SKEDSOFT

Control Systems - 1

DIFFERENTIAL EQUATIONS OF PHYSICAL SYSTEMS

 

 

Table: 2 Summary of Governing Differential Equations for Ideal Elements

 

Nomenclature

Through-variable: F = force, T = torque, i - current, Q - fluid volumetric flow rate, q = heat flow rate.

 Across-variable: v = translational velocity, ω = angular velocity, v - voltage, P = pressure, T = temperature.

Inductive storage: L - inductance, 1/k = reciprocal translational or rotational stiffness, I = fluid inertance.

Capacitive storage: C = capacitance, M = mass, J = moment of inertia, Cf – fluid capacitance, Ct= thermal capacitance.

Energy dissipators: R = resistance, b = viscous friction, Rf = fluid resistance, Rt = thermal resistance.

 

Analogous systems with similar solutions exist for electrical, mechanical, thermal, and fluid systems. The existence of analogous systems and solutions provides the analyst with the ability to extend the solution of one system to all analogous systems with the same describing differential equations.