Three-Mode Control

Although proportional plus integral controllers follow quite closely the idealized behavior of Eq. (27), most commercially available three-mode 

It can be seen from the ideal equation that the reset rate, /TiJA, is the number of times per minute that the integral action repeats the proportional action, and the rate time, Td, is the time that the derivative mode advances the control action over that of the proportional mode alone. 

The controller output becomes the input to the final control element or regulating unit as it is often called. 

The most widely used control valves for liquid and high pressure gas streams are the various sliding stem valves such as the bevel plug, V-port, parabolic plug, and for small flows the needle valve. For corrosive materials and slurries, pinch-type valves like the Saunders patent valves are used. Rotary stem valves include plug types and for gas flows butterfly valves, dampers, and louvers. 

The bevel plug valve, which is essentially a globe valve, is used with on-off and narrow band proportional control. For more difficult control systems, characterized valves like the V-port and parabolic plug are preferred because the flow-lift (valve position) behavior is more uniform over the full range of the valve. 

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Temperature is the hardest parameter to control in a fractionation system. It exhibits high process and measurement lag. Temperature can also be ambivalent as a measure of composition. Pressure changes are reflected quickly up and down the column. Temperature changes are not. It is typical to provide three-mode controllers for all temperature applications. 

The pressure controller (controller block) amplifies the transmitter signal and sends a modified signal to the final element. Depending on the system requirements, the controller block may include additional correction factors, integral and derivative (reset and rate). This is called a three-mode controller. 

Three principal functional control modes are proportional (P), integral (I) and derivative (D) control. These are performed by the ideal three-mode controller (PID), described by the equation... 

With the exception of derivative action any of these control modes may be used alone in certain applications. Integral and derivative actions are most usually combined with proportional control to give proportional plus integral control (proportional control with automatic reset) proportional plus derivative control or three-mode control, which is proportional plus integral plus derivative. 

Three-Mode Control. The transfer function for ideal three-mode control is... 

Fig. 6. Frequency response characteristics of three-mode controller.

The same result obtains with three-mode control. On the other hand the combination of proportional and derivative control gives the same steady state error as proportional alone, since the derivative contribution disappears at low frequency. 

For three-mode control with action similar to the Taylor Fulscope Controller,... 

The three-mode controller has a proportional and an integral character with derivative action (PID). The output signal of a PID controller is... 

Three-Mode Controller (PID Proportional, Integral, and Derivative)... 

All ideal three-mode controller consists of a simple combination of the individual modes as they have already been presented ... 

A remarkable fact is that at this writing all standard three-mode controllers are interacting. Although the mathematical structure of a non-interacting controller is simpler, its implementation is too costly to be competitive at present. 

From these conclusions, it is possible to formulate a rigorous adjustment procedure for three-mode controllers ... 

TABLE 4.2 Determination of Optimum Settings for Two- and Three-mode Controllers... 

Integrated area reduced by (a) 2 1, (b) 4 1, (c) 10 1. Variable dead time would prevent the three-mode controllers from being optimally tuned, particularly the noninteracting controller. So the amount of improvement possible may only be realized with the forward loop. 

Vector diagram, for first-order lag, 22 for proportional-plus-reset control, 16 for three-mode controller, 99 Velocity limit, 65 Volatility, relative, 291 Volume booster, 67... 

The main reason for interest in derivative action is to combine it with proportional and integral action to produce a three-mode controller, a PID. 

Kp= first-order process static gain = first-order valve constant K = first-order measurement constant ItjS proportional gain for the three-mode controller f= Laplace transform of the output temperature deviation f = Laplace transform of the input load temperature deviation = first-order lime constants for the process, measurement device, and process valve, respectively. 

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