Control I-PD controller and tuning

A design method of multirate I-PD controller based on multirate generalized predictive control law

This paper proposes a new design method of an I-PD controller. The I-PD controller is designed in a multirate system with fast control input and slow output sampling. In order to design PID parameters of the multirate I-PD controller, the multirate I-PD controller is designed based on a multirate generalized predictive control law. Since in the multirate system a control input is updated faster than a single-rate system with slow control input and slow output sampling, the control effect of the proposed multirate I-PD controller is greater than that of a conventional single-rate one. Finally in order to show effectiveness of the proposed method, simulation results are illustrated.

http://cat.inist.fr/?aModele=afficheN&cpsidt=17893327

An Adaptive Controller based on system Identification for plants with
uncertainties using well known Tuning formulas
Abstract
Adaptive control which adequately adjusts controller
gains according to the changes in plants, has become
attractive in recent years .The controller proposed in this
paper is tuned automatically with various tuning formulas
based on the results of frequency domain system
identification for the plant. The controller first estimates
the frequency response of the plant using FFT. The
controller gains are automatically tuned so as to minimize
the error between the open loop frequency response of
the reference model and that of the actual system at a few
frequency points. For the three example processes,
reference models are derived. The frequency responses
of the reference models and that of the actual processes
are obtained. The controller gains are determined by
applying the least squares algorithm .The responses of
the plants are verified in time domain and frequency
domain after tuning the I-PD controller.

Block diagram of an I-PD controller along with process
plant

http://www.icgst.com/acse/Volume6/Issue3/P1110626005.pdf

PI-D and I-PD Control with Dynamic Prefilters
In this lab you will be controlling the one degree of freedom systems you previously modeled using PI-D and I-PD controllers with and without dynamic prefilters.
the I-PD controller we have


http://www.rose-hulman.edu/Class/ee/throne/ECE-320%20Fall%202009/lab7a.pdf

DESIGN OF ROBUST POLE ASSIGNMENT BASED ON
PARETO-OPTIMAL SOLUTIONS
ABSTRACT
In this paper, a new design method for robust pole assignment based on
Pareto-optimal solutions for an uncertain plant is proposed. The proposed design
method is defined as a two-objective optimization problem in which optimization
of the settling time and damping ratio is translated into a pole assignment
problem. The uncertainties of the plant are represented as a polytope
of polynomials, and the design cost is reduced by using the edge theorem.
The genetic algorithm is applied to optimize this problem because of its
multiple search property. In order to demonstrate the effectiveness of the
proposed design method, we applied the proposed design method to a magnetic
levitation system.


I-PD control system


http://www.ajc.org.tw/pages/PAPER/5.2PD/PI-01-22.pdf

Study on the I-PD Position Controller Design for Linear Pulse Motor DrivesABSTRACT
In this paper, a brief discussion on I-PD position controller design for linear pulse motor drive is presented. The proposed method mainly focuses on the robusteness property of the controller, which is very important for this type of system in which the variation of external load affects plant parameters. It is considered in this paper that two types of controller design methods namely; Coefficient Diagram Method (CDM), and arbitrary Pole Assignment Method (PAM) are treated and compared them. It is shown in this paper that for the case of CDM, a stability index values are chosen such that the robust property of the controller is adequately sufficient for light and heavy load operation without excessively exciting the motor. For these stability index values and an equivalent time constant, which determines the speed of responese of the system, the closed loop pole locations are automatically fixed. For the case of PAM, the closed loop pole assignments must be iteratively tried to arrive at an acceptable response.

http://nels.nii.ac.jp/els/110000031056.pdf?id=ART0000357399&type=pdf&lang=en&host=cinii&order_no=&ppv_type=0&lang_sw=&no=1260926777&cp=

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Control Video Lecture Industrial Automation and Control - Introduction to Automatic Control ,PID Control and PID Control Tuning

Video Lecture Introduction to Automatic Control



Video Lecture P I D Control



Video Lecture PID Control Tuning

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Control Cascade Control Systems Design - Tunings

Procedure for Cascade Control Systems Design:
Choice of Suitable PID TuningsAbstract: This paper provides an approach for the application of PID controllers
within a cascade control system configuration. Based on considerations about the
expected operating modes of both controllers, the tuning of both inner and outer loop
controllers are selected accordingly. This fact motivates the use of a tuning that,
for the secondary controller, provides a balanced set-point / load-disturbance performance.
A new approach is also provided for the assimilation of the inner closed-loop
transfer function to a suitable form for tuning of the outer controller. Due to the fact
that this inevitably introduces unmodelled dynamics into the design of the primary
controller, a robust tuning is needed.

