## Levitating Globe Teardown, Part 1

November 4, 20133 comments

I've been kicking some ideas around for a long time for a simple and inexpensive platform I could use for control systems experimentation for the beginner.  I want something that can be controlled easily in a basic fashion, yet that provides some depth: I want to be able to present ever-more challenging goals to the student, that can be attained by fancier control algorithms all on the same device.

I'm currently looking at magnetic levitation.  It's fun, it has the potential to be...

## How to Build a Fixed-Point PI Controller That Just Works: Part II

March 24, 20122 comments

In Part I we talked about some of the issues around discrete-time proportional-integral (PI) controllers:

• various forms and whether to use the canonical form for z-transforms (don't do it!)
• order of operation in the integral term: whether to scale and then integrate (my recommendation), or integrate and then scale.
• saturation and anti-windup

In this part we'll talk about the issues surrounding fixed-point implementations of PI controllers. First let's recap the conceptual structure...

## How to Build a Fixed-Point PI Controller That Just Works: Part I

February 26, 20128 comments

This two-part article explains five tips to make a fixed-point PI controller work well. I am not going to talk about loop tuning -- there are hundreds of articles and books about that; any control-systems course will go over loop tuning enough to help you understand the fundamentals. There will always be some differences for each system you have to control, but the goals are the same: drive the average error to zero, keep the system stable, and maximize performance (keep overshoot and delay...

## A Second Look at Slew Rate Limiters

January 14, 2022

I recently had to pick a slew rate for a current waveform, and I got this feeling of déjà vu… hadn’t I gone through this effort already? So I looked, and lo and behold, way back in 2014 I wrote an article titled Slew Rate Limiters: Nonlinear and Proud of It! where I explored the effects of two types of slew rate limiters, one feedforward and one feedback, given a particular slew rate $R$.

Here was one figure I published at the time:

This...

## How to test a Tesla?

October 23, 20151 comment

In a previous article, I commented on the fact that Tesla cars with an "autopilot" system are about to be introduced on roads in the UK (and other places).

In the previous article I noted that Nick Reed from the UK’s Transport Research Laboratory is quoted in "The Times" newspaper (2015-10-16) as saying: “It would be legal for a driver to use Tesla’s autopilot mode in the UK, as it’s an advanced version of existing driver assistance systems”.

The

## What is Pulse Width Modulation and How Does It Work?

November 2, 2023

Pulse Width Modulation (PWM) is a technique used to control the average voltage supplied to a device or component by adjusting the width of a series of pulses. It works by rapidly turning a signal on and off at a specific frequency. The crucial element of PWM is the duty cycle, which represents the percentage of time the signal is “on” (high voltage) compared to the total time of one cycle.