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Welcome to the first lecture on Advance Control Systems. I am Professor Somabath Majhi, department
of Electronics and Electrical Engineering, IIT Guwahati. I have been working in this
department of EEE since 1999. Also I have been teaching this course since last two years.
This course, Advanced Control System, is an advanced level course and prerequisite for
this course is control system engineering. So, prerequisite for this course is control
systems engineering. Basics on control systems theory is required to fully understand the
content of the Lectures. Books or reference books for this course should be Advanced Control
Theory Relay Feedback Approach by S. Majhi, published by Cengage Asia and Cengage India
Private limited in the year 2009. Next reference book would be New Identifications and Design
Methods authored by A. Johnson and H. Moradi published by Springer- Verlag, 2005, next
book would be Control Systems Engineering a basic level book authored by N S Nise and
published by John Willey and Sons, in 2008.
Now, to fully understand the basics of advanced control theory course, one needs to know what
a control theory is. First, for that we shall consider a simple fan speed control system,
given a Fan as a system or process or plant as we are used to call, once it is subjected
to certain input voltage, we speed get some from the fan, that speed is known as actual
speed or output of the plant. Often it is controlled and it is speed can
be controlled by a controller. Now the controller output is designated by U, the Controller
the basic job of a controller is to control the speed of the fan that can be initiated
with the help of the input voltages, when we apply different input voltages different
fan speeds result in. Now, what happens? So, I wish to have a constant
or fixed fan speed, suppose I wish to have 1500 r p m from the fan for that what one
has to do, one need to put a controller in the loop and first sense the speed of the
fan with the help of a speed sensor. The output of a speed sensor will be known as y, the
measured speed that is compared with the reference speed that is known often as desired output
and the differences fed to a controller, then the controller x in such way that the speed
of the fan becomes 1500 r p m exactly provided there are no input fluctuations. So, this
gives basically the structure of a very simple control system, closed loop control systems.
How our course is different from basic control system theory, what is advanced in this control
system theory. The fan dynamics unless we know properly the
dynamics of a fan, it is very difficult to set the parameters of the controller and unless
the parameters of the controller are set accurately it is not often expected to get desired output
from the system; that means, the speed of the fan may not be 1500 r p m for that what
happens it is essential to find accurate model of a fan that comes under identification,
that will be included in this course lectures. How to model, how to properly identify the
dynamics of a plant or fan in this case.
Now, we shall see what are the basic building blocks of a control system. A control system
basic building blocks are comprised of plant as shown over here which is a fan as we have
seen earlier controller which can be made up of electronic components or one can have
software programs for this same as well now, also a sensor which is one of the most important
part of the control loop. So, plant sensor controller is the three basic components of
the building blocks of a basic control system. y a refers to the actual output of the system
for as y is known as the measured output. There could be differences between the two
depending on the accuracy of the sensor. So, it is very essential to model and employ an
accurate sensor for mini control systems.
Now, again coming to the basics of how it is advanced control, what about the advanced
control theory, what is the advanced should be the contents of an advanced control theory.
Lecture one will deal with control configurations first performance description of a control
systems what we mean by control configurations control configurations means where to put
the controller in the closed loop, it can be put in series with the plant process in
tandem with in parallel with or in both way in series feedback combination, that is known
as controller configurations. Next comes the performance description of
a control system. These things we shall learn in Lecture one, where performance description
of a control systems usually are given by time domain and frequency domain measures,
that we shall see study in Lecture two. So, Lecture two will give the performance measures
of a real time control systems in time and frequency domains. In time domain there are
certain things like time domain parameters as we are used to, as we are expected to have
learnt in basic control systems engineering course; those are right time, settling time,
steady state error, decay ratio over shoot, under shoot peak time and so on. So, these
fall under the time domain performance measures of a control system.
Similarly, coming to the frequency domain performance measures we have phase margins,
gain margins phase and gain crossover frequencies and so on. Now these two are very important,
why unless you are happy with the performance measures we need to change the dynamics of
a controller; how the controller dynamics can be changed with the help of typical type
of controllers employed in industries and academia; one of the controllers which is
quite often used in process industries is PID controller, its full form is proportional
integral derivative controller. In lecture three, we shall study in detail
what are different types of PID controller and its variants.
