• Cold Junction Compensation. Here's a conceptual/graphical explanation of how the Cold Junction Compensation technique simplifies temperature measurement using thermocouple sensors. In addition to how to do it, there is also emphasis on the relative benefits and limitations. Originally intended for publication in "Test and Measurement World", somehow this article never got submitted — no terrible tragedy, but in case you are interested, here it is.

  • Building Kalman Filters: A step-by-step development of modeling for Kalman Filters, based on first principles. Kalman filtering epitomizes the approach of building a model that embodies system behavior, and then optimizing performance for that model. There is plenty out there about Kalman Filter mathematics, but precious little about how to construct a meaningful model for applying all of that theory. The keep-it-simple, hands-on approach is intended to dispel terror, and you can look for the rigorous mathematical theory elsewhere.

  • Circuit Symbolic Analysis. Here is a tutorial showing how you can use the Maxima software package from gnu.org to derive formulas for complex electronic network properties, such as active filter transfer gain characteristics, ladder network transfer functions, driving point impedances, S-parameters, and so forth, using symbolic computation.

  • Numerical Estimation of Derivatives from Data. The Web provides lot of information about poor ways to estimate derivatives of a function from measured data. Classical methods based on exact polynomial fitting (such as the "method of central differences") have horrible noise sensitivity, while other methods with better noise response properties compromise on accuracy. Some experiments led to two new design approaches — both of which are actually old design approaches with a few important details worked out. To see exactly what that means, you will have to check the pages...

    • Background information about the problem, illustrating the difficulty of derivative estimation, and how seemingly good approaches fail to work well in practice.
    • An FFT-based design method that works exceptionally well, but at a price. The design process is complicated, with non-obvious manual tweaking of parameters. The results are attractive and very accurate, but they use about twice as much computation as other methods. If computation speed is not an issue, this could be a very good choice.
    • Further investigation produced a kind of min-max optimal design that delivers results generally suitable for most ordinary applications, where efficiency matters but requirements for noise rejection and absolute accuracy are not extreme. Accuracy is close to the FFT-based designs, with about half of the computational effort. Also see a variant design that estimates the value of the second derivative.
  • Practical Control Systems. Which is better, PID control or state space control? Perhaps this begs the real question. This page discusses how you can have both!

  • Pink Noise Synthesis. This note describes a novel approach to additive synthesis of "pink noise" using multiple non-white random generator stages. Though not the fastest known method, it is very close, with additional advantages of being simple to program, friendly to fixed-point embedded processors, and delivering quite good spectral accuracy. This is applicable for many test signal generation and digital music applications. (Since this was posted, it is possible that better methods have since been developed, so do shop around.)

  • A Better Hydraulic Actuator Model Here is an alternative to the usual prematurely-linearized models typically used to represent a hydraulic actuator for control systems. This model is nonlinear, but still simple. I think this might be a significant improvement, but who will ever know, this has never been tried! (Most systems continue to use a classic model with constant, linear compression through full range up to absolute "hard limits" of travel. This widely used but implausible approximation can cause seriously unpleasant side effects.) Hey there, ME students of the world, are you looking for an interesting Masters project?

  • Turbine and Motor Alignment. How to determine a center point offset from a nominally circular element so that maximum and minimum deviations from this adjusted point are bounded as tightly as possible. This is known as "the zone circularity problem" and is one way to test whether a mechanism is manufactured within tolerance.