As will be pointed out in the next section, the architecture presented in the previous two chapters for achieving adaptive process control requires a computer model of the problem environment. Thus, this approach is actually a form of model following control where the computer model is used for system characterization. After the parameters of the problem environment are accurately identified, the strategy used for manipulating the column flotation unit is altered or adapted to provide optimum performance. Without question, a vital component of the process control architecture is a computer model of the column flotation unit. In recent years, numerous researchers have worked to develop an accurate model of column flotation. Some of the more noteworthy research has been performed by Finch and Doby (1990), Herbst and Rajwnani (1989), Luttrell, Adel, and Yoon (1987), Sastry and Lofftus (1988), and Ynchausti, Herbst, and Hales (1988). Despite these efforts to develop a computer model of column flotation, there is still no single model that is suitable for the control system that is being proposed because each of the above models has a weakness that could seriously handicap the adaptive controller. Therefore, the current research effort includes the development of a neural network model of a column flotation unit. Previous efforts have demonstrated the ability of neural networks to accurately model conventional flotation units (Karr, Gentry, and Stanley, 1995), and therefore should be effective in developing model following controllers for column flotation units. The process control architecture that is outlined in the next section should provide a platform on which ail efficient control system can be built.

15.3 Structure of the Adaptive Controller

For convenience Figure 14.2 is repeated here as Figure 15.2. This figure shows a schematic of the adaptive process control system architecture. The heart of this control system is the loop consisting of the control element and the problem environment (the column flotation unit). The control element receives information from sensors in the problem environment concerning the status of the condition variables, i.e., grade, recovery, system capacity, etc. It then computes a desirable state for a set of action variables, i.e., wash water rate, gas rate, chemical agent addition, etc. These changes in the manipulated variables force the problem environment toward a predetermined setpoint. This is the basic approach adopted for the design of most closed loop control systems and, in the form described above, includes no mechanism for adaptive control.

Figure 15.2  The adaptive control system architecture is robust enough to be applicable to a variety of industrial systems including a column flotation system.

The adaptive column flotation control system presented here is dependent on a neural network model of column flotation. In the remainder of this section, a summary of the three requisite elements of the controller is provided. Special attention is focused on the analysis element since it is dependent on the neural network model. Recall that it is the analysis element that is most dependent on the computer model of the system being controlled.

15.3.1 Control Element

The control element receives feedback from sensors in the column flotation unit, and based on the current state of the condition variables, must prescribe appropriate values of the action variables. The control element in the current system is an FC. A valid (yet simple) rule for an FC used to manipulate a column flotation unit is:

IF {GRADE is LOW} THEN {AIR FLOW RATE is INCREASED}.

This rule says that if the grade of the product being produced by the column flotation unit is lower than desired, then the air flow rate should be increased. The fuzzy terms (LOW and INCREASED) are defined by triangular membership functions. Although the way in which a column flotation unit responds to changes in the operating parameters is not yet fully understood, there have been some strides made in this area. In fact, the basic form of a process matrix for the response of column flotation units has been established (Finch and Doby, 1990). Table 15.1 represents a summary of the current level of understanding of the response of column flotation units. Note that the table summarizes the response of the controlled variables caused by an increase in the manipulated variable (I indicates that the controlled variable increases with an increase in the manipulated variable, while D indicates that the controlled variable decreases with an increase in the manipulated variable). This table will serve as the cornerstone of a column flotation FC in that the rules for an FC are written based on the logic included in the process matrix. Unfortunately, there are situations for which the process matrix is not as accurate as one would like. However, the adaptive process control architecture includes a mechanism for dealing with such situations.

15.3.2 Analysis Element

The analysis element recognizes changes in parameters associated with the problem environment not taken into account by the rules used in the control element. In the column flotation unit, the main parameter of concern is the composition of the feed into the column. Changes in the concentration of the feed can dramatically alter the way in which the column flotation unit responds to changes in the manipulated variables; thus, forming a new problem environment requiring an altered control strategy. Recall that the FC used for the control element will not include the composition of the feed in the rules it uses to manipulate the column flotation unit. Therefore, some mechanism for altering the prescribed actions must be included in the control system. But before the control element can be altered, the control system must recognize that the problem environment has changed, and compute the nature and magnitude of the changes.