Proportional controller gain

Proportional control, gain A lfV/m) Control signal U s) = KfX is) - ZmCv))... 

Proportional control can be based on the temperature of the third stage. Here FO is the base flow rate, KC is the proportional controller gain, and TSET is the temperature set point. Note that in order to guard against the unrealistic condition of negative flow, a limiter condition on F should be inserted into the DYNAMIC region. This can be accomplished with ISIM by the following statement... 

Example 15.6 demonstrated that the root locus of a system not only provides information about the stability of a closed-loop system but also informs us about its general dynamic response characteristics as Kc changes. Therefore, the root locus analysis can be the basis of a feedback control loop design methodology, whereby the movement of the closed-loop poles (i.e., the roots of the characteristic equation) due to the change of the proportional controller gain can be clearly displayed. 

The reader should show the conditions for the stability of the system also show the effect of the proportional controller gain on stability, speed of response, and offset. 

In Figure 4.14, MV is the proportional portion of the output and MVd is the derivative portion. In the example, the measurement changes at a fixed rate of change therefore, the derivative portion of the output is constant and depends on the rate of change, the derivative time T, and proportional gain K. This dependency is evident from Equation 4.18. The proportional output is a ramp whose slope is a function of the proportional controller gain K. ... 

The controller gain is inversely proportional to the process gain for constant dead time and time constant. 

The Ziegler and Nichols closed-loop method requires forcing the loop to cycle uniformly under proportional control. The natural period of the cycle—the proportional controller contributes no phase shift to alter it—is used to set the optimum integral and derivative time constants. The optimum proportional band is set relative to the undamped proportional band P , which produced the uniform oscillation. Table 8-4 lists the tuning rules for a lag-dominant process. A uniform cycle can also be forced using on/off control to cycle the manipulated variable between two limits. The period of the cycle will be close to if the cycle is symmetrical the peak-to-peak amphtude of the controlled variable divided by the difference between the output limits A, is a measure of process gain at that period and is therefore related to for the proportional cycle ... 

Kcar is the gain used in the proportional control algorithm for the carriage. 

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. 

Example 5.2 Derive the closed-loop transfer function of a system with proportional control and a second order overdamped process. If the second order process has time constants 2 and 4 min and process gain 1.0 [units], what proportional gain would provide us with a system with damping ratio of 0.7 ... 

The system steady state gain is the same as that with proportional control in Example 5.1. We, of course, expect the same offset with PD control too. The system time constant depends on various parameters. Again, we defer this analysis to when we discuss root locus. 

Ziegler-Nichols Continuous Cycling (empirical tuning with closed loop test) Increase proportional gain of only a proportional controller until system sustains oscillation. Measure ultimate gain and ultimate period. Apply empirical design relations. 

We can now state the problem in more general terms. Let us consider a closed-loop characteristic equation 1 + KCG0 = 0, where KCG0 is referred to as the "open-loop" transfer function, G0l- The proportional gain is Kc, and G0 is "everything" else. If we only have a proportional controller, then G0 = GmGaGp. If we have other controllers, then G0 would contain... 

If we want to increase the margin, we either have to reduce the value ofKc or increase One possibility is to keep = 1.58 min and repeat the Bode plot calculation to find a new Kc which may provide a gain margin of, say, 2 (6 dB), as in the case of using only the proportional controller. To do so, we first need to find the new ultimate gain using the PI controller ... 

Example 7.2D. Back in the last example with a proportional controller, a gain margin of 1.7 created a system with a very small phase margin. What proportional gain should we use to achieve a phase margin of at least 45° ... 

MATLAB will return the vector [0 1.29], meaning that K, = 0, and K2 = 1.29, which was the proportional gain obtained in Example 7.5A. Since K, = 0, we only feedback the controlled variable as analogous to proportional control. In this very simple example, the state space system is virtually the classical system with a proportional controller. 

Establish limits on the controller gain. Usually applies to relatively simple systems with the focus on the proportional gain. Need be careful on interpretation when the lower limit on proportional gain is negative. 

Three terms commonly used to describe the proportional mode of control are proportional band, gain, and offset. 

A proportional controller is used to control a process which may be represented as two non-interacting first-order lags each having a time constant of 600 s (10 min). The only other lag in the closed loop is the measuring unit which can be approximated by a distance/velocity lag equal to 60 s (1 min). Show that, when the gain of a proportional controller is set such that the loop is on the limit of stability, the frequency of the oscillation is given by ... 

A control loop consists of a proportional controller, a first-order control valve of time constant rv and gain Kv and a first-order process of time constant T and gain Kx. Show that, when the system is critically damped, the controller gain is given by ... 

Assuming that Gi and H are constant and written as Ki and K2 respectively, that is the time constants of the final control element and measuring element are negligible in comparison with those of the process, and that the proportional controller has a gain Kc,... 

The steady-state gain of 0.9 can be included in two ways either start the overall AR plot at AR = 0.9 instead of AR = 1, or plot AR/0.9 on the vertical scale and start at AR = 1. In the latter case, the gain of the proportional controller calculated for the given... 

Operate with proportional control only and a step change in flowrate (set rj very high, controller 1 stepflow=l steptemp=0). Increase KP until oscillations in the response occur at KP0. Use this oscillation frequency, f0, to set the controller according to the Ultimate Gain Method (KP=0.45 KP0, rj = 1/(1.2 f0)), where f0 is the frequency of the oscillations at KP = KP0 (see Sec. 2.3.3). How high is EINT2 ... 

Most controllers are calibrated in minutes (or minutes/repeat, a term that comes from the test of putting into the controller a fixed error and seeing how long it takes the integral action to ramp up the controller output to produce the same change that a proportional controller would make when its gain is 1 the integral repeats the action of the proportional controller). 

---