Integral action time

In equation (4.68), T is called the integral action time, and is formally defined as The time interval in which the part of the control signal due to integral action increases by an amount equal to the part of the control signal due to proportional action when the error is unchanging . (BS 1523). 

Information flow in model 7 Integral action time 182 Integral control 97, 547 Integral control constant 97, 507 Integrated extraction 335 Integration... 

A proportional plus integral controller is used to control the level in the reflux accumulator of a distillation column by regulating the top product flowrate. At time t = 0, the desired value of the flow controller which is controlling the reflux is increased by 3 x 10-4 m3/s. If the integral action time of the level controller is half the value which would give a critically damped response and the proportional band is 50 per cent, obtain an expression for the resulting change in level. 

The overall design problem is to select number of tanks, sizes of tanks, number of controllers and controller gains, and integral action times to achieve a required disturbance rejection at minimum cost. The generic problem is represented in Fig. 4. 

Tj is the integral action time, also known as the reset time. It is the time that would be taken for the change in the integral term to build up and equal the proportional term, given a sustained, constant error. 

Ps power supplied to the pump W Ti integral action time or reset ... 

Eodt (13-174) where V and are initial values, Kc and T are respectively feed-back-controller gain and feedback-reset time for integr action, and E is the error or deviation from the set point as given by ... 

Integral action is brought in with high Xi values. These are reduced by factors of 2 until the response is oscillatory, and Tj is set at 2 times this value. 

In practice, integral action is never used by itself. The norm is a proportional-integral (PI) controller. The time-domain equation and the transfer function are ... 

B. INTEGRAL ACTION (RESET). Proportional action moves the control valve in direct proportion to the magnitude of the error. Integral action moves the control valve based on the time integral of the error, as sketched in Fig. 7.9b. 

C. PROPORTIONAL-INTEGRAL (PI) CONTROLLER. Most control loops use PI controllers. The integral action eliminates steadystate error in T (see Fig. 7.11c). The smaller the integral time r, the faster the error is reduced. But the system becomes more underdamped as t( is reduced. If it is made too small, the loop becomes unstable. 

When a controller with integral action (PI or PID) sees an error signal for a long period of time, it integrates the error until it reaches a maximum (usually 100 percent of scale) or a minimum (usually 0 percent). This is called reset windup. 

Calculate the Zicgler-Nichols value for ly for a PI controller. Hold this value constant for the rest of the design. We only add integral action to eliminate steadystate offset, so it is not too critical what value is used, as long as it is reasonable, i.e., about the same magnitude as the process time constant. For our example, the ZN value for ty with a PI controller is 3,03 minutes. 

The integral and derivative modes are normally used in conjunction with the proportional mode. Integral action (or automatic reset) gives an output which is proportional to the time integral of the error. Proportional plus integral (PI) action may be represented thus ... 

It can be seen from equation 7.3 and Fig. 7.7 that the controller output will continue to increase as long as e > 0. With proportional control an error (offset) had to be maintained so that the controlled variable (i.e. the temperature at Y—Fig. 7.1) could be kept at a new control point after a step change in load, i.e. in the inlet temperature of the cold stream. This error was required in order to produce an additional output from the proportional controller to the control valve. However, with PI control, the contribution from the integral action does not return to zero with the error, but remains at the value it has reached at that time. This contribution provides the additional output necessary to open the valve wide enough to keep the level at the desired value. No continuous error (i.e. no offset) is now necessary to maintain the new steady state. A quantitative treatment of this is given later (Section 7.9.3). 

This is essentially a compromise between the advantages and disadvantages of PI and PD control. Offset is eliminated by the presence of integral action and the derivative mode reduces the maximum deviation and time of oscillation, although the latter are still greater than with PD control alone (Fig. 7.5). 

Hence, we must choose initially a value of Kc < 5.9 for stability. Suppose Kc is put equal to 3, then, for the system to be stable (from (ii)), x, must be greater than 5.8 min. If Kc is reduced to 1.8, then the minimum possible value of x, to retain stability will be 3.5 min. This is as expected since a reduction in Kc will increase system stability—thus allowing the amount of integral action to be increased before the system becomes unstable (reflected in a smaller value of integral time). (See also Section 7.2.3 and Example 7.8.)... 

In order to make sure that the pressure controller (PC-01) set point is changed slowly and in a stable manner, the valve position controller (VPC-02) is provided with integral action only, and its integral time is set to be about 10 times that of PC-01. In order to prevent reset windup when PC-01 is switched to manual or local control from cascade, the valve position controller is also provided with an external feedback signal off the pump speed. 

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. 

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