Types of Control Systems

Control Systems is classified into the following categories:

Difference between Linear and Non-linear systems

Linear	Non-Linear
The relationship of *output with the input is linear*.	The relationship of *output with the input is non-linear.*
Satisfy Homogeneity & Superposition theorems.	Doesn’t satisfy Homogeneity & Superposition
Example : Register R= V/I	Example: Diode: I = I₀( e^v/t-1)

Difference between Static system and Dynamic system

Static systems	Dynamic systems
At any time output of the systems depends only on the present input of the systems.	At any time output of the systems depends only on the present as well as the past input of the systems.
Memory less systems	Presence of Memory Element
Y(t) = f (u(t)) This function is just dependent on present time like mentioned before.	Y(t) = f (u(t), u(t-1), u(t-2), …..) This function also possess effects of their past inputs.

Difference between Time invariant and Time-varying

Time invariant	Time-varying
At any time the output of the systems depends only on the present input of the systems.	At any time output of the systems depends only on the present as well as the past input of the systems.
Memory less systems	Presence of Memory Element
Y(t) = f (u(t)) This function is just dependent on the present time like mentioned before.	Y(t) = f (u(t), u(t-1), u(t-2), …..) This function also possess the effects of their past inputs.

Difference between Causal Systems and Non-causal Systems

Causal Systems	Non-causal Systems
The output of any casual system depends only on past and present inputs.	At any time output of the non-causal system depends only on the present as well as the past input of the systems.
It does not take part in any thing which is future (Non-anticipating) eg: y(t) = f(x(t), x(t-1),.....)	System anticipates future inputs based on past. for Eg: y(t) = f(x(t), x(t+1),....)
Examples of practical systems include Motor, Generator, temperature control, Etc.	Examples of practical systems are weather forecast, guided missile, etc.

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