## What is Control Engineering

**Control system engineering** is the branch of engineering which deals with the principles of control theory, to design a system which gives yields the desired behavior in a controlled manner. Hence, although control engineering is often taught within electrical engineering at university, it is an interdisciplinary topic.

Control system engineers analyze, design, and optimize complex systems which consist of highly integrated coordination of mechanical, electrical, chemical, metallurgical, electronic or pneumatic elements. Thus control engineering deals with a diverse range of dynamic systems which include human and technological interfacing. These systems are broadly referred to as control systems.

Control system engineering focuses on the analysis and design of systems to improve the speed of response, accuracy, and stability of the system.

The two methods of control system include classical methods and modern methods. The mathematical model of the system is set up as the first step followed by analysis, designing and testing. Necessary conditions for the stability are checked and finally, optimization follows.

In the classical method, mathematical modeling is usually done in the time domain, frequency domain or complex domain. The 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 the frequency domain to find the open loop gain, phase margin, bandwidth etc of the system. The concept of the transfer function, Nyquist stability criteria, sampling of data, Nyquist plot, poles and zeros, Bode plots, system delays all come under the umbrella of classical control engineering stream.

**Modern control engineering** deals with Multiple Input Multiple Output (MIMO) systems, State space approach, Eigenvalues, 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 the process, will be reduced increasing its quality and productivity.

## History of Control Systems

The application of Automatic control system is believed to be in use even from the ancient civilizations. Several types of water clocks 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 the 19^{th} 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 – a thermostat in 1885. He started the company now named as Honeywell.

The beginning of the 20^{th} 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 the 1920s. Meanwhile, the concept of stability was put forward by Nyquist and followed by Evans. The transforms were applied in control systems by Oliver Heaviside. Modern Control Methods were developed after the 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. The main types of control engineering include:

- Classical Control Engineering
- Modern Control Engineering
- Robust Control Engineering
- Optimal Control Engineering
- Adaptive Control Engineering
- Nonlinear Control Engineering
- Game Theory

### Classical Control Engineering

The systems are usually represented by using ordinary differential equations. In classical control engineering, these equations are transformed and analyzed in a transformed domain. Laplace transform, Fourier transform and z transform are examples. This method is commonly used in Single Input Single Output systems (SISO).

### 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 the frequency domain is not possible. Nonlinearities with multiple variables are solved by modern methodology. State space vectors, Eigenvalues, and Eigen Vectors belong to this category. State Variables describe the input, output and system variables.

### Robust Control Engineering

In robust control methodology, the changes in the performance of the system with the 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 inaccuracies, noises, and disturbances are considered to reduce the fault in the system.

### Optimal Control Engineering

In **optimal control engineering**, the problem is formulated as a mathematical model of the 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.

### 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.

In this kind of controllers, an additional loop for parameter adjustment is present in addition to the normal feedback of process.

### Nonlinear Control Engineering

**Nonlinear control engineering** focuses on the nonlinearities which cannot be represented by using linear ordinary differential equations (i.e. they are not linear control systems). 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 the linear part and the nonlinear part.

### 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 cooperation. The disturbances will try to maximize the cost function. This theory is related to robust and optimal control engineering.