IntermediateTopic 65 of 101Signals, Control & Comms
Discretisation methods
Convert continuous controllers to discrete equivalents.
In depth
Convert continuous controllers to discrete ones: forward Euler (s≈(z-1)/T, may be unstable), backward Euler (stable), Tustin/bilinear (s≈2(z-1)/(T(z+1)), preserves stability, with frequency warping), zero-order-hold equivalent and pole-zero matching. Choice affects accuracy at high frequencies.
Key points
- Prewarping
- Stability preservation
- Matched Z-transform
ExamplePID derivative terms are discretised using backward differences.
What is Discretisation methods?
Convert continuous controllers to discrete equivalents.
Why is it important to understand discretisation methods?
Discretisation converts a continuous controller into a form that runs on a computer, and the method chosen affects accuracy and stability.
What is zero-order hold?
A model where the control signal is held constant between samples, which is how a DAC output usually behaves.
Why does the bilinear transform keep stability?
It maps the left half of the s-plane inside the unit circle, so a stable analogue controller stays stable in discrete form.
How is Discretisation methods used in practice?
Typical applications include converting an analogue PID into a digital one with a bilinear transform, using zero-order hold to model the output of a digital controller and choosing between forward and backward Euler for an integrator in a controller.
What should I learn before Discretisation methods?
Study "Digital control" first (topic 64 of 101 in Signals, Control & Comms). It covers the groundwork this topic builds on.
What are the key points of Discretisation methods?
Prewarping. Stability preservation. Matched Z-transform.
Can you give an example of Discretisation methods?
PID derivative terms are discretised using backward differences.
What comes after Discretisation methods?
The next topic is "Nonlinear systems", which builds directly on this one.
How difficult is Discretisation methods?
It is classed as Intermediate in Signals, Control & Comms (topic 65 of 101). It is an intermediate topic. Work through the beginner topics in Signals, Control & Comms first.