Control Systems – Lecture 4 – Modeling: electrical systems, transfer function, state space

Lecture 4 – Modeling: electrical systems, transfer function, state space

Kontrol Sistemleri – Modeling: electrical systems, transfer function, state space

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Differential eq for any dynamical system describes the exact response of the system for any desired input

DE → Represented (analized) in Time domain → State Space representation

Freq domain representation (Transfer function)

graphically respresented by block-diagram or signal flow graphs

General forms appearing in engineering (DE)

Electrical Systems (circuits, opamp)

Mechanical Systems (Vibration) (oscillating, gears)

Thermal and fluid system (hydrolic, pneumatic, fluid surface control, thermal)

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The order of input is less than the output

V_o : output according to the order of derivative

→ integration in time gives the response

You have to know initial conditions

RLC circuit in series

RLC circuit in parallel

Here we have the derivative of input

Methods of Complex impedences

Impedance in Series Z_eq=Σ Z_i

There is no dynamic behavior there is

summation of impedances in mesh: (R_1+Ls)

impedance of the common element: Ls

Voltage source in mesh: V

impedance on the common element ( Ls I_1 )

State space equation

2^nd order O.E s.s. 2 first order O.E

x : output 2^nd order O.E

Lecture 4 – Modeling: electrical systems, transfer function, state space

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