IMC based PID Controllers Retuning and It’s Performance Assessment

M.Divya O.Saraniya
Dept. of Electronics and Comunication Engineering Dept. of Electronics and Comunication Engineering
Government College of Technology Government College of Technology
Coimbatore, Tamilnadu, India Coimbatore, Tamilnadu, India
divyaaa.murugan@@gmail.com deepap05@gmail.com

methodologies. IMC is a commonly used technique, which

Abstract— Internal Model Control (IMC) is the provides a transparent mode for various types of control
basis of a systematic program Q on the parameters of the
concept and is based on the many modern control technology design and tuning. The proportional-integral (PI), in order to
control system design. The present research work presents a meet the target of most of the control capacity and
novel control scheme for tuning PID controllers using Internal proportional - integral - derivative (PID) controllers, leading to
Model control with the filter time constant optimized using its widespread acceptance in the control industry. Internal
Bee colony Optimization technique. The robustness is Model Control (IMC) based approach to the design of the
measured by a two-block structured singular value, and the controller is using the IMC, which is equivalent to the use of
disturbance rejection is measured by the minimum singular one of the IMC PID control in industrial applications. IMC
value of the integral gain matrix. PID controllers are used allows a transparent controller design procedure where control
widely in Industrial Processes. Criteria based on disturbance quality and robustness are influenced in a direct manner. The
rejection and system robustness are proposed to assess the IMC concept was conceptualized by approximating the
performance of PID controllers. Tuning of PID controllers is feedback transfer function by Maclaurin’s series. the PID
accomplished using Internal Model control scheme. In this controller usually requires some a prior manual retuning to
paper, we propose an optimal filter design IMC IMC-PID make a Successful industrial application. To bypass this
controller for unstable process better set point tracking. IMC obstacle, an adaptive PID (APID) controller is proposed in this
includes tuning of filter constant λ. The controller is suitable paper which is composed of a PID controller and a fuzzy
for different values of the filter tuning parameters to achieve compensator. Without needing introductory offline learning,
the desired response in due IMC method is based on pole-zero the PID controller can automatically online tune the control
offset, including IMC design principle method causes the gains located on the gradient descent method and the fuzzy
response sets a good point. However, in a stable long lag time compensator is designed to eliminate the effect of the
of load disturbances leading to undesirable process which is approximation errors introduced by the PID controller upon
the result of the IMC control industry. Therefore, IMC has the system stability in the Lyapunov sense. PID controllers
been a popular design process processing industry, especially are widely used as the preferred controller approach due to
as a means for adjusting the single-loop, PID controllers. their design simplicity and its reliable operation. The Tuning
approaches can be detached into two groups which are the
Keywords — Internal Model Control, PID controller, Bee conventional and the alternative approaches. Time delay
colony optimization, Filter constant, Q-parameters. degrades the performance of control system in many industrial
application. That too when the time delay is very large, PID
controller degrades. The conventional outlooks include the
I. INTRODUCTION & RELATED WORK observed methods and the methodical methods which widely
used by control designers. The possible approaches are
restricted to methods that employ the stochastic process in the
During the past decades, the process control
tuning rules.
techniques have made great advance. Numerous control
Yu Z. Wang et.al., [1] the paper presents the industrial
methods like adaptive control, neural control, fuzzy logic
control, ANFIS control are developed. Still, PID controllers feedback control loops, setpoint changes are often in the form
are considered as the workhorse of almost all the industrial of step, ramp or other general types, and controllers are
process control applications due to their structural simplicity usually restricted to the PID form. This paper establishes the
and robust performance in a wide range of operating condition
. PID controller mainly depends on tuning of the gains the lower bounds of integrated absolute errors (IAEs), based on
proportional gain, integral time and the derivative time. the widely-used internal model control (IMC) principle, from
Tuning the PID controller gains play a major role in deciding closed-loop responses subject to these setpoint changes.
the performance. Literature provides many tuning
Taking the lower bound as a benchmark, an IMC-IAE-based
XXX-X-XXXX-XXXX-X/XX/$XX.00 ©20XX IEEE
index is proposed to assess the performance of PID index is proposed to assess the performance of PID
controllers. Numerical and experimental examples, as well as controllers. Numerical and experimental examples, as well as
an industrial case study, are provided to verify the lower an industrial case study, are provided to verify the lower
bound as the performance benchmark, and to illustrate the bound as the performance benchmark, and to illustrate the
effectiveness of using the proposed index for performance effectiveness of using the proposed index for performance
