BRIGHTNESS CONTROL

The UAC was installed in the bleach plant of a pulp and paper mill to control the compensated brightness of the pulp in the first bleaching stage.

The objective of this control is to regulate the dosage of chlorine dioxide (ClO2) in order to achieve a given pulp brightness after a brief reaction time (about 1 minute) with some residual ClO2 remaining to complete the bleaching reaction in the 30-minute retention tower. A measurement of pulp brightness after the tower is used to determine the set point for the compensated brightness controller. A control schematic is given in Figure 7.

The compensated brightness signal is created from a measurement of the optical brightness of the pulp and the level of residual ClO2 before the pulp enters the retention tower.

The existing controller was a distributed control system (DCS) based PID controller.

The control problems on this loop consist of:

- 1 minute dead time between ClO2 dosage change and change in compensated brightness,
- process gain changes due to sensitivity changes of the residual ClO2 sensor at different levels of ClO2 substitution for chlorine (Cl2) (60% ClO2 or 100% ClO2),
- process gain changes due to different wood species and variations in lignin content (K-number) from the pulp digester.

Figure 8 is a comparison of PID versus UAC performance over a period of 16 hours. Figure 9 shows the distribution of data compared to the set point for the PID control, and Figure 10 gives the distribution for the UAC. The PID had a standard deviation of 0.84, while the standard deviation of the UAC was 48.8% lower at 0.43.

CONCLUSIONS

The Universal Adaptive Controller provides an effective solution for those process control applications which cannot be handled by self-tuning PID controllers. The Universal Adaptive Controller provides all the control benefits of adaptive control without the user having to perform the complex process analysis and the detailed modeling required by other adaptive controllers.

The unique ability of the UAC to control 1st, 2nd or higher order processes with or without long delay times and with changing process dynamics makes the UAC the ideal choice for those process loops which cannot be adequately controlled by conventional controllers.