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In The Name of Allah The Most Beneficent The Most Merciful. ECE 4545: Control Systems Lecture: Performance of Feedback Control: Advanced. Engr. Ijlal Haider UoL , Lahore. Effect of Disturbance & Noise. Effect of Disturbances & Noise. Effect of Disturbances & Noise.
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ECE 4545:Control Systems Lecture:Performance of Feedback Control: Advanced Engr. Ijlal Haider UoL, Lahore
Loop Shaping (Gain Design) • In order to minimize the tracking error both S(s) and C(s) needs to be small • Constraint • Both S(s) and C(s) cannot be minimized at the same time • Design compromises must be made
Loop Shaping (Gain Design) • To reduce the influence of the disturbance, D(s), on the tracking error, E(s),L(s) needs to be large. • The transfer function G(s)/(1 + L(s)) will be small, thereby reducing the influence of disturbance. • To attenuate the measurement noise, N(s), and reduce the influence on the tracking error, L(s) needs to be small. • The transfer function L(s)/(1 + L(s)) will be small, thereby reducing the influence of N(s).
Loop Shaping (Gain Design) • All gains are function of G(s) and Gc(s), where G(s) is fixed for a given plant and Gc(s) is the controller which the control design engineer must select. • what it means for a transfer function to be "large" or to be "small." !! • The magnitude of the gain Gc(s) by considering the magnitude | Gc(jw)| over the range of frequencies, w, of interest. • **Bode magnitude plot
Loop Shaping (Gain Design) • Conflict of designing loop gain smaller or larger is addressed by the fact that • Disturbances are characterized by low frequency components • Noise is characterized by high frequency components • Hence, Gc(s) should be designed to have • Larger gain at low frequencies to reject disturbances • Smaller gain at high frequencies at high frequencies to attenuate noise
Sensitivity to Parameter Variation • A process, represented by the transfer function G(s), whatever its nature, is subject to a changing environment, aging, ignorance of the exact values of the process parameters and other natural factors that affect a control process. • The process (or plant) G(s) undergoes a change such that the true plant model is G(s) + ∆G(s).
The system sensitivity is defined as the ratio of the percentage change in the system transfer function to the percentage change of the process transfer function.
For small incremental changes, • System sensitivity is the ratio of the change in the system transfer function to the change of a process transfer function (or parameter) for a small incremental change.