2 Cascade Control


3 g-tuning for balanced Servo/Regulation
4 Approach for Cascade Control Design
4.1 Inner loop and outer loop process models
4.2 Inner loop controller tuning
Set-point tuning settings
Load-disturbance tuning settings
4.3 Model for Outer loop tuning
4.4 Outer loop controller tuning
5 Equivalent model approximation
6 Example
7 Conclusions
http://www.journal.univagora.ro/download/pdf/134.pdf

How to Tune Cascade Loops
1 An overview of Cascade Control.
What's The Inner Loop For?
• Reduces phase lag of inner process
• Disturbances to the inner loop are
compensated for before they upset the
outer loop
• Prevents non-linearities in the inner loop
from reaching the outer loop

2 Tuning Cascade Control Loops.
What happens when cascade loops
are poorly tuned?
• Loops “fight” each other
• Create oscillations
• Neither variable is properly controlled
• Operator puts loop in manual.
Tuning Cascade Loops
1. Always check for measurement and
valve-related issues.
2. Inner Loop Tuning - put slave into
Local Auto or Manual and tune the
slave controller as a normal PID loop.
3. Outer Loop Tuning - put slave into
Cascade and tune master controller
as a normal PID loop.
4. Adjust outer loop tuning values to
ensure that the RRT (Relative
Response Time) of outer loop is 3-5
times slower than the inner loop.

3 Case Study.

http://www.expertune.com/articles/UG2007/CascadeTuning.pdf

Cascade Control
Handle Processes that Challenge Regular PID Control

In previous columns we have named lags in a process as major obstacles to good temperature control. When they are inconveniently long and come in multiple stages, first try to determine where changes to process design can avoid or reduce lags. Then do your best with PID control and if you fail to obtain the response you hoped for you can turn to cascade control.



Tuning.Tune the slave loop first. Set TC1 to manual. Remove integral and derivative action from TC2 and tune it aiming for tight control. Absence of derivative avoids excessive activity of the slave loop. Overall integral action to remove offset in the vessel temperature is already provided by the master controller.

When tuning the master loop, return to cascade control, remove derivative action and tune in the normal way. Note that the slave loop now becomes part of the master loop that you are tuning at TC1. Bumpless transfer between auto, manual and cascade will be a standard feature of TC1.
Set point limits on the slave loop. If you know the range of TC2 (fluid) temperatures needed to hold the vessel temperature under all expected conditions, put those values as limits on the set point of TC2.

http://www.pacontrol.com/download/Cascade%20Control%20-%20Handle%20Processes%20that%20Challenge%20Regular%20PID%20Control.pdf


Cascade Controller - Auto Tuning

Relay Auto Tuning Of Parallel Cascade Controller
Abstract
The present work is concerned with relay auto tuning of
parallel cascade controllers. The method proposed by
Srinivasan and Chidambaram [10] to analyze the conventional
on-off relay oscillations for a single loop feedback controller is
extended to the relay tuning of parallel cascade controllers.
Using the ultimate gain and ultimate cross over frequency of
the two loops, the inner loop (PI) and outer loop (PID)
controllers are designed by Ziegler-Nichols tuning method. The
performances of the controllers are compared with the results
based on conventional relay analysis. The improved method of
analyzing biased auto tune method proposed for single
feedback controller by Srinivasan and Chidambaram [11] is
also applied to relay auto tune of parallel cascade controllers.
The proposed methods give an improved performance over that
of the conventional on-off relay tune method.

http://www.iaeng.org/publication/WCECS2007/WCECS2007_pp158-162.pdf

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Control 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
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
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


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
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
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

