Simple proportional controller

Consider the binary batch distillation column, represented in Fig. 3.58, and based on that of Luyben (1973, 1990). The still contains Mb moles with liquid mole fraction composition xg. The liquid holdup on each plate n of the column is M with liquid composition x and a corresponding vapour phase composition y,. The liquid flow from plate to plate varies along the column with consequent variations in M . Overhead vapours are condensed in a total condenser and the condensate collected in a reflux drum with a liquid holdup volume Mg and liquid composition xq. From here part of the condensate is returned to the top plate of the column as reflux at the rate Lq and composition xq. Product is removed from the reflux drum at a composition xd and rate D which is controlled by a simple proportional controller acting on the reflux drum level and is proportional to Md-... 

To tackle a problem, consider a simple proportional controller first. This may be all we need (lucky break ) if the offset is small enough (for us to bear with) and the response is adequately fast. Even if this is not the case, the analysis should help us plan the next step. 

If simple proportional control works fine (in the sense of acceptable offset), we may try PD control. Similarly, we may try PID on top of PI control. The additional stabilizing action allows us to use a larger proportional gain and obtain a faster system response. 

Based on the linearized models around the equilibrium point, different local controllers can be implemented. In the discussion above a simple proportional controller was assumed (unity feedback and variable gain). To deal with multivariable systems two basic control strategies are considered centralized and decentralized control. In the second case, each manipulated variable is computed based on one controlled variable or a subset of them. The rest of manipulated variables are considered as disturbances and can be used in a feedforward strategy to compensate, at least in steady-state, their effects. For that purpose, it is t3q)ical to use PID controllers. The multi-loop decoupling is not always the best strategy as an extra control effort is required to decouple the loops. 

The distributed control objectives for this process involve the stabilization of the individual unit holdups (Mr, Me, and Mb), which, according to our prior analysis, should be addressed in the fast time scale. The design of the distributed controllers for the stabilization of the three holdups can easily be achieved, using the large flow rates F, D, and V as manipulated inputs and employing simple proportional controllers - note that only these three flow rates (i.e., the components of u1) affect the fast dynamics. More specifically, the proportional control laws... 

The overshoot oscillations occurring after a change in set point can be reduced greatly by adding to the simple proportional control a second control signal proportional to the time derivative of the temperature. This feature anticipates the magnitude of future error... 

Linear C02 absorption Simple proportional control for ventilation curves for C02 in blood and in terms of tissue pc02. Effect of 02 changes tissues. not considered. Cardiac output fixed. 

Cascade control. Consider a cascade control system similar to that of Figure 20.4a. The open-loop transfer function for the secondary loop is given by eq. (20.1) and assuming a simple proportional controller, we find that... 

If possible, use simple proportional controller. Simple proportional controller can be used if (a) we can achieve acceptable offset with moderate values of Kc or (b) the process has an integrating action (i.e., a term 1/5 in its transfer function) for which the P control does not exhibit offset. Therefore, for gas pressure or liquid-level control we can use only P controller. 

This type of temperature controller has three characteristics (1) the actual temperature of a single proportional controller will never be at the set point (2) the error in temperature, or droop, of a proportional controller, will vary over a considerable portion of a proportional band as the process varies and (3) in the case of a large time lag, the proportional band of a simple proportional controller will have to be quite large. A considerable portion of the proportional band will normally be used so the temperature will vary considerably during normal operation of the extruder. Thus a sim-... 

The choice of control mode is influenced by the extent to which an offset or oscillatory behaviour may be tolerated. With pneumatic mechanisms the cost advantage of a simple proportional controller was significant—this is no longer the case. 

The Ki term operates exactly as in a simple proportional controller. The integration term Kj has to be made long enough so that it will be negligible at the frequencies when the control loop has 180 degrees phase shift. These are the critical frequencies for loop stability. If this is done, the K2 term will not have an effect on the stability of the loop, but it will accomplish its task, i.e., eliminate the offset. 

Figure 6.31 shows the a schematic representation of this two-phase fluidized-bed reactor with a simple proportional control. It should be noted that the proportional control is based on the exit temperature (the average between the dense-phase and the bubble-phase temperatures), which is the measured variable, and the steam flow to the feed heater is the manipulated variable. 

Figure 6.32 shows that the desired steady state (corresponding to the highest yield of intermediate desired product B) corresponds to a middle unstable steady state. In order to stabilize this desired steady state, the use of a simple proportional controller is proposed and the behavior is studied for different values of the proportional gain as shown in Fig. 6.32B. It can...

The servo system of an ultrasonic motor is easily constructed due to the high holding torque and the responsiveness. Here, a simple proportional control has only to be applied as ... 

A number of convergence procedures are available ft>r step 6. We have, for example, used a simple proportional controller, that is, we multiply the error yx — jcd by a constant with the proper polarity ft>r n ative feedback. This requires some trial and error to achieve a balance between oscillation and excessively slow response. A better method is a mcxlified intorval-halving tedmique that provides moderately rapid convergence without instability. 

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