Now, what are PID controllers? To know that, let us see one simple block diagram. A controller
is subjected to error inputs which are made up of the difference between the reference
input and the measured output of a system. So, set point shown over here is nothing but
the reference input and plant output shown over here is the measured output, these are
the two inputs to a controller and the output from the controller is control output. As
we have seen in the fan speed control system, unless the controller is there in the loop
it is very hard to get the desired 1500 r p m from the control system from the fan speed
control system. Now, what are those three components of APID
controller? This is the proportional controller we have, integral control and derivative controller,
all in parallel this form of the PID control is known as parallel PID controller. Now you
see there are some other parameters involved in the control controller structure those
are lambda 1 and lambda 2, depending on various values of lambda 1 and lambda 2, we get the
variants of PID controller, variants means now if I said lambda 1, lambda 2 equal to
1, I get PID parallel form controller; when lambda 1, lambda 2 becomes zero, I get only
PI controller. Similarly various combinations of lambda 1 and lambda 2 will give us variants
of the PID controller. Now why we have the PID controller in this typical form. The main
reason is that we have got some important effects generated by APID controller, those
are derivative kick and integral windup those two actions are not desirable in real time
systems. Therefore, we do have one derivative filter along with the derivative controller,
similarly the integral controller has been put in such a way if you look at this then
you can make out that basically the integral controller is available in the feedback path
of a system, inner feedback path of a system avoiding integral windup action. So, to initiate
anti-integral windup actions one has to have different type of controller configurations.
So, all these things we shall study in lecture three.
Now coming to the next lecture, the fourth one, which has got PID controller design for
single-input single-output processes. What are single-input single-output processes;
you are used that mostly control systems engineering course at basic level deals with single-input
single-output processes. The process is subjected to one p input and one output. So, we shall
discuss in detail difference simple methods available for design of PID controllers based
on the model of dynamic model of SISO processes. Dynamic model of SISO processes can be obtained
by various ways, all those things we shall discuss in subsequent lectures.
Now, coming to Lecture five which is about the design of PID controllers for two input
two output processes. How that is different from single-input single-output process that
can be explained with the help of the block diagram given over here.
So, this block diagram represents the control system for a two input two output process.
Now this G S represents G S represents the two input two output process or plant. So,
if a plant is subjected to interactions from different internal loops that type of processor
plant is known as two multi variable or two input two output plant. These two input two
output plants can be extended to multivariable plants with the help of lots of interactions
within the system. Now, for TITO systems generally two PID controllers
are used for getting satisfactory closed loop performance from the system. So, the two PID
controllers can be designed provided the dynamics of the TITO process is known accurately all
those things can be discussed in lecture five.
After Lecture five we shall have the next lecture on limitations of PID controllers.
Here what are the structural limitations of PID controllers, basic limitations of PID
controllers, why do we have different type of PID controllers then the classical parallel
or series form of PID controller, all those things will be discussed in detail in lecture
six. We will show how PID is unable to perform well for some typical processes like unstable
processes integrating processes, processes possessing double integrators and so on and
what is to be done to overcome the limitations of PID controller.
Lecture seven introduces another form of PID controller often known as PI-PD controller
where the PI controller will be in series with the Plant in the feedback in the feed
forward path whereas, PD controller will be in the feedback path. PI-PD controller for
SISO processes is very important in the sense that this control technique can be used for
controlling a variety of processes, a class of processes that can include stable, unstable
and integrating processes.
What is API-PD controller? The PI-PD controller can be depicted in this form, this block diagram
represents a closed loop system where we have got a controller in the feed forward path
and a controller in the feedback path. The job of this feed feedback controller is
primarily to stabilize the process dynamics. This process could be stable, unstable or
integrating; when it is unstable and integrating unless its dynamics is stabilized or its closed
loop poles are located at some proper locations, often it has been found that it is difficult
to design a suitable controller, a feed forward controller that will meet design specifications.
