Loop Transfer Function. Imaginary. B( i w ). Plane of the Open Loop Transfer Function. 1 is called the critical point. 1. B(0). Professor Walter W. Olson Department of Mechanical, Industrial and Manufacturing Engineering University of Toledo. Real. Stable. B( i w ). Unstable.
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Loop Transfer Function
Imaginary
B(iw)
Plane of the Open Loop
Transfer Function
1 is called the
critical point
1
B(0)
Professor Walter W. Olson
Department of Mechanical, Industrial and Manufacturing Engineering
University of Toledo
Real
Stable
B(iw)
Unstable
Disturbance/Noise
Reference
Input
R(s)
Error
signal
E(s)
Output
y(s)
Controller
C(s)
Plant
G(s)
Prefilter
F(s)
Open Loop
Signal
B(s)
Sensor
H(s)
+
+


The plant is that which is to be controlled with transfer function G(s)
The prefilter and the controller define the control laws of the system.
The open loop signal is the signal that results from the actions of the
prefilter, the controller, the plant and the sensor and has the transfer function
F(s)C(s)G(s)H(s)
The closed loop signal is the output of the system and has the transfer function
Error
signal
E(s)
Output
y(s)
Input
r(s)
Controller
C(s)
Plant
P(s)
Open Loop
Signal
B(s)
1
+
+
Note: Your book uses L(s) rather than B(s)
To avoid confusion with the Laplace transform, I will use B(s)
Error
signal
E(s)
Output
y(s)
Input
r(s)
Controller
C(s)
Plant
P(s)
Open Loop
Signal
B(s)
Sensor
1
+
+
Error
signal
E(s)
Output
y(s)
Input
r(s)
Controller
C(s)
Plant
P(s)
Open Loop
Signal
B(s)
Imaginary
B(iw)
Plane of the Open Loop
Transfer Function
Sensor
1
1
B(0)
Real
+
+
B(iw)
1 is called the
critical point
Error
signal
E(s)
Output
y(s)
Input
r(s)
Imaginary
Controller
C(s)
Plant
P(s)
B(iw)
Plane of the Open Loop
Transfer Function
Open Loop
Signal
B(s)
1 is called the
critical point
1
B(0)
Sensor
1
Real
Stable
B(iw)
Unstable
+
+
Simple Nyquist Theorem:
For the loop transfer function, B(iw), if B(iw) has no poles in the right hand side, expect for simple poles on the imaginary axis, then the system is stable if there are no encirclements of the critical point 1.
Im
1
Re
Stable
Im
1
Re
Unstable
Im
1
Re
Unstable
Next Class: Stability Margins