assessment of PID control loops assessment of PID control loops.
B.K. Panigrahi et al., [2] the research work presents a novel J.G. Ziegler, [5]  the paper discusses the concept and design
control scheme for tuning PID controllers using Internal procedure of genetic algorithm as an optimization tool.
Model control with the filter time constant optimized using Further, the paper reconnoiters the deep-rooted methodologies
Bee colony Optimization technique. PID controllers are used of the literature to realize the workability and applicability of
widely in Industrial Processes. Tuning of PID controllers is GA for process control applications. The simulation result
accomplished using Internal Model control scheme. IMC showed better optimization of hybrid genetic algorithm
includes tuning of filter constant λ. Compromise is made in controllers than fuzzy standalone and conventional
selecting the filter constant λ since an increased value of λ controllers.
results in a sluggish response whereas decreased value of filter Maher M.F. Algreer [6], the research aims at manually carrying
constant leads in an aggressive action. In the present work, an through the optimization of the experimental way adopted for
attempt has been made to optimize the value of the λ by Bee traditional PID controller parameters, an optimization method
colony optimization technique. Simulation results show the based on improved ant colony optimization for PID
validity of the proposed scheme for the PID controller tuning. parameters of BP neural network presented. The results shown
D. Prasanth Sai, [3] the paper presents the Internal Model by numerical simulation that the optimization strategy on PID
Control (IMC) is the basis of a systematic program Q on the parameters as stronger pliability and adaptability and are
parameters of the concept and is based on the many modern further verified practicability and validity of proposed method.
control technology control system design. What makes IMC Te- Jen Su, et al., [7]the paper describes an efficient and fast
particularly attractive is that it presents a method to design the tuningmethod based on modified genetic algorithm (MGA) str
Q-parameterization controller has two basic demands of ucture to find the optimal parameters of the proportional-
reality. Therefore, IMC has been a popular design process integral-derivative(PID) controller so that the desired system
processing industry, especially as a means for adjusting the specifications are contended. To demonstrate the effectiveness
single-loop, PID controllers. In this paper, we propose an of presented method, the step responses of closed loop system
optimal filter design IMC IMC-PID controller for unstable were compared with that of GA. Simulation
process better set point tracking. The controller is suitable for of the PID controlled system can be significantly improved by
different values of the filter tuning parameters to achieve the the MGA- based method.
desired response in due IMC method is based on pole-zero Zhou Ying , [8] the paper described an efficient and fast
offset, including IMC design principle method causes the tuning method based on modified genetic algorithm (MGA)
response sets a good point. However, in a stable long lag time structure to catch the optimal parameters of the proportional-
of load disturbances leading to undesirable process which is integral-derivative(PID) controller so that the anticipated
the result of the IMC control industry. system specifications were satisfied. To exhibit the
Zhenpeng Yu, [4] the research represents the industrial effectiveness of presented method, the step responses of closed
feedback control loops, setpoint changes are often in the form loop system were compared with that of GA. Simulation
of step, ramp or other general types, and controllers are results indicated that the performance of the PID controlled
usually restricted to the PID form. This paper establishes the system can be significantly improved by the MGA- based
lower bounds of integrated absolute errors (IAEs), based on method.
the widely-used internal model control (IMC) principle, from Ahmed Rubaai , [9] the paper represented a hybrid model
closed-loop responses subject to these setpoint changes. Sugeno fuzzy logic to regulate the optimal parameters of a pro
Taking the lower bound as a benchmark, an IMC-IAE-based portional (PID)controller. The approach used the rule base of
the Sugeno fuzzy system and fuzzy PID controller of the is used to develop an efficient face spoof detection approach.
automatic voltage regulator (AVR) to progress the system As per the experiments conducted it is seen that to detect the
sensitive response. The rule base was developed by proposing face spoofs of both, cross-database and intra-database testing
a feature mining for genetic neural fuzzy PID controller environments, the proposed approach provided effective
through integrating the GA with radial basis function neural results. There were around 20 participants included within the
network. The GNFPID controller was found to possess evaluations which showed that the performance of proposed
excellent features of easy implementation, stable convergence approach within real applications was very good. Alotaibi and
characteristic, good computational efficiency and high-quality Mahmood et.al ,proposed an efficient mechanism using static
solution. It was asserted that GNFPID was highly efficient and frame of sequenced frames in order to solve the face spoofing
robust in refining the sensitive response of an AVR system. attack issues. For creating a speed-diffused image, an AOS-
