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PID tuning

Được đăng lên bởi Huy Vu Ngoc
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Chapter 4

Experimental tuning of PID
controllers
4.1

Introduction

This chapter describes several methods for experimental tuning of
controller parameters in P-, PI- and PID controllers, that is, methods for
finding proper values of Kp , Ti and Td . The methods can be used
experimentally on physical systems, but also on simulated systems.
The methods described can be applied only to processes having a time
delay or having dynamics of order higher than 3. Here are a few examples
of processes (transfer function models) for which the method can not be
used:
K
(integrator)
(4.1)
H(s) =
s
K
H(s) =
(first order system)
(4.2)
Ts + 1
K
(second order system)
(4.3)
H(s) = s 2
s
( ω0 ) + 2ζ ω0 + 1
Controller tuning for processes as above can be executed with a transfer
function based method, cf. Chapter 7.
The methods described in this chapter can be regarded as general methods
since their procedure is the same, regardless the dynamic properties of the
process to be controlled. There are processes for which the methods does
not fit well, for example a first order process with a time delay much larger
than the time constant. Chapter 7 describes tuning methods which are
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Finn Haugen: PID Control

based on the given dynamic properties of the process as expressed in a
transfer function model, and the PID parameters are then tailored for this
process. You can expect that such model-based tuning methods will give
the control system better performance (as faster control) than if the
controller was tuned with a general tuning method. Despite this, the
general tuning methods are important because they have proven to work
well and because they are simple to use (they do not require an explicit
process model).

4.2

A criterion for controller tuning

A reasonable criterion for tuning the controller parameters is that the
control system has fast control with satisfactory stability. These two
requirements — fast control and satisfactory stability — are in general
contradictory: Very good stability corresponds to sluggish control (not
desirable), and poor stability (not desirable) corresponds to fast control. A
tuning method must find a compromise between these two contradictory
requirements.
What is meant by satisfactory stability? Simply stated, it means that the
response in the process output variable converges to a constant value with
satisfactory damping after a time-limited change of the setpoint or the
disturbance. Satisfactory damping can be quantified in several ways....
Finn Haugen: PID Control 97
Figure 4.6: Example 4.2: Time responses with PID parameters tuned using the
Ziegler-Nichols’ closed loop method
Some comments to the Ziegler-Nichols’ closed loop method
1. You do not know in advance the amplitude of the sustained
oscillations. The amplitude depends partly of the initial value of the
process measurement. By using the Åstrøm-Hägglund’s tuning
method described in Section 4.5 in stead of the Ziegler-Nichols’
closed loop method, you have full control over the amplitude, which
is benecial,ofcourse.
2. For sluggish processes it may be time consuming to nd the ultimate
gain in physical experiments. The Åstrøm-Hägglund’s method
reduces this problem since the oscillations come automatically.
3. If the operating point varies and if the process dynamic properties
depends on the operating point, you should consider using some kind
of adaptive control or gain scheduling, where the PID parameter are
adjusted as functions of the operating point.
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