Mathematical Model of Electrical Systems
Next, an electrical RLC network is considered
An input voltage v(t) is applied generating a current i(t) flowing through the Resistor ‘R’, Inductor ‘L’ and Capacitor ‘C’. According to Kirchhoff’s Voltage Law, the algebraic sum of potential differences in a loop must be equal to zero. Employing this law, the equation for this RLC network is given by
[Tex]V(t) – V_R – V_L – V_c = 0 [/Tex]
Writing this equation in terms of the currents flowing through the RLC elements,
[Tex]V(t) = R i(t) + L\frac{di(t)}{dt} + \frac{1}{c} \int i(t) \, dt [/Tex]
Taking the Laplace Transform of this equation leaves us with,
[Tex]LsI(s) + RI(s) + \frac{1}{c} \frac{I(s)}{s} [/Tex]
Although this equation describes a differential model of an electrical network, it isn’t comparable to Eq. 1 derived for a mechanical system just yet since the powers of ‘s’ are one order higher in every term of the mechanical systems equation.
Since current is nothing but the rate of flow of electric charge
[Tex]i(t) [/Tex] = [Tex]\frac{dq(t)}{dt} [/Tex]
taking the Laplace Transform of this equation gives
[Tex]I(s) = sQ(s) [/Tex]
Hence, modeling the electrical networks equation with replace [Tex]I(s) [/Tex] with [Tex]sQ(s) [/Tex] instead, we get a more comparable s-domain equation modeling an electrical RLC system
[Tex]Ls^2Q(s)+RsQ(s)+\frac{Q(s)}{c} [/Tex] ⇒ Eq. 2
Force Voltage Analogy
In this Article, We will be going to Know what is Force Voltage Analogy, We will go through the Mathematical Model of the Mechanical System Which is Classified into Two types Translational and Rotational Systems. Then we go through the Mathematical Model of the Electrical System, Then we go through the Force Voltage Analogy, At last, we will Conclude our Article With its Applications and Some FAQs.
Table of Content
- What is the Force Voltage Analogy?
- Mathematical Model of Mechanical Systems
- Mathematical Model of Electrical Systems
- Force-Voltage Analogy
- Translational Mechanical to Electrical System Conversion Example