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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

ECE 4545:Control Systems Lecture:Performance of Feedback Control: Advanced

Engr. Ijlal Haider

UoL, Lahore

loop shaping gain design
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 design1
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 design2
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 design3
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
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).
slide11

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.

slide12

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.