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Control Tuning Servo Motor

Introduction
To paraphrase an adage, there are two types of motion
control engineers, those that are comfortable tuning a
servo loop, and those that aren’t. And if you are one of
those engineers that aren’t comfortable, you in turn, have two
options. The first is to use a non-servo device such as a step motor,
and the second is to get comfortable!
Whether you are a relative novice, or an experienced hand with
servo tuning, this article will help. It provides an overview of
PID (proportional, integral, derivative) based servo loops, and
introduces two standard manual tuning methods that work well
for a large variety of systems. It will also provide an introduction
to the increasingly popular technique of auto-tuning, which, despite
the name, isn’t necessarily as automatic is it may seem. Finally,
we will look at advanced servo techniques such as feedforward
and frequency domain bi-quad filtering.

Using your in-tune-ition
One of the reasons PID compensators are so popular is that it
is easy to conceive of how each term contributes to the overall
output. The D (derivative) term introduces resistance or drag,
the P (proportional) term introduces a linear restoring force,
and the I (integral) introduces a time-dependent windup term.

more pdf


Tuning a Servo System
Any closed-loop servo system, whether analog or
digital, will require some tuning. This is the process
of adjusting the characteristics of the servo so that
it follows the input signal as closely as possible.
Why is tuning necessary?

A servo system is error-driven, in other words, there
must be a difference between the input and the
output before the servo will begin moving to reduce
the error. The “gain” of the system determines how
hard the servo tries to reduce the error. A high-gain
system can produce large correcting torques when
the error is very small. A high gain is required if the
output is to follow the input faithfully with minimal
error.

Now a servo motor and its load both have inertia,
which the servo amplifier must accelerate and
decelerate while attempting to follow a change at
the input. The presence of the inertia will tend to
result in over-correction, with the system oscillating
or “ringing” beyond either side of its target (Fig. 3.1).
This ringing must be damped, but too much
damping will cause the response to be sluggish.
When we tune a servo, we are trying to achieve the
fastest response with little or no overshoot.

more pdf


Tuning the P.I.D. Loop
There are two primary ways to go about selecting the P.I.D. gains. Either the operator uses a trial and error or an analytical approach. Using a trial and error approach relies significantly on the operator's own prior experience with other servo systems. The one significant downside to this is that there is no physical insight into what the gains mean and there is no way to know if the gains are optimum by any definition. However, for decades this was the approach most commonly used. In fact, it is still used today for low performance systems usually found in process control.

To address the need for an analytical approach, Ziegler and Nichols [1] proposed a method based on their many years of industrial control experience. Although they originally intended their tuning method for use in process control, their technique can be applied to servo control. Their procedure basically boils down to these two steps.
more

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Control Servo Motion Control Tuning the PID Loop

There are two primary ways to go about selecting the PID gains.
Either the operator uses a trial and error or an analytical approach.
Using a trial and error approach relies significantly on the
operator’s own prior experience with other servo systems. The one
significant downside to this is that there is no physical insight into
what the gains mean and there is no way to know if the gains are
optimum by any definition. However, for decades this was the
approach most commonly used. In fact, it is still used
today for low performance systems usually found in process control.
To address the need for an analytical approach, Ziegler and Nichols
[1] proposed a method based on their many years of industrial
control experience. Although they originally intended their tuning
method for use in process control, their technique can be applied to
servo control. Their procedure basically boils down to these two steps.

Step 1:
Set Ki and Kd to zero. Excite the system with a step command.
Slowly increase Kp until the shaft position begins to oscillate.
At this point, record the value of Kp and set Ko equal to this value.
Record the oscillation frequency, fo.

Step 2:

Set the final PID gains using equation (6).



Loosely speaking, the proportional term affects the overall response

of the system to a position error. The integral term is needed to force
the steady state position error to zero for a constant position
command and the derivative term is needed to provide a damping
action, as the response becomes oscillatory. Unfortunately all three
parameters are inter-related so that by adjusting one parameter will
effect any of a previous parameter adjustments. As an example of
this tuning approach, we investigate the response of a Compumotor
BE342A motor with a generic servo drive and controller.

