PI control algorithm

Proportional integral derivative (PID) control A control algorithm that enhances the PI control algorithm by adding a component that is proportional to the rate of change of the deviation of the controlled variables. 

From eqs. (30.2) and (30.3) we can easily derive the discrete transfer functions for the velocity form of PID and PI control algorithms. Thus we take ... 

What is a discrete transfer function, and what is it needed for Develop the discrete transfer function for (a) a proportional control algorithm, (b) the velocity form of a PI control algorithm, and (c) a second-order digital filter. 

Find the closed-loop response of a first-order process using the velocity form of the PI control algorithm. Show that the steady-state offset of the closed-loop response to a unit step change in the set point is zero. 

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

On the other hand, conventional control approaches also rely on models, but they are usually not built into the controller itself. Instead the models form the basis of simulations and other analysis methods that guide in the selection of control loops and suggest tuning constants for the relatively simple controllers normally employed [PI, PID, I-only. P-only, lead-lag compensation, etc. (P = proportional, PI = proportional-integral, PID = proportional-integral-derivative)]. Conventional control approaches attempt to build the smarts into the system (the process and the controllers.) rather than only use complex control algorithms. 

An alternative form for the PI and PID control algorithms is the so-called velocity form. In this form, one does not compute the actual value of the controller output signal at the nth sampling instant, but its change from the preceding period. Thus consider the PID control action at the nth and (n - l)th sampling instants. From eq. (27.7) we take... 

Cohen-Coon settings (see Section 16.5) From the process reaction curve we can estimate the process static gain K, the dominant time constant r, and the process dead time td Then, from eqs. (16.9) through (16.11c), we can compute the parameters Kc, r/, and rD of a P, PI, or PID control algorithm. The effect of the sampling period T has been accounted for by the nature of the experiment itself, because the reaction curve has been determined using sampled-values of the process output. 

Describe in your own words the difference between the position and velocity forms of PI or PID control algorithms. Do we have these two forms for a proportional controller ... 

In actual operation, the operator s actions in accordance with the above guidance should be conducted in a different manner depending on the reactor power level as described in Figure 23. A fuzzy algorithm based on linguistic rules is employed to control non-linear characteristics, whereas this is a difficult problem for the conventional PI controller. 

Most sampled-data control systems employ discrete versions of PI and PID control algorithms although computers are certainly not limited to only these types. Special-purpose algorithms can be construaed in the software to deal with the multivariable, nonlinear nature of a distillation column. Adaptive control, for example, updates the parameters in control algorithms and sampling rates to compensate for nonlinearities in the process. Optimal control is a... 

Control Algorithms—Part III, Tuning PI and PID Controllers, Inst. Contr. Syst. (Dec. 1973). 

In Equation 4.18, the PD controller equation contains a bias term. A bias term will normally appear in any controller algorithm that does not contain integral action. This bias term does not appear when integral action is present, since integral action is in effect an automatic adjustment of bias. As with the PI controller, the proportional gain acts on the error as well as the derivative time T. Figure 4.14 shows the controller output MV for a typical input e test signal for the proportional and derivative portions of a PD controller. 

The first objective of the antisurge control system is to protect the compressor. This can be accomplished for some disturbances by using the PI algorithm with a large value of bj. However, it is also necessary to maximize the region in which the compressor can operate with the recycle valve closed. This increases the efficiency of the compressor at lower throughputs. Steady-state operation with recycle is extremely inefficient. Therefore, from this perspective, small values of bj are highly desirable. 

Equation 7.237 is termed the position form of the algorithm as it gives the actual value (or position) of the controller output signal. In this form, at the nth sampling instant, the PI algorithm saves only the current value of the error e and the sum... 

The computational power and flexibility of the computer is much used now to simulate controllers having characteristics other than the standard P, PI, etc., modes. Controllers are described in the following for which the design algorithm is derived directly from a specification of the discrete time character of the response of the controlled variable to a given change in set point. 

The controller is a digital PI algorithm in the velocity form. Its discrete transfer function will be developed in Section 30.1, but for the time being consider it is known and given by... 

The foregoing two digital approximations for PI and PID controllers are known as the position form of the algorithms, because at each sampling instant they compute the actual value (position) of the con-... 

The lowest level is controller tuning, i.e., determining the values of controller tuning constants that give the best control. The next level is algorithms-deciding what type of controller to use (P, PI, PID, multivariable, model predictive, etc.). 

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