Proportional integral response

Proportional integral (PI) control A control algorithm that combines the proportional response and integral response control algorithms. 

When an error is introduced to a PID controller, the controller s response is a combination of the proportional, integral, and derivative actions, as shown in Figure 30. 

W.L. Luyben, Tuning of proportional-integral controllers for processes with both inverse response and deadtime, Ind. Eng. Chem. Res. 39 (2000) 973-976. 

Response of a system with (a) proportional + derivative (PD) control and (6) proportional + integral + derivative (PID) control when the gain is 15 percent of the critical gain. Part (c) shov the response with PID control when the gain is 50 percent of the critical gain, a practical limit for good regulation. Compare these responses to that shown in Fig. 10 for simple proportional (P) control. 

The design of the valve, process, and measurement should be made such as to minimize deadtime in the loop while providing a reliable, more linear response, then the controller can be tuned to provide the best performance, with an acceptable operating margin for robustness. The PID controller is the most widespread and applicable control algorithm, which can be tuned to provide near optimal responses to load disturbances. PID is an acronym for Proportional, Integral, and Derivative modes of control. 

Example 11.4 demonstrates very clearly how the simple first-order dynamic behavior of a tank can change to that of a second-order when a proportional-integral controller is added to the process. Also, it indicates that the control parameters Kc and r can have a very profound effect on the dynamic behavior of the system, which can range from an underdamped to an overdamped response. 

Fortunately, we can select the most appropriate type of feedback controller using only general qualitative considerations stemming from the analysis in Chapter 14. There we had examined the effect of the proportional, integral, and derivative control modes on the response of a system. In summary, the conclusions were as follows ... 

Let us now examine how the response of a normal, uncontrolled process is changed when a simple proportional, integral, or derivative feedback controller is incorporated. In this section we consider only the proportional controller and its effect on the most commonly encountered first- and second-order systems. The effects of integral and derivative control actions will be studied in the following two sections. 

Proportional-integral-derivative (PID) control PID control takes advantage of PE, PI, and PD controls by finding the gains (Kp. Kp and Kj to balance the proportiontil response, steady state reset ahUity, and rate of response control, so the plant can be weU controlled. 

The slope of the ramp applied is critical because biological membranes show PI behavior. This means that the response to a stimulus is only partly proportional to the stimulus. Another, often greater part, is an integrating response (dose effect) (Figure 8.45). 

A three point control configuration based on a proportional-integral controller with dynamic estimation of unknown disturbances was implemented in a Petlyuk column. The proposed controller comprises three feedback terms proportional, integral and quadratic actions. The first two terms act in a similar manner as the classical PI control law, while the quadratic term (double integral action) accounts for the dynamic estimation of unknown disturbances. Comparison with the classical PI control law was carried out to analyze the performance of the proposed controller in face to unknown feed disturbances and set point changes. The results show that the closed-loop response of the Petlyuk column is significantly improved with the proposed controller. 

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