By Konstantinos G. Papadopoulos
An instructive reference that would support keep watch over researchers and engineers, drawn to quite a few business procedures, to exploit a robust tuning procedure for the ever-popular PID keep an eye on paradigm.
This monograph provides specific PID tuning ideas for linear keep watch over loops despite technique complexity. It indicates the reader how such loops in achieving 0 steady-position, pace, and acceleration blunders and are hence in a position to tune quickly reference signs. The theoretical improvement occurs within the frequency area by way of introducing a general-transfer-function-known technique version and via exploiting the main of the significance optimal criterion. it truly is paralleled by way of the presentation of genuine commercial keep watch over loops utilized in electrical motor drives. the appliance of the proposed tuning principles to a wide classification of methods exhibits that regardless of the complexity of the managed technique the form of the step and frequency reaction of the keep an eye on loop indicates a selected functionality. This particular functionality, in addition to the PID particular answer, formulates the root for constructing an automated tuning technique for the PID controller parameters that's an issue frequently met in lots of applications—temperature, pH, and humidity regulate, ratio regulate in product mixing, and boiler-drum point keep an eye on, for instance. the method of the version is taken into account unknown and controller parameters are tuned instantly such that the aforementioned functionality is accomplished. the aptitude either for the specific tuning principles and the automated tuning procedure is confirmed utilizing a number of examples for benchmark procedure versions habitual often in lots of applications.
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Additional info for PID Controller Tuning Using the Magnitude Optimum Criterion
3 where G(s), C(s) stand for the process and the controller transfer functions, respectively. Output of the control loop is defined as y(s) and kh stands for the feedback path for the output y(s). Signal r (s) is the reference input to the control loop, do (s) and di (s) are the output and input disturbance signals, respectively, and n r (s), n o (s) are the noise signals at the reference input and the process output, respectively. 2) di ( s ) u ( s) + do ( s) + y f ( s) S Ffp (s) y(s) = , r (s) 1 + Fol (s) + kp kh G ( s) + y ( s) + + n o ( s) Fig.
With respect to the above analysis, it is concluded that by using a rough model of the plant and applying only integral control through the conventional design method via the Magnitude Optimum criterion, a closed loop system with satisfactory response results. The features of these response are listed below. 3). 3). 3). Gain margin αm = 205 db. 27◦ . 13) i=2 stands for the parasitic time constant of the plant. 14) the following closed loop transfer function results T (s) = kp (1 + sTn ) . 15), T c T 1p and T 1 = T 1p + T c = T − Tp1 has been set.
4) it is apparent that u(s) S(s) = r (s)C(s) or finally u(s) = r (s)C(s)S(s). 15) In a similar fashion, it can be proved that u(s) = −di (s)kh T (s) assuming all other inputs within the control loop are set to zero. From Fig. 3 it is obvious that u(s) + di (s) = − or u(s) + u(s) kp kh C(s)G(s) u(s) + di (s) = 0. 19) which is equal to u(s) = −kh di (s)T (s). 4 Robustness Robust performance is of primary importance when designing a control law. In other words, it is related to the ability of the controller to deliver the necessary command signal to the plant, which both makes the plant achieve perfect tracking of the reference along with satisfactory disturbance rejection and regardless of the changes that might take place within the process during its operation.