Full- and Reduced-Order Linear Observer Implementations in Matlab\/Simulink [Lecture Notes]

A process on how to implement full- and reduced-order observers in Matlab/Simulink is discussed. A standard rule of thumb is that an observer should be designed such that its response is much faster than the system. This is especially important when the observed state variables are used for the purpose of feedback control. Namely, since the system changes in time, its estimated state variables must be as current as possible, otherwise the feedback signals represent considerably delayed estimates of the actual state variables, which can make the controller inaccurate and inefficient. After the system eigenvalues are determined, the observer eigenvalues are placed in the desired locations by selecting the corresponding observer gain K using the eigenvalue assignment technique. An observer, being an artificial dynamic system of the same order as the original system, can be built by a control engineer using either capacitors and resistors or using masses, springs, and frictional elements or simply using a personal computer that simulates and solves the corresponding differential equation, which is something that anybody with a basic knowledge of control systems and differential equations can do, especially those familiar with Matlab and Simulink. Hopefully, control engineers will use observers more often in practice because they are easily implemented on personal computers.