• Observers are used to estimate the next system state. They can also be used to predict future state values.

• As an example, an observer might be used for a targeting system that is tracking a moving object. The estimator can be used to direct a missle to an estimated location so that the missle and target arrive at the same time.

• An observer is shown in block diagram form


Figure 21.2 Block diagram of an observer


• A closed loop estimatior is shown below. It uses a learning matrix L to adjust the convergence rate. A larger L value will result in faster convergence, but the exponent must now be checked to ensure observability.

• Estimator gain selection


• Consider the example below, for a second order system. The learning rate values are selected to determine how quickly the model converges.


• This can also be done with Ackermann’s formula,


• The open loop estimator will normally ignore the response to initial conditions and will have long term errors resulting from modeling errors and random disturbances in the system.


XXXXXXXXXX Example of learning parameter estimator to obtain desired responses.