Adaptive control programmed

Fig. 7.97. Block diagram of scheduled (programmed) adaptive control system...

Gain Scheduling Adaptive Control is a special application of this procedure. For example we may have a control valve whose characteristic (input signal/valve stem position relationship) is non-linear. In this case, the valve stem position would be measured in order to obtain the gain of the valve (the appropriate relationship must be known) and the valve gain is used then to adjust the gain of the controller. If the auxiliary variable relationships are more complicated then it may be necessary to employ a Programmed Adaptive Control procedure. 

Suppose that the process is well known and that an adequate mathematical model for it is available. If there is an auxiliary process variable which correlates well with the changes in process dynamics, we can relate ahead of time the best values of the controller parameters to the value of the auxiliary process variable. Consequently, by measuring the value of the auxiliary variable we can schedule or program the adaptation of the controller parameters. Figure 22.1 shows the block diagram of a programmed adaptive control system. We notice that it is composed of two loops. The inner loop is an ordinary feedback control loop. The outer loop includes the parameter adjustment (adaptation)... 

From previous experimental data we know how the optimal fuel/air ratio changes with air temperature for maximum efficiency. Therefore, to maintain the ratio continuously at its optimal value despite any changes in the air temperature, we can use a programmed adaptive control system. Such a system is shown in Figure 22.3b. It measures the temperature of the air (auxiliary measurement) and adjusts the value of the fuel/air ratio. Notice again that the ratio adjustment mechanism is like feedforward compensation. 

What is programmed adaptive control, and what is self-adaptive control Give one example of each, different from those in Section 22.1. When would you recommend the programmed and when the self-adaptive scheme ... 

An adaptive control system can automatically modify its behaviour according to the changes in the system dynamics and disturbances. They are applied especially to systems with non-linear and unsteady characteristics. There are a number of actual adaptive control systems. Programmed or scheduled adaptive control uses an auxiliary measured variable to identify different process phases for which the control parameters can be either programmed or scheduled. The "best" values of these parameters for each process state must be known a priori. Sometimes adaptive controllers are used to optimise two or more process outputs, by measuring the outputs and fitting the data with empirical functions. 

In two papers of great interest, Roberts (1960a,b) has considered the dynamic programming formulation of a catalyst replacement problem. It will not be possible to discuss the whole of his work here as it goes a long way towards a consideration of adaptive control we shall content ourselves with one of his simpler models which brings out some features of stochastic dynamic programming. 

The heat duty to the furnace is manipulated in order to control the conversion in the reactor. The same control loop can be used to compensate for any changes in the heating value of the fuel supply. Finally, a programmed adaptive ratio controller can be used to regulate the fuel/air ratio at its best value for maximum efficiency (see Example 22.2). 

As discussed in Section 22.1, the purpose of an adaptive controller is not to keep the controlled output at its desired set point this is accomplished by the regular feedback loop. What, then, is the criterion or objective function that guides parameter adjustment of an adaptation mechanism How is this objective evaluated by the programmed and self-adaptive schemes ... 

Exact compensation may be obtained by programming the settings of the controller as functions of flow. Because the period of the loop varies directly with dead time, derivative and reset time ou t to vary inversely with flow. And since process dynamic gain varies inversely with flow, the proportional band should too. Knowing this, it is possible to write a flow-adapted control algorithm ... 

At this writing, programmed adaptive systems have been used for certain critical applications such as temperature control in once-through boilers and heat exchangers. But there apparently is no published report on a self-tuned controller operating successfully on a critical loop in a process plant. (They have been used in aircraft controls.) From the foregoing discussion it should be evident that, no matter how skillfully mechanized, a self-tuning controller is by no means a panacea. 

If a reasonably accurate mathematical model of the process may be obtained in a simple form, it may be differentiated to solve for the adaptive control program. In the following expressions, let Kr represent the desired gain of the process. Consider the example of a variable-gain process affected by a load term q ... 

An important observation is that any control program may be followed, even one that would cause the process gain dc/dm to change sign. Hence feedforward is the logical means to achieve optimizing (steady-state adaptive) control. This has already been demonstrated in Chap. 6. 

Yet another approach to this situation would be to adjust the controller parameters, the controller gain for example, with the variation in load of set point to compensate for the variation in process gain. This approach is termed gain scheduling [5,6] or programmed adaptation [7,8] and can be considered to be form of adaptive control [5],... 

There are few field studies of underwater robotics in Brazil. Dominguez (1989) realized a study on modeling and developed a program to dynamically simulate underwater vehicles. Cunha (1992) proposed an adaptive control system for tracking trajectories. Hsu et al. (2000) presented a procedure to identify the dynamic model of thrusters. Barros and Soares (1991) presented a proposal for a low cost vehicle that can operate as ROV or AUV. Souza e Mamyama (2012) investigated different control techniques for dynamic positioning. 

---