An Introduction to System Modeling and Control

16State Estimators and Parameter Identification

16.1 State Estimators

A problem with state feedback is that one needs the full state measurement, i.e., values of all the state variables. If we do not have a measurement of the full state, then we need to estimate the state variables that are not directly measured. Let's see how to do this by starting with a concrete example.

Example 1 Speed Estimator for the Cart

Consider the cart on the track system from Chapters 6 and 15 where an optical encoder was used to measure position. With the sample period the speed at time is computed by numerically differentiating the position measurement according to

This is the backward difference speed estimate and it is noisy due to the finite resolution of the encoder. Another approach is to estimate the rotor speed using an observer to obtain a hopefully smoother (less noisy) estimate of speed. In this example we will assume the cart is on a flat track. From Example 2 of Chapter 15 (page 568) the equations describing the cart on the track are

(16.1)

In matrix form we have

(16.2)

(16.3)