Lalit Chandra et al., [10] presented the controller gains were based scheme was applied along with a large time step size.
optimized using a more recent powerful evolutionary The sharp edges and texture features present within the input
optimization technique called "Cuckoo Search". Investigations image are extracted by applying large time step parameter.
revealed that When the input video was recaptured twice, it was seen that
in presence of BES obtained at nominal conditions and at around the eyes, nose, lips and cheek areas, there were few
nominal parameter was robust and needed not be reset to sharp edges and flattened regions present within the fake face
uncertain change in system loading, inertia constant and images. Thus, the sharp edges were destructed and the
location and magnitude of step load perturbation. locations of pixels were changed due to this. The edges were
K. Prem Kumar [11], the paper describes two different speed destroyed using a large time step. The sparse auto-encoder was
controllers i.e., fuzzy online gain tuned anti wind up to be explored such that a diffused frame could be achieved in
Proportional Integral and Derivative (PID) controller and the future work. Therefore, the diffused frame would be
fuzzy PID oversees online ANFIS controller for the speed generated to be given to the deep CNN network by generating
control of brushless dc motor had been proposed. In order to an auto-encoder within the overall architecture within the
approve the effectiveness of future work.
the brushless dc motor was operated under constant loadcondit Shervin, et.al presented a study related to the issues faced
ion, varying load conditions and varying set speed conditions. when detecting the face spoof. It is possible to include new
The simulation results under MATLAB environment have means of spoofing attackers as per the various observations
pictured better performance with fuzzy PID managed online made. The image sensor inter-operability issue and the
ANFIS controller under all running conditions of the drive, minimal size of a sample are few of the issues that have come
position of LED match, the direction of eye is observed once forward within this work. This paper initially proposed a new
the selected LED is activated. The data that includes liveness evaluation protocol through which the effects of unseen attack
information is given as output by the algorithm in case if the types could be known on the basis of certain existing factors.
compliance’s needs are satisfactory. High success ratio is This paper proposed a novel and highly realistic formulation
achieved as per the experiments conducted using this proposed of the spoofing detection issue with respect to the conceptual
approach. Keyurkumar, et.al presented a study on the innovations. To train the systems, only the positive samples
smartphone unlock systems that are today very popular within were needed by the new formulation. Towards the end, the
several mobile phones and also within the systems that include experiments conducted showed that there was still the need to
mobile payments. An unconstrained smartphone spoof attack improve the detection rates since the performance of both the
database (MSU USSA) that includes not less than 1000 schemes was not up to the mark.
subjects is generated here. Using the front as well as rear
camera of a smartphone, the images of print and replay attacks 1.2. IMC TUNING RULE FOR PID CONTROLLERS
are gathered. Various intensity channels, image areas, as well
as feature descriptors are used for analyzing the image The PID controller based on the IMC tuning rule
distortion of print and replay attacks. The Android smartphone usually leads to a control loop with a good balance among
setpoint tracking, disturbance rejection and robustness, and has
been widely adopted in industrial practice for years. From fig
1.2.1 representing the block diagram , the IMC tuning rule for
PID controllers is briefly reviewed. Fig. 1. A SISO feedback
control loop Consider a SISO feedback control loop depicted
in Fig. 1. Here P(s) and C(s) are the process and the PID
controller, respectively; r(t), u(t) and y(t) are the setpoint, the Fig 1.2.2 . Closed-loop Systems
control signal, and the process output, respectively. In this
context, P(s) is confined to be a process that is stable, without Fig 1.2.2 represents the closed loop system where a simple
integrals and negative zeros; hence, the process can be PID structure consists of three terms which are Kp, Ki and Kd
approximated by a first-order plus dead time (FOPDT) model, referring to Proportional ,integration and derivative gains
P(s) = K T1s + 1 e −θs , (1) or a second-order plus dead time respectively. The parallel design of PID controller (after this
(SOPDT) model, P(s) = K T1s 2 + T2s + 1 e −θs . (2) As θ is refers as PID controller)sums the all the error signal, e(t) after
crucial to the subsequent performance index, it is worthy to being multiplied by PID gains, Kp, Ki and Kd to produce the
mention that θ is the time delay of the low-order model (1) or input signal, u(t).The adjustment process of the values
(2), instead of the time delay of the actual process. For
instance, the positive zero of a process can be removed by
lumping it into the time delay part of a low-order
approximated model . The PID controller C(s) takes a non-
interactive formulation, C(s) = Kp 1 + 1 Tis + Tds . (3) The
IMC tuning rule gives the controller setting for the FOPDT
Fig 1.2.3 . Performance Assessment of Closed-loop
model as Kp = T1 K(τc + θ) , Ti = T1, Td = 0, and that for the
Systems
SOPDT model as Kp = T2 K(τc + θ) , Ti = T2, Td = T1 T2 .