This servomotor has the following parameters:

Motor Total Inertia J = 50E-6 kgm^2
Motor Damping b = .1E-3 Nm/ (rad/sec)
Torque Constant Kt = .6 Nm/A

We begin with observing the response to a step input command with
no disturbance torque (Td = 0).

Step 1:
Fig. 2a shows the result of slowly increasing only the proportional term.
The system begins to oscillate at approximately .5 Hz (fo = .5Hz) with
Ko of approximately 5E-5 Nm/ rad.

Step 2:

Using these values, the optimum P.I .D. gains according to
Ziegler-Nichols (Z-N) are then (using equation (6)):

Kp = 3.0E-4 Nm/ rad
Ki = 3.0E-4 Nm/ (rad/sec)
Kd = 7.4E-5 Nm/ (rad/sec)

Fig. 2b shows the result of using the Ziegler Nichols gains.
The response is somewhat better than just a straight proportional gain.
As a comparison, other gains were obtained by trial and error. One set
Of additional gains is listed in Fig. 2b. Although the trial and error gains
gave a faster, less oscillatory response, there is no way of telling if a
better solution exits without further exhaustive testing.

One characteristic that is very apparent in Fig.2 is the length of
the settling time. The system using Ziegler Nichols takes about
6 seconds to finally settle making it very difficult to incorporate
into any highperformance motion control application. In contrast,
the trial and error settings gives a quicker settling time, however
no solution was found to completely remove the overshoot.

Source ( pdf )
http://www.compumotor.com/whitepages/ServoFundamentals.pdf

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Control Servo Motion - Control PIV Control

In order to be able to better predict the system response, an
alternative topology is needed. One example of an easier to
tune topology is the PIV controller shown in Fig.3. This
controller basically combines a position loop with a velocity loop.
More specifically, the result of the position error multiplied
by Kp becomes a velocity correction command. The integral
term, Ki now operates directly on the velocity error instead of
the position error as in the PID case and finally, the Kd term
in the PID position loop is replaced by a Kv term in the PIV
velocity loop. Note however, they have the same units,
Nm/ (rad/sec).

PIV control requires the knowledge of the motor velocity,
labeled velocity estimator in Fig.3. This is usually formed by
a simple filter, however significant delays can result and must
be accounted for if truly accurate responses are needed.
Alternatively, the velocity can be obtained by use of a velocity
observer. This observer requires the use of other state variables
in exchange for providing zero lag filtering properties. In either
case, a clean velocity signal must be provided for PIV control.
As an example of this tuning approach, we investigate the
response of a Compumotor Gemini series servo drive and built in
controller using the same motor from the previous example.
Again, we begin with observing the response to a step input
command with no external disturbance torque (Td = 0).

Tuning the PIV Loop
To tune this system, only two control parameters are needed,
the bandwidth (BW) and the damping ratio (z). An estimate
of the motor’s total inertia, ˆ J and damping, ˆ b are also required
at set-up and are obtained using the motor/drive set up utilities.
Figure 4 illustrates typical response plots for various bandwidths
and damping ratios.

With the damping ratio fixed, the bandwidth directly relates to
the system rise time as shown in Fig.4 a). The higher the bandwidth,
the quicker the rise and settling times. Damping, on the other hand,
relates primary to overshoot and secondarily to rise time. The less
damping, the higher the overshoot and the slightly quicker the rise
time for a fixed bandwidth. This scenario is shown in Fig. 4 b).
The actual internal PIV gains can be calculated directly from
the bandwidth and damping values along with the estimates of
the inertia, ˆ J and motor viscous damping, ˆ b , making their use
straightforward and easy to implement. The actual analytical
expressions are described in equations (7) - (9).

In reality, the user never wants to put a step command into their
mechanics, unless of course the step is so small that no damage
will result. The use of a step response in determining a system’s
performance is mostly traditional. The structure of the PIV
control and for that matter, the PID control is designed to reject
unknown disturbances to the system. Fig.1 shows this unknown
torque disturbance, Td as part of the servo motor model.

Source ( pdf )
http://www.compumotor.com/whitepages/ServoFundamentals.pdf

Control and Automation Home

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