### Classification of Control Systems

Broadly control system can be classified as,
1) Natural Control Systems : the biological systems, systems inside human being are of natural type.
Example 1 : The perspiration system inside the human being is a good example of natural control system. This system activates the secretion glands, secreating sweat and regulates the temperature of human body.
2) Manmade Control Systems : The various systems, we are using in our day to day life are designed and manufactured by human beings. Such systems like vehicles, switches, various controllers etc. are called manmade control systems.
Example 2 : an automobile system with gears, accelerator, braking system is a good example of manmade control system.
3) Combinational Control Systems : Combinational control system is one, having combination of natural and manmade together i.e. driver driving a vehicle. In such system, for successful operation of the system, it is necessary that natural systems of driver alongwith systems in vehicles which are manmade must be active.But for the engineering analysis, control systems can be classified in many different ways. Some of the classifications are given below.
4) Time Varying and Time – Invariant Systems : Time varying control systems are those in which parameters of the systems are varying with time. It is not depending on whether input and output are functions of time or not. For example, space vehicle whose mass decreases with time, as it leaves earth. The mass is a parameter of space vehicle system. Similarly in case of a rocket, aerodynamic damping can change with time as the air density changes with the altitude. As against this if even though the inputs and outputs are functions of time but the parameters of system are independent of time, which are not varying with time and are constants, then system is said to be time invariant system. Different electrical networks consisting of the elements as resistances, inductances and capacitances are time invariant system as the values of the elements of such system are constant and not the functions of time. The complexity of the control system design increases considerably if the control system is of the time varying type. This classification is shown in the Fig.1.

5) Linear and Nonlinear Systems : A control system is said to be linear if it satisfies following properties.
a) The principle of superposition is applicable to the system. This means the response to several inputs can be obtained by considering one input at a time and then algebraically adding the individual results.Mathematically principle of superposition is expressed by two properties.
i) Additive property which says that for x and y belonging to the domain of the function f then we have,
f(x+y) = f(x) + f(y)
ii) homogeneous property which that for any x belonging the domain of the function f and for any scalar constant we have,
f(α x) = α f(x)
b) The differential equation describing the system is linear having its coefficient as constants.
c) Practically the output i.e. response varies linearly with the input i.e. forcing function for linear systems.
Real time example : A resistive network shown in the Fig.1(a) is a linear system.The Fig.1 (b) shows the linear relationship existing between input and output.

A control system is said to be nonlinear, if,
a. It does not satisfy the principle of superposition.
b. The equations describing the system are nonlinear in nature.
The function f(x) = x2 is nonlinear because

The equations of nonlinear system involves such nonlinear functions.
c. The output does not vary linearly for nonlinearly systems.
The various nonlinearities practically present in the system are shown in the Fig.3 (a), (b) and (c).

The saturation means if input increases beyond certain limit, the output remains constant i.e. it does not remain linear. The flux and current relation i.e. B-H curve shows saturation in practice. In some big valves, through force increase upto certain value, the valve does not operate. So there is no response for certain time which is called dead zone.
The voltage-current equation of a diode is exponential and nonlinear thus diode circuit is an example of nonlinear system. This is shown in the Fig.4.

It can be seen that as long as Vin increase upto certain value, current remains almost zero. This is a dead zone and therefore voltage-current are exponentially related to each other which is a nonlinear function.
Note : In practice it is difficult to find perfectly linear system. Most of the physical msystems are nonlinear to certain extent.
But if the presence of certain nonlinearity is negligible and not affecting the system response badly, keeping response within its linear limits then the nonlinearity can be neglected and for practical purpose the system can be treated to be linear.
Procedure for finding the solutions of nonlinear system problems are complicated and time consuming, because of this difficulty most of the nonlinear systems are treated as linear system for the limited range of operation with some assumptions and approximations. The number of linear methods, then can be applied for analysis of such linear systems
6 ) Contineous Time and Discrete Time Control Systems : In a continuous time control system all system variables are the functions of a continuous time variable 't'. the speed control of a d.c. motor using a tachogenerator feedback is an example of continuous data system. At any time 't' they are dependent on time. In discrete time systems one or more system variables are known only at certain discrete intervals of time. They are not continuously dependent on the time. Microprocessor or computer based systems use such discrete time signals. The reasons for using such signals in digital controller are,
1) Such signals are less sensitive to noise.
2) Time sharing of one equipment with other channels is possible.
3) Advantageous from point of view of size, speed, memory, flexibility etc.
The systems such digital controllers or sampled signals are called sampled data systems.
Continuous time system uses the signals as shown in the Fig. 5(a) which are continuous with time while discrete system uses the signals as shown in the Fig. 5(b).

7) Deterministic and Stochastic Control Systems : A control system is said to be deterministic when its response to input as well as behavior to external disturbances is predictable. If such response is unpredictable, system is said to be stochastic in nature.
8) Lumped Parameter and Distributed Parameter Control Systems : Control system that can be described by ordinary differential equations is called lumped parameter control system. For example, electrical networks with different parameters as resistance, inductance, etc are lumbed parameter systems. Control systems that can be described by partial differential equations are called distributed parameter control systems. For example, transmission line having its parameter resistance and inductance totally distributed along it. Hence description of transmission line characteristics is always by use of partial differential equations. The lumped parameters are physically separable and can be shown to be located at a particular point while representing the system. The distributed parameters can not be physically separated and hence can not be represented at a particular place.
9) Single Input Single Output (SISO) and Multiple Input Multiple Output (MIMO) Systems : A system having only one input and one output is called single input single output system. For example, a position control system has only one input (desired position) and one output (actual output position). Some systems may have multiple type of inputs and multiple outputs, these are called multiple input multiple output systems.
10) Open Loop and Closed Loop Systems : This is another important classification. The features of both these types are discussed in detail in coming sections.