 Kp , Ki and Kd  is called‗tuning‘ or ‗design‘ of PID

controller. The Tuning approaches can be detached into two
groups which are the conventional and the alternative
approaches. The conventional outlooks include the observed
Fig 1.2.1 . Block Diagram Of Imc Tuning
methods and the methodical methods which widely used by
control designers. The possible approaches are restricted to
(4) By taking the IMC tuning rule, the desired closed-loop
methods that employ the stochastic process in the tuning
response will be GCL(s) = 1 (θ + τc)s + e−θs e −θs ≈ 1 τcs + 1
rules .Stochastic process mentions to one whose behaviour is
e −θs . (5) Here the user-selected parameter τc stands for the
non-deterministic, where any of its sub-system resolute by
desired closed-loop time constant.
the process of deterministic action and a random behaviour.
The PID control strategy is named after its three modifying
II. PERFORMANCE ASSESSMENT OF CLOSED-LOOP SYSTEMS terms, whose sum integrates the manipulated variable (MV).
From the fig 1.2.3 Performance Assessment of Closed-loop
Systems , the proportional, integral, and derivative terms are
It is well-known that a well-designed control system should
computed to calculate the output of the PID controller.
meet the following requirements besides nominal stability:
Representing u(t) as the controller output, the final form of the
• Disturbance attenuation
PID algorithm is:
• Setpoint tracking
• Robust stability and/or robust performance The first two
requirements are traditionally referred to as ‘performance’ and
the third, ‘robustness’ of a control system.
 parameter the filter constant. Consider a linear transfer
function model of the process.

