# 幻灯片 1 Principle of Automatic Control Prof by liamei12345

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```									Principle of Automatic Control

Prof. Xie Hongwei

College of Mechatronic and Automation
National University of Defense Technology
April ~July 2008
Chapter 8 The Design
of Feedback Control System

8.1 Review on the Performance Indices and their Regulation
8.2 Concept of Compensation
8.3 Compensation Networks
8.4 Phase-Lead Design Using the Bode Diagram
8.5 Phase-Lag Design Using the Bode Diagram
8.6 Phase-Lead Design Using the Root Locus
8.7 Phase-Lag Design Using the Root Locus
8.8 PID Controller
8.9 Feedback Compensation Design
8.10 Comprehensive Example
Lecture 20: Feedback Compensation and
Comprehensive Example
（8.9,8.10, 2 Hours）

8.9 Feedback Compensation Design
8.10 Comprehensive Example
8-9 Feedback compensation and noise
compensation
1. feedback compensation
The compensators can be also inserted in the
feedback path.

Compensation       Process
—                  —

Feedback
Compensation
Example 8.9 Velocity feedback control. The typical
Velocity feedback control system is as:

R(s)
(s)
+
E(s)
(s)
K
-
-

K1

or
R(s)
(s)
+
E(s)
(s)
-       K

1+K1s

A PD controller is inserted into the feedback path.
With this feedback, the system will be adjusted according
to the information about the error signal and its prediction
( velocity signal for future change).
R(s)
(s)
+
E(s)
(s)
-        K

1+K1s

CL transfer function becomes

the damping ratio and corresponding indices,
such as settling time, can be adjusted by velocity
feedback controller.
If we require PO<5%,the settling time less than 250ms,
then, from

We have:
The compensated CL transfer function is

This will satisfy the requirements.
2. noise compensation
In idea case, the steady-state system response to
any noise should approach to 0, but this is almost
impossible in control system engineering.
If the noise is measurable, in theory, we can
totally eliminate the noise by feedback compensation,
or, noise compensation, to improve the system
accuracy.
The error induced by the noise is right the negative
of the system response, and it is hoped to approach to 0 .
One of the compensation scheme is as:

N(s)
Gn(s)
+                                   Y(s)
R(s) E(s)
G1(s)             G2(s)
-
The response to the noise is:

The key is the choice of the feedback compensator
Example 8.10 Noise compensation
N(s)

R(s)=0                                   Y(s)

-

The output is:
If we choose                         , the output has
nothing to do with the noise, but this is not realizable.

If we choose               , then, the steady-state
output will
8-10 Comprehensive example---inverted pendulum

goal:
to design suitable PID controller for
inverted pendulum, without given the form of
assumption: moving in the plain with
noise considered; mass of the
bar is 0, no friction.
measurement: angle sensor
compensators:（P，PD，PID）
Input: torque
1. System modeling

torque
linearization
denote

For convenience, let

， （☆）
2. Control plans
（1） OL control in theory
Given        ，       ，to find suitable
input        ，so that   ，  approach to 0 (when
t is big enough.)
if we choose         ，then：

and        will approach to 0.

But, we need know exactly the initial condition.
Not really realizable.
Consider feedback control, the model and diagram is

OL marginally stable

R(s)       E(s)
+
-

？
(2) P controller
assumption: no sustained out force!
angle can be measured without error

stable
unstable

can not keep the vertical pendulum always stable.
(only angle information is feed backed)
(3) PD controller
assumption: no sustained out force!
angle and the velocity can be measured without error

CL transfer function become:

(both angle and the velocity information is feed backed)
this scheme can satisfy the design requirements,
and allocate the CL zero and pole by adjusting the
αandβ.
but, the PD feedback control can not eliminate
the disturbance quite well, for example,

when

it is hard to keep the vertical pendulum stable.
(3) PD controller
assumption: no sustained out force!
angle, the velocity and the accumulation
can be measured without error

so, the past (accumulation), the future (velocity)
and the on-time (angle) information is feed backed.
Better performance can be expected.
CL transfer function is:

This PID control plan is used in practical
systems. You are encouraged to implement it in our
lab.
Thanks！

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