For that reason there is the need for this PI-PD controller where we shall have a PI
controller in the feed forward path and a PD controller in the feedback path. Now GC
1 can usually be PI or phase-lag type GC 2 is generally of proportional derivative or
proportional derivative time these combinations make and give us PI-PD control.
So, the design of PI-PD controller will be discussed in Lecture seven and we will also
show how the PID controllers outperform the PID controllers. For many SISO processes the
SISO processes shall include stable, unstable and integrating processes in our discussions.
Lecture eight is also about PID controllers design for TITO processes, as we have seen
we can employ two PID controllers for TITO processes, but if two PID controllers can
be employed in place of the PID controllers then it is expected to get improve performances
from the closed loop systems. Lecture nine will introduce effects of measurement
noise and load disturbances in closed loop control system, and also we shall discuss
about measures to deal with effects of measurement noise and load disturbances. Lecture ten will
be on relay control system for identification, what is identification of a system identification,
is meaned by finding the dynamics of a plant or process with available information, any
plant or process is subjected to process input and output; input and output can be collected
and the set of input and output can give us information that can be used for finding the
dynamic model of a process. That is known as identification relay control system, for
identification why relay why not any other mechanism for identification. It is one of
the most simple non-linear devices that can be employed for identification of many systems.
Now, what a relay control system is. Here this block diagram shows a relay in autonomous
closed loop relay is replacing a PID controller and the job of the relay is to find the dynamics
to estimate the dynamic model of a plant. When the relay is put in the closed loop the
plant is expected to get output of this form; look at the output carefully, the output of
the plant when the relay is in the loop becomes oscillatory. So, it gives a typical oscillatory
output a periodic output as well which has got some peak amplitude given by AP the peak
amplitude given by AP and the time period given by two tau. Now the input to the plant
at that time becomes either rectangular or square and that is of this typical form. So,
this relay, a symmetrical relay that can be shown as of this form having amplitude h and
minus h gives us a typical output of the plant. So, this plant output and input information
can be used to find the dynamic model of this plant. Why relay again, this relay is going
to drive the plant action in such a way that its output becomes not only oscillatory, but
becomes periodic and oscillatory. So, when the relay is symmetrical we get some symmetrical
output of this typical form and using the information we can find the dynamic of model
of the plant; now these things will be studied in Lecture ten.
Now, why there is describing function for the relay, the relay can be approximately
represented by some gain known as describing function. Different type of describing functions
for non-linear system also will be discussed in this lecture.
Lecture eleven will be on DF of the relay describing function of a relay and we shall
discuss what are critical gain critical period of the output of a plant when relay is in
the closed loop and we shall also try to estimate process model parameters assuming certain
form of the process dynamics. A process dynamics can be assumed in the form of either first
order plus delay transfer function form given as ke to the power of minus theta s upon T
1 s plus 1 where theta represents the time delay of a Process model, k is the steady
state gain, t one is the time constant of the first order process model. Similarly we
can have a second order plus time delay model for the dynamics of stable unstable and integrating
Plants that can be given as ke to the power minus theta s T 1 s plus1 s and T to s plus
1. So, this gives the transfer function model of a stable second order plus time delay Plant.
Now, when I put minus over here I get an unstable second order transfer function model and when
we limit the values of T 2 to infinity T 2 tends to infinity such that k of n T 2 tends
to some finite value, in that case we get a transfer function model that can be shown
as ke to the power of minus theta s s upon T 2 s plus one that gives us a model transfer
function model for integrating second order Plant. So, all these are all these transfer
function models can be realized from the basic second order plus time delay model that is
why it is known as the general second order plus time delay model for different type of
Plants. Lecture twelve will discuss about the offline
and online identification. What are offline and online identification, in the offline
identification the controller is replaced by relay and the parameters of dynamic model
of the plants are estimated first then the controller parameters are tuned based on the
acquired model, that is known as offline identification and tuning of controller. In the offline identification
the controller will be replaced by the relay whereas, in the online identification the
controller will always be in action, will be in the loop and the relay will be connected
in parallel with the controller that gives us online identification schemes for different
type of closed loop control systems. Now, again using the describing function method
we shall try to identify the parameters of a model based on offline identification scheme.
