Control Systems: Modeling dynamic systems and transfer functions · Differential Equation Models
How engineers turn mechanical, electrical, thermal and fluid systems into differential equation models, and the analogies that link them.
Try 3 questions
1. In a mass-spring-damper model, the damper's force is proportional to what?
- The mass's acceleration
- The mass's displacement
- The mass's velocity
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Answer: The mass's velocity
A viscous damper resists motion in proportion to speed (F = b·v); the spring responds to displacement and the mass to acceleration.
2. Why is a single mass-spring-damper modeled by a second-order differential equation?
- It stores energy in two independent elements
- It has two external forces acting on it
- It moves in two spatial directions
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Answer: It stores energy in two independent elements
The order of a lumped model equals its number of independent energy stores: kinetic energy in the mass and potential energy in the spring.
3. A circuit with one resistor and one capacitor driven by a voltage source is modeled by an equation of what order?
- Zero order (purely algebraic)
- Second order
- First order
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Answer: First order
The capacitor is the only energy-storage element, so one first derivative (of its voltage) describes the whole circuit.
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