Tuesday, October 13, 2009

PID Controllers Auto Tuning - Relay Feedback

Relay Feedback Auto Tuning of PID Controllers

IntroductionFor a certain class of process plants, the so-called \auto tuning" procedure
for the automatic tuning of PID controllers can be used. Such a procedure
is based on the idea of using an on/off controller (called a relay controller)
whose dynamic behaviour resembles to that shown in Figure 1(a). Starting
from its nominal bias value (denoted as 0 in the Figure) the control action
is increased by an amount denoted by h and later on decreased until a value
denoted by -h.

The closed-loop response of the plant, subject to the above described ac-
tions of the relay controller, will be similar to that depicted in Figure 1(b).
Initially, the plant oscillates without a de¯nite pattern around the nominal
output value (denoted as 0 in the Figure) until a de¯nite and repeated out-
put response can be easily identi¯ed. When we reach this closed-loop plant
response pattern the oscillation period (Pu) and the amplitude (A) of the
plant response can be measured and used for PID controller tuning. In fact,
the ultimate gain can be computed as:
Having determined the ultimate gain Kcu and the oscillation period Pu
the PID controller tuning parameters can be obtained from the following
Example of Relay Feedback Auto Tuning of PID Controllers
Relay-based PID Tuning

Relay-based auto tuning is a simple way to tune PID controllers
that avoids trial and error, and minimises the possibility
of operating the plant close to the stability limit.


An Improved Relay Auto Tuning of PID Controllers for SOPTD

Difficulties of loop tuning
When you discuss loop tuning with instrument and control
engineers, conversation soon turns to the Zeigler-Nichols
(ZN) ultimate oscillation method. Invariably the plant engineer
soon responds with ‘Oh yes, I remember the ZN tuning
scheme, we tried that and the plant oscillated itself into
oblivion — bad strategy. Moreover when it did work, the
responses are overly oscillatory’
So given the tedious and possibly dangerous plant trials
that result in poorly damped responses, it behoves one to
speculate why it is often the only tuning scheme many instrument
engineers are familiar with, or indeed ask if it has
any concrete redeeming features at all.
In fact the ZN tuning scheme, where the controller gain
is experimentally determined to just bring the plant to the
brink of instability is a form of model identification. All
tuning schemes contain a model identification component,
but the more popular ones just streamline and disguise that
part better. The entire tedious procedure of trial and error
is simply to establish the value of the gain that introduces
half a cycle delay when operating under feedback. This is
known as the ultimate gain Ku and is related to the point
where the Nyquist curve of the plant in Fig. 1(b) first cuts
the real axis.

The problem is of course, is that we rarely have the luxury
of the Nyquist curve on the factory floor, hence the
experimentation required.
Abstract Using a single symmetric relay
feedback test, a method is proposed to identify
all the three parameters of a stable second order
plus time delay (SOPTD) model with equal time
constants. The conventional analysis of relay
auto-tune method gives 27% error in the
calculation of ku,. In the present work, a method
is proposed to explain the error in the ku
calculation by incorporating the higher order
harmonics. Three simulation examples are given.
The estimated model parameters are compared
with that of Li et al. [4] method and that of
Thyagarajan and Yu [8] method. The open loop
performance of the identified model is compared
with that of the actual system. The proposed
method gives performances close to that of the
actual system. Simulation results are also given
for a nonlinear bioreactor system. The open loop
performance of the model identified by the
proposed method gives a performance close to
that of the actual system and that of the locally
linearized model. SOPTD model, symmetric relay, auto-tuning


An auto-tuning industrial PID is presented. The autotuning
is realized in three steps. The process is first
adequately excited in order to generate good quality data
for the second step, the process identification. The last step
is the PID tuning based on the evaluated parametric model.
The auto-tuning PID has been implemented on two
different control systems and successful applications to
processes of the pulp and paper industry are analyzed.


Auto-tune system using single-run relay feedback test
and model-based controller design

In this paper, a systematic approach for auto-tune of PI/PID
controller is proposed. A single run of the relay feedback experiment
is carried out to characterize the dynamics including the type
of damping behavior, the ultimate gain, and ultimate frequency.
Then, according to the estimated damping behavior, the process
is classified into two groups. For each group of processes,
modelbased rules for controller tuning are derived in terms of
ultimate gains and ultimate frequencies. To classify the processes,
the estimation of an apparent deadtime is required. Two artificial
neural networks (ANNs) that characterize this apparent deadtime using
the ATV data are thus included to facilitate this estimation of
this apparent deadtime. The model-based design for this auto-tuning
makes uses of parametric models of FOPDT (i.e. first-order-plus-dead-time)
and of SOPDT (i.e. second-order-plus-dead-time)
dynamics. The results from simulations show that the controllers
thus tuned have satisfactory results compared with those from
other methods.

Tuning strategy for the model-based auto-tune system.



Abstract. This contribution presents a modified autotuning algorithm of the PID controller.
The motivation for the modification of the basic autotuning algorithm is to enlarge the class
of processes to which it can be applied. The basic autotuning algorithm introduced by
Åstrom and Hägglund is extended by the preliminary identification procedure and through
the usage of the dead time compensating controller. These modifications are detailed
through the description of the algorithms’ functioning. The proposed algorithm has been
implemented in the programmable logic controller (PLC) Siemens SIMATIC S7-300. The
experimental results confirm the good robustness properties of the proposed algorithm,
which were demonstrated in a simulation study.

Structure of the modified autotuning PID controller.


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