Proportional-integral controller

Example 5.3 Derive the closed-loop transfer function of a system with proportional-integral control and a first order process. What is the offset in this system ... 

The proportional-integral control equation, as given in Section 2.3.2.2, is ... 

The equation describing a proportional-integral controller in the time... 

Figure 20. Isotherms and interface shapes for the time t = 1.0 for batchwise simulations of CZ growth. Results are shown for (a) uncontrolled, (b-d) integral control, and (e) proportional-integral control simulations. Isotherms are spaced as described for Figure 19. The figure is taken from Atherton et al. (153).

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

Repeat Example 9-6 using a proportional-integral controller instead of only ijn integral controller. 

Combining the proportional with the integral action we take a new control law known as proportional-integral control. According to this law the value of heat input Q is given by... 

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. 

The control action described by eq. (11.36) is called proportional-integral control, because the value of the manipulated variable is determined by two terms, one of which is proportional to the error h, and the other proportional to the time integral of the error. 

From eq. (13.4) it is easy to show that the transfer function of a proportional-integral controller is given by... 

The disturbance is a drop in inlet Feed temperature Tq from 90°F to 70°F at time = 0 hours. Proportional and proportional-integral controllers are used. The ODEs describing the system are... 

PI (proportional-integral) control models, 160 Placement systems electronic components, 425-429 3D PCBs, 435-438... 

To obtain a more uniform film, the design team could consider design changes and/or a control strategy. One approach is that described by Armaou and Christofides (1999), who adjust the concentration of silane as a function of the radial position in the showerhead. Using three PI (proportional-integral)-controllers to attain a near-uniform Si deposition rate at radial positions across the wafer, they show how to obtain a nearly uniform film. ... 

Proportional-integral control. The proportional-integral (or PI) mode is also often referred to as proportional plus reset since this control mode eliminates the offset associated with proportional control alone. The... 

Temperature control of the reactor is achieved by varying the analog signal to the valve controlling the cooling water flow. A simple proportional integral controller was used in the experimental model determination. 

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. 

The expectance that the dynamic properties of Petlyuk columns may cause control difficulties, compared to the rather well-known behavior of the conventional direct and indirect sequences for the separation of ternary mixtures, has been one of the factors that has contributed to their lack of industrial implementation. In this work, we analyze the closed-loop behavior of Petlyuk columns when a proportional-integral controller with dynamic estimation of unknown disturbances is implemented (Alvarez-Ramirez et al., 1997). The performance of the integrated column under such a controller is compared to the behavior under a traditional proportional-integral controller. The analysis is based on rigorous dynamic simulations, and two cases are considered (i) set point tracking and (ii) output regulation under load disturbances in the feed mixture. 

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