Mathematical Techniques
Myke King · 2016
This chapter discusses the complex mathematical techniques for process control, including Fourier transform, recursive filters, Lagrangian interpolation, Padé approximation, and proportional-on-error (PI-D) algorithm. Lagrangian interpolation is a technique for determining intermediate values on curves defined by a series of data points. For example one may require an adaptive controller where tuning constants must be changed as process conditions vary. It is possible to predict, from the process dynamics and proportional, integral, derivative (PID) tuning constants, at what point the control will become oscillatory as the process dynamics change. This can be used to check on the robustness of the controller tuning. The method of partial fractions is most often used by control engineers in developing z-transforms, which in turn are used to convert analog systems to digital. One use z-transforms to describe the behaviour of processes and controllers in much the same way as he use Laplace transforms.