Lecture thirteen will be on online identification of stable unstable and integrating Plants
where the controller will always be in action along with relay at the time of identification
and once the identification process is over then the relay will be taken out of the loop
thus giving us the normal operation of the closed loop system.
Now, going to the next Lecture, Lecture fourteen will be based on basically analytical expressions
for online identification of stable unstable and integrating plants .We shall assume some
specified form of transfer function models and we will try to estimate the unknown parameters
of the models. So, analytical expressions will be based on describing function analysis.
Next, model parameter accuracy and sensitivity will be discussed in Lecture fifteen. These
two things are very important whether our identification schemes are giving us desired
results or not that can be ascertained from the study of accuracy and sensitivity of the
identification methods .
Now, next lecture shall be on effects of static load and measurement noise disturbances during
the identification tests we shall make use of some simulation studies to see how our
identification schemes are giving us results in the phase of static load disturbances or
low frequency noise disturbances and measurement noise disturbances known as high frequency
disturbances. Now to elevate those problems there are certain techniques one can make
use of 4ier series or wavelet based techniques to get rid off of problems associated with
the output of a plant which is subjected to static load and measurement noise disturbances.
All those things will be studied in lecture sixteen and finally, in lecture seventeen
we shall have reviews of describing function based identification methods.
Lecture eighteen will be on time domain based identification. We shall make use of state
space analysis techniques for identification and accuracy in identification will be discussed
as well using the technique of small value theorem.
Now, Lecture nineteen will be analytical expressions for identification of stable unstable and
integrating plants. The analytical expressions will be based on the shape of the output the
shape of the output of the plant which is subjected to a relay feedback. As we have
seen earlier the output will be mostly of a symmetrical periodic output with certain
peak amplitude and period. So, based on the peak amplitude and period one can estimate
the model parameters of stable, unstable and integrating plants, but based on the shape
of the output one can also derive a number of analytical expression, those expressions
can be used further for estimation of the unknown plant model parameters. So, we shall
make use of state space analysis to obtain the analytical expressions based on the shape
of the output oscillatory output from the plants. Next we shall also derive a set of
general analytical expressions that can be made use of for identifying stable, unstable
and integrating plants. Why those are known as general analytical expressions, the analytical
expression need not be derived one each for stable or unstable or integrating plants rather
the same set of expressions with certain limiting values can be used to estimate the unknown
parameters. Lecture twenty-one will be on special case
like a plant having multiplicity of a Pole which can be shown as ke to the power minus
theta s T 1 s plus minus 1 to the power n this is known as the plan model having multiplicity
of poles where n can assume various values starting from two three onwards.
So, we shall have a few more special cases on this when n equal two. When n equal to
three, what should be the analytical expressions and how we can solve the set of analytical
expressions using a certain non-linear equation solvers and find the unknowns of the plant
model parameters which are K theta T 1 and n. Again we shall deal with another special
case a plant model with right half plant pole which can again be shown as k minus t zero
s plus one upon t one s plus one to the power n. So, here this type of plant model is supposed
to have model with right half plant poles.
Next Lecture will also deal with a special case plant having complex conjugate poles.
In this case when the T 1 n T 2 we have been discussing so far, when they become complex
or complex numbers in that case the plant model are often given in the form of ke to
the power minus theta s a square plus b s plus one and. So, where b is such that we
get under damped action given or shown by these types of models. So, this is also falling
under one special case and we shall try to derive a set of analytical expressions for
such cases. Next we shall study estimation of dead time
parameter of a transfer function model. A second order transfer function model can have
three to four unknowns, if some of the unknowns can be estimated by some others technique
then that will reduce the burden on us in estimating the number of unknowns. It has
been found that some other simple techniques can be made use of to estimate some of the
known unknowns of the second order transfer function model. Dead time parameter which
is often given as theta in all Lectures can be estimated by some other techniques considering
the output symmetrical output of the plant subjected to relay feedback using some derivative
of the output signal and so on and zero crossings we can easily find this unknown parameter
of the model transfer functions. So, that will be discussed in Lecture twenty-four.
