types of systems


Control systems types

Linear & Non-Linear System.

A system is said to be linear if it follows the superposition principle and homogeneity whereas a Non-Linear System does not follow at least one of these rules.
Mathematically, it can be written as:

Additivity  If the input signals are time varying  x1(t) and x2(t) then  corresponds to output signals y1(t) and y2(t), then 

x1(t) + x2(t) = y1(t) + y2(t) ( additivity)

Homogeneity  If the input signals x1(t) corresponds to output signal y1(t) , and “a” be any scalar then their product will be
a.x1(t)=a.y1(t)  ( Homogeneity)

Digital or Discrete System
In these types of control systems, we have a discrete signal (or signal may be in the form of pulse) as the input to the system. We can convert various input signal like sinusoidal type signal into square type signal etc into a discrete form using the electronic switch.
Single Input Single Output Systems
These are also known as SISO type system. In this, the system has single input for a single output. Various example of this kind of system may include temperature control, position control system, etc.
Multiple Input Multiple Output Systems
These are also known as MIMO type system. In this, the system has multiple outputs for multiple inputs. Various example of this kind of system may include PLC type system etc.

Dynamic & instantaneous System
A instantaneous system is a system where the output signal at any specific time depends upon the input signal at that time.
This system has no memory means no energy storing element like capacitor or inductor .

Whereas, dynamic system is a system whose output depends upon present input as well as past or future values of input. Dynamic System contains energy storing element like capacitor .


Active & Passive System
Active System which is capable of generating energy For eg- Electric Circuit containg OPAMP, batteries etc.
A system that does not have any source of energy is called passive system. For eg- resistance , capacitance , inductance , etc.

Invertible  and non invertible system
 
 A system is called invertible if it produces distinct output signals for distinct input signals.

 If an invertible system produces the output y(t) for the input x(t), then its inverse produces the output x(t) for the input y(t) i.e. signal is recover from output signal. 

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