Control
Engineering
Control system engineering focuses on analysis and design of
systems to improve the speed of response, accuracy and stability of system. The
two methods of control system include classical methods and modern methods. The
mathematical model of system is set up as first step followed by analysis,
designing and testing. Necessary conditions for
the stability are checked and finally optimization follows.
In
classical method, mathematical modeling is usually done in time domain,
frequency domain or complex s domain. Step response of a system is
mathematically modeled in time domain differential analysis to find its
settling time, % overshoot etc. Laplace
transforms are
most commonly used in frequency domain to find the open loop gain, phase
margin, band width etc of system. Concept of transfer function, sampling of
data, poles and zeros, system delays all comes under the classical
control engineering stream.
Modern control engineering deals with Multiple Input Multiple
Output (MIMO) systems, State space approach, Eigen values and vectors etc.
Instead of transforming complex ordinary differential equations, modern
approach converts higher order equations to first order differential equations
and solved by vector method.
Automatic control systems are most commonly used as it does not involve manual
control. The controlled variable is measured and compared with a specified
value to obtain the desired result. As a result of automated systems for
control purposes, the cost of energy or power as well as the cost of process
will be reduced increasing its quality and productivity.
Historical Review of Control Engineering
The application of Automatic control system is believed to be in use even from
the ancient civilizations. Several types of water clock were designed and
implemented to measure the time accurately from the third century BC, by Greeks
and Arabs. But the first automatic system is considered as the Watts Fly ball
Governor in 1788, which started the industrial revolution. The mathematical
modeling of Governor is analyzed by Maxwell in 1868. In 19th century,
Leonhard Euler, Pierre Simon Laplace and Joseph Fourier developed different
methods for mathematical modeling. The second system is considered as Al Butz’s
Damper Flapper - thermostat in 1885. He started the company now named as
Honeywell.
The
beginning of 20th century is known as the golden age of control
engineering. During this time classical control methods were developed at the
Bell Laboratory by Hendrik Wade Bode and Harry Nyquist. Automatic controllers
for steering ships were developed by Minorsky, Russian American Mathematician.
He also introduced the concept of Integral and Derivative Control in 1920s.
Meanwhile the concept of stability was put forward by Nyquist and followed by
Evans. The transforms were applied in control system by Oliver Heaviside.
Modern Control Methods were developed after 1950s by Rudolf Kalman, to overcome
the limitation of classical Methods. PLC’s were introduced in 1975.
Types of Control Engineering
Control engineering has its own categorization depending on the different
methodologies used, which are as follows.
1. Classical
Control Engineering : The systems are usually represented by using ordinary
differential equations. In classical control engineering, these equations are
transformed and analyzed in transformed domain. Laplace transform, Fourier transform and z transform are
examples. This method is commonly used in Single Input Single Output systems.
2. Modern Control Engineering
: In
modern control engineering higher order differential equations are converted to
first order differential equations. These equations are solved very similar to
vector method. By doing so, many complications dealt in solving higher order
differential equations are solved. These are applied in Multiple Input Multiple
Output systems where analysis in frequency domain is not possible.
Nonlinearities with multiple variables are solved by modern methodology. State
space vectors, Eigen values and Eigen Vectors longs to this category. State
Variables describe the input, output and system variables.
3. Robust Control Engineering
: In
robust control methodology, the changes in performance of system with change in
parameters are measured for optimization. This aids in widening the stability
and performance, also in finding alternate solutions. Hence in robust control
the environment, internal in accuracies, noises and disturbances are considered
to reduce the fault in system.
4. Optimal Control Engineering : In optimal
control engineering, the problem is formulated as mathematical model of
process, physical constraints and performance constraints, to minimize the cost
function. Thus optimal control engineering is the most feasible solution for
designing a system with minimum cost.
5. Adaptive Control Engineering
: In
adaptive control engineering, the controllers employed are adaptive controllers
in which parameters are made adaptive by some mechanism. The block diagram
given below shows an adaptive control system.
6.
In this kind of controllers an additional loop for parameter adjustment is
present in addition to the normal feedback of process.
7. Nonlinear
Control Engineering : Non linear control engineering focuses on the non
linearity’s which cannot be represented by using linear ordinary differential
equations. This system will exhibit multiple isolated equilibrium points, limit
cycles, bifurcations with finite escape time. The main limitation is that it
requires laborious mathematical analysis. In this analysis the system is
divided into linear part and non linear part.
8. Game Theory
: In
game theory, each system will have to reduce its cost function against the
disturbances / noises. Hence it is a study of conflict and co operation. The
disturbances will try to maximize the cost function. This theory is related to
robust and optimal control engineering.