SISO System Input Output SIMO System InputOutputs MISO System Input Output MIMO System InputOutput (a)(b) (c)(d) A general way of classifying the systems is based on their input and output strength. For instance, when the number of input to the system is one and the number of output is also one then such system is called Single Input and Single Output or simply SISO system. Systems with other combinations such as Single Input Multiple Output (SIMO), Multiple Input Single Output (MISO) and Multiple Input Multiple Output (MIMO) also exist

Noise Input energy sourceOutput Loss SYSTEM Input domain Output domain The inputs are the sources of energy, which are available. The noise is the unwanted energy that enters into the system at any time. The noise energy is considered as the unwanted available input energy. So the total input energy is the available input energy plus unwanted available input energy. The output energy is the difference between the total input energy and the loss.

Ideal/Pure spring (k) Force Displacement If the input to a spring element is force then the output is displacement. The spring element is sometimes referred to as stiffness element. Stiffness is a kind of transfer function. The value of output depends on the transfer function.

Force = F F Mechanical structure exerted by Force Spring model of the mechanical structure A typical simple example of modeling a mechanical structure using spring element.

Force Loss (resistance) Torque Damper System Force Torque No output In order to follow up the principle of conservation of energy a loss element should exist in order to describe the system completely, i.e., the energy must be balanced. Indeed, the loss is reflected through the damper element. Damper element does not store any energy. It consumes energy, which cannot be recovered. Other name of the damper is dashpot that symbolizes resistance, more appropriately mechanical resistance.

J = Moment of inertia w = Angular velocity w J Mass Force Translational mass element Rotational inertia element Mass/Inertia Linear acceleration/Angular acceleration (Output)Force/Torque (Input) Input-Output relationship Mass element refers to translational movement where as inertia element corresponds to rotational movement. Both mass and inertia elements govern the law in terms of storing kinetic energy.

(a) (b) (c) Basic modeling elements of electrical systems; (a)An inductor; (b)A Resistor; (c)A capacitor

Q Area = A Length An element in which the stored energy is a function of fluid pressure is defined as fluid capacitor. The element possessing inertance is known as inertor. An ideal inertor characterizes frictionless incompressible flow in a uniform passage.

_ _ _ _ _ _ _ _ _ _ _ Q Area = A g An element in which the stored energy is a function of fluid pressure is defined as fluid capacitor.

A fluid resistor dissipates energy. A flow of fluid through a fluid system gives rise to a pressure drop analogous to voltage drop across an electrical resistance element. The drop signifies loss.

k R m k m (a)(b) Figure (a) illustrates a translational mechanical system described by spring damper and mass element. This is the schematic representation of a typical translational mechanical systems inheriting all the basic elements. Figure (b) shows another mechanical system with only spring and mass element. Such a system is called undamped system due to the reason that when a force is applied the systems oscillates, since the loss is zero.

J k R Torque = T = angular displacement = rotational spring Figure illustrates a rotational mechanical system with spring damper and mass. This is the schematic representation of many kinds of rotational mechanical systems inheriting all the basic elements.

+-+- R k J The equivalent electrical circuit of a DC motor is illustrated. is the supply voltage across the armature, is armature current, is total armature resistance, is the total armature inductance, back emf (that opposes the input voltage). As already stated the induced voltage is generated by the rotation of the electrical coil through the flux lines.

Pressure Q The energy stored in an ideal fluid capacitor is,

Tank Compressor Regulator Solenoid valve Spool x y LOAD Chamber-1 Chamber-2 Cylinder Piston Rod air P1P1 P2P2 Area The major components of a pneumatic system is a compressor, a main tank, a coarse regulator, a valve (controlled regulator), the piston-cylinder, and the load.