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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
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Effect of Disturbance & Noise
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Effect of Disturbances & Noise
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Effect of Disturbances & Noise
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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
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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).
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Loop Shaping (Gain Design)



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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
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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
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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).
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 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.
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 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.
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Thank You!