II.INTERNAL MODEL CONTROLLER BASED PID DESIGN

Internal Model Controller involves a model based

Where: Proportional gain, a tuning parameter: Integral gain, a procedure, where the process model is embedded in the
tuning parameter: Derivative gain, a tuning parameter: Error: controller. IMC involves a single tunable parameter the filter
Time or instantaneous time (the present) , Շ= Variable of constant. Consider a linear transfer function model of the
integration; takes on values from time 0 to the present time t. process. Figure 1 shows the block diagram of the IMC
Various combinations of P, I, & D can be used according to structure. Internal Model controller involves a model based
the requirement is various tuning strategies based on an open- procedure, where the process model is embedded in the
loop step response. controller. IMC involves a single tunable parameter the filter
constant. The time delay estimation has been an interesting
research topic for years in various areas; see a recent survey in
[9]. However, most of the existing methods have their own
limitations; in particular, extra experiments are usually
required to introduce special signals such as white noise to
excite the unknown process. By contrast, it is desired for
industrial practice to estimate θ based on the closed-loop step,
ramp or some other simple response, without introducing extra
experiments.
• The appearance of τc makes ηIAE a user specified
benchmark, which is indeed an advantage comparing to the
Table 1 . Control actions
MVC benchmark. In other words, users can determine τc as
While they all follow the same basic idea from the above table
the desired closed-loop time constant, and evaluate the
1 of the control actions, they differ in slightly in how they
performance of the current control loop against the desired
extract the model parameters from the recorded response, and
one. However, an improper selection of τc could make ηIAE
also fluctuate marginally as to relate appropriate tuning
too large or too small, leading to erroneous conclusion on the
constants to the model parameters. There are four different
control-loop performance. A fair selection of τc is to take the
methods, the classic Ziegler-Nichols open loop test, the
current closed-loop time constant (to be estimated based on the
Cohen-Coon test, Internal Model Control (IMC) and
collected data) as τc. If ηIAE → 1, the current control-loop
Approximate M-constrained Integral Gain Optimization
performance is close to the expected by using the IMC-tuning
(AMIGO). Naturally if the response is not sigmoidal or ‗S‘
rule. Note that ηIAE = 1 is achievable in practice, while the
shaped and exhibits overshoot, or an integrator, then this
MVC based index for PID control loops is usually quite far
tuning method is not applicable. Internal Model Controller
away from 1 even though the control-loop performance is
involves a model based procedure, where the process model is
satisfactory. Another practical issue is about the noise effect
embedded in the controller. IMC involves a single tunable
on ηIAE. First, the noise affects the estimates of τc and θ,
parameter the filter constant. Consider a linear transfer
whose accuracies are up to the open- and closed-loop
function model of the process. Figure 1 shows the block
identification techniques. Thus, the quality control of the two
diagram of the IMC structure. Internal Model controller
estimates are out of context here. Second, the noise affects
involves a model based procedure, where the process model is
also the calculation of the actual IAE, and may result in an
embedded in the controller. IMC involves a single tunable
incorrect estimate of ηIAE, despite a fact that the summation
in (14) may enable ηIAE somehow robust to noise. To resolve design 1. Find the IMC controller transfer function, q(s),
this issue, the noise-free closed-loop response yˆ(t) is obtained, which includes a filter, f(s), to make q(s) semiproper or to give
i.e., Yˆ (s) = Pˆ(s)C(s) / 1 + Pˆ(s)C(s) R(s). Based on yˆ(t) and it derivative action (order of the numerator of q(s) is one order
r(t), a noise-free estimate of ηIAE can be calculated. greater that the denominator of q(s)). Notice that this is a
major difference from the IMC procedure. Here, in the IMC-
III. IMC STRATEGY
based procedure, we may allow q(s) to be improper, in order to
The process output, y(s), is compared with the output find an equivalent PID controller. The bad news is - you must
of the model resulting in the signal d*(s). know the answer that you are looking for, before you can
decide whether to make q(s) proper or improper in this
procedure.

