4
Root Locus
unstable
4
K
3 G(s) s2 (s 2)
2
1
Imag Axis
0
-1
-2
-3
-4
-6
-5
-4
-3
-2
-1
0
1
2
Real Axis
5
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compensated root locus.
5. Evaluate the total system gain at the desired root
location and then calculate the error constant.
6. If the error constant is not satisfactory, a Phase-lag
R(s) Gc(s) + -
Y(s) G(s)
H(s)
(d) Input compensation
3
2. Phase-lead design using the root locus Adding a single zero moves root locus to
the left and achieves the higher stability.
Chapter 5 Root Locus Method
5.1 The Root Locus Concept 5.2 Tபைடு நூலகம்e Root Locus Procedure 5.3 Examples for Drawing Root Locus 5.4 Parameter Design by the Root Locus Method 5.5 Relationship between Performance and the
location (or to the left of the first two real poles).
4. Determine the pole location so that the total angle at the
desired root location is 180° and therefore is on the
compensator is needed.
10
Example 5.15 Lead compensator using root locus
The uncompensated loop transfer function is
distributing of close-loop zeros and poles 5.6 Compensation by Using Root Locus Method 5.7 Summary 5.8 Three-term (PID) Controllers
1
5.6 Compensation by Using Root Locus Method
whether the desired root location can be realized.
3. If a compensator is necessary, place the zero of the
phase-lead network directly below the desired root
j
0
0
9
1. List the system specification and translate them into a
desired root location for the dominant roots.
2. Sketch the uncompensated root locus, and determine
1. Introduction
The design of a control system is concerned with the arrangement, or the plan, of the system structure and the selection of suitable components and parameters.
Gc (s) 1 Td s The noise is amplified, especially, the higher frequency noise.
8
Phase-lead network
Gc (s)
s 1 s 1

sz s p
j
1, or p z 0
The alteration or adjustment of a control system in order to provide a suitable performance is called compensation.
2
A compensator is an additional component or circuit that is inserted into a control system to compensate for a deficient performance.
R(s) + -
Gc(s)
G(s) Y(s)
H(s) (a) Cascade compensation
R(s) + -
Y(s) G(s)
Gc(s)
H(s)
(b) Feedback compensation
R(s) + -
Y(s)
G(s)
Gc(s)
H(s) (c) Output compensation
Root Locus
4
K (s 0.5) 3 G(s) s2 (s 2)
2
stable
1
Imag Axis
0
-1
-2
-3
-4
-2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2
0
Real Axis
7
Shortcomings It is difficult to realize