**Relay Feedback Auto Tuning of PID Controllers**

**Introduction**For 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

table:

Example of Relay Feedback Auto Tuning of PID Controllers

http://200.13.98.241/~antonio/cursos/control/notas/siso/atv.pdf

**Relay-based PID Tuning**

ABSTRACT

ABSTRACT

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.

http://homepages.ihug.co.nz/~deblight/AUTResearch/papers/relay_autot.pdf

**An Improved Relay Auto Tuning of PID Controllers for SOPTD**

Systems

Systems

**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

http://ntur.lib.ntu.edu.tw/bitstream/246246/87370/1/09.pdf

DEVELOPMENT OF AN AUTO-TUNING PID AND

APPLICATIONS TO THE PULP AND PAPER INDUSTRY

Abstract

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.

http://www.iaeng.org/publication/WCECS2007/WCECS2007_pp175-181.pdf

**Auto-tune system using single-run relay feedback test**

and model-based controller design

Abstract

and model-based controller design

Abstract

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.

http://w3.gel.ulaval.ca/~desbiens/publications/DevelopmentOfAnAutoTuningPID.pdf

**MODIFICATION AND APPLICATION OF AUTOTUNING**

PID CONTROLLER

PID CONTROLLER

**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.

http://act.rasip.fer.hr/old/papers/MED00_062.PDF