Advanced Mechanism Design: Analysis and Synthesis Vol. II by Sandor, Arthur G. Erdman

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By Sandor, Arthur G. Erdman

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5. The aforementioned statement is true only in the Fig. 6 Sensitivity and Complementary Sensitivity Function 23 case where the angle φcl of T is very low. 44) T ( jω) ≈ 1∠0◦ . Since practically this kind of design cannot be achieved, control engineers have to design control loops such that the frequency response of the closed-loop control system does not exhibit any resonance all over the low- and high-frequency regions. 44) in a closed-loop control system, in this section the principle of the Magnitude Optimum criterion is introduced.

4, the conventional and the revised PID control law are compared via simulation examples for benchmark processes met in many industry applications. The comparison focuses on the performance of the control law in terms of disturbance rejection and reference tracking. Finally, after the verification of the proposed control law, the validity of the several negative comments toward the Magnitude Optimum criterion presented in this section, is investigated in Sects. 10. 2 Conventional PID Tuning Via the Magnitude Optimum Criterion For presenting the conventional PID tuning via the Magnitude Optimum criterion, the closed loop system of Fig.

From the control loop structure presented in Fig. 3, it is seen that the difference between the reference signal r (s) and the output of the control loop y(s) is expressed by the error signal e(s), because e(s) = r (s) − y(s). Since r (s) is bounded and r (s) = e(s) + y(s), for checking the internal stability of the control loop, it is sufficient to track either the response of the output signal y(s) or the error signal e(s). Assuming a stable controller design of C(s) it is apparent that u(s) is also stable, since u(s) = C(s)e(s).

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