Controller gain and reset

Assume that it is required to tune PI controllers on a 2 x 2 MIMO process. The ATV results are used to select the controller gain and reset time based on, for example, Zeigler-Nichols tuning. Then, a single tuning factor, Fj, is applied to the tuning parameters for both control loops ... 

Calculate feedback-controller gain and reset settings and control-loop natural frequencies. Check feed-tank material balance and mixing time constants for adequacy. 

Figure 16.14 gives relay-feedback test results for both loops used in this structure. Although the amplitude and period look reasonable for the Foa/Ti6 pairing, the shark-tooth shape of the tray 26 temperature response is characteristic of a process with an inverse response. This is confirmed by the controller gain and reset time values calculated from test data. As given in Table 16.3, the values for the Fqa/T 6 loop have reasonable values. However, the controller for tray 26 has an unrealistic reset time of 8600 min. 

Figure 16.18 gives relay-feedback test results for both loops Fqa/xa,20 nd Vy/Tig. The unusual sharp spikes in the composition on tray 20 are caused by the step changes in Fqa, which is fed directly on tray 20. The amphtudes and periods look reasonable for both loops. These results are also confirmed by the controller gain and reset time values listed in Table 16.4. There is no inverse response (huge reset times) problem. There is also no action related problem because both loops have the same action. 

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 ... 

Thus we have found that the appropriate structure for the controller is PI, and we have solved analytically for the gain and reset time in terns of the parameters of the process model and the desired closedloop response. 

One of the major questions in multivariable control is how to tune controllers in a diagonal multiloop SISO system. If PI controllers are used, there are 2N tuning parameters to be selected. The gains and reset times must be specified so that the overall system is stable and gives acceptable load responses. Once a consistent and rational tuning procedure is available, the pairing problem can be attacked. 

IV.37 Select the gain and reset time settings of a PI controller, employing the minimum ISE criterion for a unit step change in the set point. The process is first-order with Kp = 10, and xp = 1.0. Assume that Gm(s) = Gf(s) = 1. The selected settings must satisfy the restrictions... 

The controller should have auto overrides (see Chapter 9), or perhaps adaptive gain and reset, to compensate for changes in condenser dynamics as condensate rate changes. An override from coohng-water exit temperamre is also normally needed. 

With such a controller it will be necessary, as indicated earlier, to use auto overrides or a controller with nonlinear gain and reset. 

The speed of the controller is adjusted by the proportional band and reset rate (proportional and integral gains). These parameters also influence the stability of the control loop. All control loops are limited to a gain of less than one at their critical frequency. Higher closed-loop gain will make the loop unstable. 

Controllers can be adjusted by changing the values of gain Kp, reset time Xi and derivative time Td- The controller can be set by trial and error by experimenting, either on the real system or by simulation. Each time a disturbance is made the response is noted. The following procedure may be used to test the control with small set point or load changes ... 

Initially use proportional-only controllers in all loops except flow7 controllers, where the normal tight tuning can be used K = 0.5 and T = 0.3 minutes). Set the gains in all level controllers (except reactors) equal to 2. Adjust the temperature, pressure, and composition controller gains by trial and error to see if you can line out the system with the proposed control structure. If P-only control cannot be made to work, PI will not w7ork either. When stable operation is achieved, add a little reset action to each PI controller (one at a time) to pull the process into the setpoint values. 

Equation (14.26b) indicates that the form of the closed-loop response (i.e., overdamped, critically damped, underdamped) depends on the values of the controller gain Kc and reset time t/. Therefore, tuning the integral control action for the appropriate values of Kc and T is an important question and will be discussed in Chapters 16 and 18. 

IV.35 A first-order process is controlled with a PI controller. Find the values of the controller gain Kc and reset time t/ so that (a) the closed-loop gain to load changes is 10 and (b) the decay ratio of the closed-loop response is 1/4. The following information is given ... 

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