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Models of some Common Systems
H62SPC Dr. Alan Watson
Common Electrical Circuit
RL Circuit
V1 VL VR
R
i
V1
V(s)
di
VL L
dt
di
V1 L iR
dt
V1 sLI ( s ) RI ( s )
L
1
Ls R
I(s)
H62SPC Dr. Alan Watson
I (s)
1
V1 ( s ) Ls R
Rotational Inertia with Friction
e.
Time Delays System Response and Laplace
Transforms
H62SPC Dr. Alan Watson
Time delays and system response
So far, we have only considered gains in out block diagrams. These change instantaneously
with variation in input. Were more likely to encounter sy
Real and Complex Roots of the Characteristic
Equation
H62SPC Dr. Alan Watson
Real Roots of the C.E.
A real root, = , corresponds to a factor (s+) in the
characteristic equation
This gives rise to an exponential decay component in the time
domain. i.e.
Single Loop Feedback System and
Roots of the Characteristic
Equation
H62SPC Dr. Alan Watson
Basic Single Loop Feedback System
R(s)
+
E(s)

G(s)
H(s)
G(s) forward path transfer function
H(s) feedback path transfer function
C(s) Controlled output transfor
Transfer function response to changes in
inputs
H62SPC Dr. Alan Watson
Transfer function response to inputs
If we wanted to see how our transfer function responds to an input, we simply need to transform our
input signal into the Laplace Domain and then
Introduction to Control Systems
H62SPC Dr. Alan Watson
Control Systems
System: A collection of elements connected together to form a single unitary whole
A Control System consists of two main parts:
Plant the machines process or element which is being c
Final and Initial Value Theorems
H62SPC Dr. Alan Watson
Final Value Theorem
The FINAL VALUE THEOREM can be used to deduce the value at which a system will settle,
once all of the transients have died away
This is very useful for looking at STEADY STATE
Control Block Diagrams
H62SPC Dr. Alan Watson
Control Block Diagrams
Block Diagrams are used extensively in control engineering as they give a simple
representation of a system with all inputs and outputs.
During this module we will consider Linear, Tim
Frequency Response of Systems
H62SPC Dr. Alan Watson
Stability and Feedback
Consider a simple system G(s) with a constant input, and unity feedback: how can we predict
a specific condition for instability?
If G(s) = 1 T(s) =
For a simple transfer fu
Performance Specification and System Error
H62SPC Dr. Alan Watson
Performance Specification
Lets consider a second order response
Mp Peak Overshoot
Mp
Maximum amount by which the
response passes the reference in the
first oscillation
ess
tr Rise Time