V. EXPERIMENTAL EXAMPLES

This section provides experimental examples to

Fig 3.1 IMC STRATEGY illustrate the procedure of assessing the performance of a PID
In the above figure 3.1, d(s) is the unknown control loop using the proposed IMC-IAE-based index. 18th
disturbance affecting the system. The manipulated input u(s) is IFAC World Congress (IFAC'11) Milano (Italy) August 28 -
introduced to both the process and its model. Hence the September 2, 2011 7489 In the experiments, the process is a
feedback signal send to the controller is d*(s) = [Gp(s) – water tank system, whose cross-sectional area is about 320
Gp*(s)].u(s) + d(s) The error signal r’(s) comprises of the cm2 . The water level of the tank is selected as the process
model mismatch and the disturbances which is send as variable (PV), with the range [0, 100]. The opening of the
modified set-point to the controller and is given by r’(s) = r(s) outlet valve is fixed, while the input valve is driven by a
– d*(s) And output of the controller is the manipulated frequency convertor to control the inlet flow, i.e., the
variable u(s) which is send to both the process and its model. u frequency of the converter is the manipulated variable. The
(s) = r’(s) *Qc(s) = [r(s) – d*(s)] Qc(s) = [r(s)–{[Gp(s)– PID controller is in the non-interactive form . The sampling
Gp*(s)].u(s)+d(s)}] . Qc(s) u (s) = [[r(s)–d(s)]*Qc(s)] / [1+ period is 0.5 sec. Two experiments are performed for two
{Gp(s) – Gp*(s)} Qc(s)] But y(s) = Gp(s) * u(s) + d(s) Hence, different sets of PID controller parameters. In both
closed loop transfer function for IMC is y(s) = {Qc(s). Gp(s). experiments, the setpoint has initially been staying at the value
r(s) + [1 – Qc(s) . Gp* (s)] . d(s)} / { 1 + [Gp(s) – Gp* (s)] 20 for a sufficient long time for the PV to initiate at the steady
Qc(s) } Also improve the system model mismatch effects state. The setpoint experiences a ramp change as r(t) = 20 +
should be minimized robustness. Since mismatch between the 0.8t, 0 6 t < 25, 40, 25 6 t < 250. (17) 0 50 100 150 200 250
model and the actual process usually occurs in the high 300 15 20 25 30 35 40 45 50 55 Time/s Water level of tank
frequency response of the system frequency, the low pass filter Closed loop ramp response Reference Kp=1.2,Ti=10,Td=0
F (s) is added to prevent mismatch of. Therefore, the internal Kp=2.025,Ti=233.94,Td=0 Fig. 4. The ramp setpoint (dashed),
model controller is designed to process model, which in series the measured PV (solid) for Kp = 1.2, Ti = 10 and Td = 0, and
with a low pass filter, i.e. the inverse Q(s) = Qc(s)*f(s) Order the measured PV (dashed-dotted) for Kp = 2.0249, Ti = 233.94
of the filter is selected to be suitable to correct or at least half and Td = 0. In the first experiment, the PID controller
(e.g., the order is equal to the molecular order of the parameters are Kp = 1.2, Ti = 10 and Td = 0, and the
denominator). The resulting closed loop becomes y(s) = corresponding ramp response is shown in Fig. 4 (solid line).
{Q(s) . Gp(s) . r(s) + [1 – Q(s) . Gp* (s)] . d(s)} / { 1 + [Gp(s) Based on this closed-loop ramp response, an FOPDT model
– Gp* (s)] Q(s) }. for the open-loop process is estimated, Pˆ(s) = 5.7256 211.28s
+ 1 e −1.2143s . (18) The current closed-loop time constant is
IV. SYSTEM DESIGN AND IMPLEMENTATION
estimated by fitting another FOPDT model for the closed-loop
The IMC-Based PID Control Design Procedure The
system, τc = 8.8196. Thus, the lower bound of the IAE is IAE0
following steps are used in the IMC-based PID control system
= 200.6780. As the actual IAE of the response is 742.3969, the
IMC-IAE-based index is ηIAE, y(t) = 0.2703. To avoid an VI. CONCLUSION
incorrect estimate of ηIAE due to the noise, a noise free
In the proposed method, This paper established the
closed-loop response yˆ(t) is obtained as described in Section
lower bound of the IAE for PID controllers tuned by following
3, based on Pˆ(s) in (18) subject to the same setpoint r(t) in
the IMC principle, from closed-loop responses subject to step,
(17); the resulted IAE (based on yˆ(t) and r(t)) is 681.1547 and
ramp or other types of setpoint changes. Based on the lower
the IMC-IAE-based index is ηIAE, yˆ(t) = 0.2946. The two
bound, an IMC-IAE-based index was proposed in (14) to
indices are close to each other, saying that the current control-
assess the performance of PID control loops. Numerical
loop performance has a quite large space for improvement. All
examples validated the obtained lower bound as the
these results are summarized in Table 3 for clarity. In the
performance benchmark. Experimental examples and an
second experiment, a different set of PID controller parameters
industrial case study illustrated the effectiveness of the IMC-
is adopted, Kp = 2.0249, Ti = 233.94 and Td = 0.
IAE-based index. The IMC and IMC-based PID controller can
successfully achieve any industrial process because it is
present in the plant uncertainty parameters sufficiently strong.
IMC-based PID controller algorithm is robust and simple
processing model uncertainty, therefore, IMC-PID tuning
method seems to be a useful tradeoff between performance
Table 4.1 Experimental examples closed-loop systems, we achieved robust build inaccurate
The resulted ramp response experiences little overshooting, single-mode tuning parameters. It also provides a good
(dashed-dotted line). Based on this closed-loop ramp response, solution in the process of a significant time delay is actually
an FOPDT model for the open-loop process is estimated, Pˆ(s) working in the real-time situation. IMC has to compensate the
= 6.6469 241.3700s + 1 e −1.1122s . model uncertainty and disturbance open-loop control does not
have the ability to attach advantage.

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