• Natural control systems: Biological systems, system inside human being are of natural type.

• Manmade control systems: The various systems used in daily life are designed and manufactured by human being.

• Systems like vehicles, switches, various controllers, etc. are called manmade control systems.

• Combinational control systems: The systems which are combination of natural & manmade systems. Example: Driver driving vehicle.

• Time varying & Time invariant systems: Time varying control systems are those in which parameters of the systems are varying with time. It is not dependent on whether input and output are functions of time or not.

Example:

Space vehicle whose mass decreases with time as it leaves earth. The mass is a parameter of space vehicle system.

The inputs and outputs are function 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.

Linear and Non-Linear systems: A system is linear if the principle of superposition applies to it.

In actual practice most of the systems are non linear in nature because of the saturation, friction, dead zone, etc. Most of the physical systems are non linear to certain extent. There are some areas of dynamic characteristics where it is possible to make a linearization. Procedure for finding the solutions of non linear system problems are complicated and time consuming and therefore most of the non linear systems are treated as linear systems for the limited range of operations with some assumptions & approximations.

Continuous Time and Discrete Time control system

In continuous time control system all system variables are the functions of a continuous time variable‘t’.

In discrete time systems one or more system variables are known at certain discrete intervals of time. They are not continuously dependent on the time. Microprocessor or Computer based systems use such discrete time signals.

Deterministic & 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 and repeatable.

• If such response is unpredictable, system is said to be stochastic in nature.

Lumped Parameter & Distributed Parameter Control Systems:

• Control Systems that can be described by ordinary differential equations is called lumped parameter systems.

• The system which can be described by partial differential equations is called as distributed parameter control systems.

Single Input Single Output (SISO) and Multiple Input Multiple Output Systems(MIMO):

SISO:

Consider a system which has one input & one output, for instance fan has a regulator using which we regulate the speed & the output is controlled. There is no feedback; only one input set point i.e. the regulator setting, and only one input set point i.e., the regulator setting, and only one output. SISO are open loop systems.

MIMO:

Any system that has more than one input or output. The inputs may be set point or feedback or cascaded set points and outputs can be controlled/set point for next loop. In general such systems are complex.

Open Loop & Closed Loop Systems:

A system in which output is dependent on input but controlling action or input is totally independent of the output or changes in output.

A system in which the controlling action or input is somehow dependent in the output or changes in the output is called closed loop system. To have dependence of input on the output, such system uses the feedback property.

Significance of Transfer Function:

• Transfer function gives mathematical models of all system components and hence of the overall system.

• Individual analysis of various components is also possible by the Transfer Function approach.

• As it uses a laplace approach, it converts time domain equations to simple algebraic equations.

• Transfer function is the property and characteristics of the system itself. Its value is dependent on the parameters of the system and independent of the values of inputs.

• Once Transfer Function is known, output response for any type of reference input can be calculated.

• Transfer Function helps in determining the important information about the system i.e., Poles, Zeroes, Characteristic equation, etc.

• It helps in stability analysis.

• The system differential equation can be easily obtained by replacing variables ‘S’ by d/dt.

• By finding inverse of laplace, the required variable can be easily expressed in the time domain. This is much easier than to analyze the entire system in the time domain.

• Construct the block diagram that combined the following set of equations expressed in the ‘S’ notation (Laplace notation)

(1) $w = x – y$ ,

(2) $v = w – z$

(3) $z (S + 6) = v (S + 2)$

(4) $y (s^2+6s+8)=z$.

Given x is the input in the system and y is the output from the block diagram. Find the transfer function. (Dec – 14)

$\frac{Y}{X}$=$\frac{(s+2)/(2s+8)( s^2+6s+8 )}{((2s+8)(s^2+6s+8)+s+2)/(2s+8)(s^2+6s+8)}$

=$\frac{(s+2)}{(2s^3+12s^2+16s+8s^2+48s+64+s+2)}$

$\frac{Y}{X}$=$\frac{(s+2)}{(2s^3+20s^2+65s+66)}$