IntermediateTopic 46 of 101Signals, Control & Comms
Modelling mechanical and electrical systems
Derive transfer functions from physical laws.
In depth
Mechanical systems: Newton's laws give m ẍ+c ẋ+kx=F; rotational J θ̈+bθ̇=τ. Electrical: Kirchhoff's laws give RLC equations. Analogies map force↔voltage, mass↔inductance, spring↔1/capacitance. Result as transfer function or state-space model; linearise nonlinear ones.
Key points
- Free-body diagrams
- DC motor model
- Nondimensionalisation
ExampleA DC motor's transfer function from voltage to speed is first order.
What is Modelling mechanical and electrical systems?
Derive transfer functions from physical laws.
Why is it important to understand modelling mechanical and electrical systems?
Physical laws give the transfer functions used in control, so modelling mechanical and electrical parts is the first step in design.
How do I start a model?
Write the physical laws for each element, such as Kirchhoff's laws or Newton's law, then take the Laplace transform with zero initial conditions.
Why use an electrical analogy?
Mechanical and electrical systems share the same equation structure, so circuit tools can analyse mechanical systems too.
How is Modelling mechanical and electrical systems used in practice?
Typical applications include deriving the transfer function of a motor from its electrical and mechanical equations, modelling a spring-mass-damper for a suspension design and finding the transfer function of an RC network used as a sensor filter.
What should I learn before Modelling mechanical and electrical systems?
Study "Plant, sensor, controller, actuator" first (topic 45 of 101 in Signals, Control & Comms). It covers the groundwork this topic builds on.
What are the key points of Modelling mechanical and electrical systems?
Free-body diagrams. DC motor model. Nondimensionalisation.
Can you give an example of Modelling mechanical and electrical systems?
A DC motor's transfer function from voltage to speed is first order.
What comes after Modelling mechanical and electrical systems?
The next topic is "First-order system response", which builds directly on this one.
How difficult is Modelling mechanical and electrical systems?
It is classed as Intermediate in Signals, Control & Comms (topic 46 of 101). It is an intermediate topic. Work through the beginner topics in Signals, Control & Comms first.