Lecture twenty-five will be on exactness of identification in the phase of measurement
noise and static load disturbances. So, accuracy of identification can be studied in this Lecture.
Now, next lecture will be on time domain based offline and online identification. Now offline
identification of SISO plant models can be extended for TITO plant models, that we shall
see in the lectures twenty seven and twenty eight.
Then we shall review the identification schemes based on state space or time domain before
going to the next lecture which is on model-tree controller design. After identification phase
is over, we shall go to the controller design. Controllers can be designed by two ways either
model based or model free. In the model free controller design, plant information will
be acquired online and that information will be feed to the controller simultaneously when
the controller is in action. That is known as model free controller design and we shall
see also automatic tuning of industrial controllers and their advantageous and limitations
in Lecture thirty.
Now, some advanced level of controllers to handle plants with long dead time known as
smith predictor controllers will be discussed in the three lectures, Lecture thirty-five,
thirty-six and thirty-seven. Here we shall present one Advanced Smith predictor controller
which can be used for controlling stable, unstable and intergrading plants.
The smith predictor controller can give us freedom to tune various controllers independently. That is one of the benefits
of the advanced smith predictor controller. Standard form based controller design will
be made use of while designing the controllers of advanced smith predictor and controller.
Standard forms based controller design techniques have not drawn the attention it deserves.
We shall show how simple the technique is and how standard form based controller design
can give better results compared to some existing one. Then online controller of smith predictor
control structure also will be discussed employing relay in tandem with in tandem or in parallel
with the controller in Lecture thrity-seven.
In Lecture thirty-eight, we shall discuss about software and hardware implementation
of PID controller and its variants. Software implementation of PID controller is relatively
easy. Coming to the hardware implementation one can have analog PID controller, digital
controller and so on. Digital PID controllers can be effected with the help of many processors,
DSP processors, FPGA and so on whereas; analog PID controller can be designed using field
programmable analog arrays. We shall see in Lecture thirty-nine, how in real time one
can make use to field programmable analog arrays to design analog PID controllers. There
we shall also study how that is superior to field programmable gate array based digital
PID controllers.
In the hardware implementation using op-amp or so, we can have various form of PID controllers
as you can see over here, a PI controller can be realized using op-amp, resistor, capacitor
and resistor connected in the typical fashion. This gives us the realization hardware realization
of a PI controller whereas, the bottom one can be made use of the design of PD controller
based on the op-amp, resistor, capacitor and capacitor and the way one can find the transfer
function of the controllers is given over here. It is very to derive all those expressions.
So, one can design PI, PD or their combinations using op-amp or operational amplifiers. This
is how we get in hardware the implementation of PI,PD and PID controllers.
In FPAA field programmable analog array based controller design, one has to know the structure
of FPAA based controllers. So, one has to go through the modules given in the package
and then design FPAA based controllers. So here, this part actually gives us the PID
controller action and relay is shown over here. When relay is there, there are choices
to design offline and online PID controllers based on the acquired plant information. Now
that is all about the content of this course advanced control systems. In nutshell, it
can be summarized in this fashion what we are expected to learn from this course. First
of all, this course will introduce us certain classical control theory, PID controllers
and their limitation, PI-PD controller overcoming the structural limitations of PID controller.
Then we have also the control configurations for controlling two input two output processes
which can ultimately be extended to control of multi variable processes.
Now, next we shall learn in the course what a relay control system is and how that is
useful for identification of plant dynamics. Relay control using describing function analysis
and using state space analysis will be studied. Next we shall learn offline and online identification
of systems offline and online tuning of controllers. Lastly, we shall learn how to implement controllers
in real life and how real time controller can be developed, how real time control systems
can be developed. That is all about this course Advanced Control Systems.