Why is an observer designed?

It comes (mostly) from state-space control.

In a control system, an observer is designed to estimate the state(s) of the plant (or, more accurately, it is designed to estimate the modeled states of the plant). A properly operating observer will estimate these states accurately without being confused by the control input to the plant.

An observer is usually part of a two-step design process. The first step is to design a controller as if you knew the states of the (modeled) plant perfectly. The second step is to design an observer that estimates these plant states.

In theory if your observer has some collection of poles and your controlled plant using a perfect-knowledge controller has some collection of poles, then the aggregate system will have both sets of poles, unchanged.

In practice if your model of the plant is not accurate then your assumptions about the observer's behavior break down; this is generally the point where you realize that state-space control is a great tool for understanding control theory, but not always a good practical tool for designing control systems. Then you get yourself a book on robust control.

I am a big believe in observers. We use observers to estimate the velocity, acceleration and sometimes the jerk of the object were are controlling. T his allows use to use derivative and, more importantly, second derivative g ains. Normally taking the second derivative of a position feed back with 1 micron resolution results in a an acceleration that jumps in steps of 1 me ter/second squared if sampled at 1 millisecond. With out observer control w e can estimate a much more accurate actual acceleration to compare with our target acceleration. This results in being able to use the second derivati ve gain in addition to the normal derivative gain. There are HUGE advantag es to using a second derivative gain in some systems.

Peter Nachtwey

Peter is right (he usually is). An observer is a filter, and provides filte red estimates of the states, allowing the use of higher order derivative st ates in the control algorithm that may be incredibly noisy if trying to tak e them from measurements.

A couple of other thoughts on observers:

I once had a fellow faculty member teaching state-space control ask why ful l-order observers would ever be designed since reduced-order observers coul d be developed that were simpler structures with lower computational demand . The answer is that a reduced-order observer does not filter the measureme nt prior to its use in the state feedback control algorithm, whereas a full

-order observer does. Sometimes that filtering is needed.

Interestingly enough, if attempting to add an integrator to the state feedb ack control structure, it's important to also add the integrator to the obs erver structure. If it isn't included, while the outputs of the observer wi ll converge to the output of the plant due the the observer acting on the d ifference of the plant and observer outputs, the observer states will not n ecessarily converge to the plant's states. The control may still be good, b ut it may not be as good as it could be.

This is true, but you have to be careful: getting a smooth response from choppy data means that you're doing heavy filtering. Getting a good high- frequency response from an observer with heavy filtering means that you're adding in a lot of feed-forward. Adding in lots of feed-forward at high gain, when the model you used to concoct your observer does not match the real system well enough means that your system stability and performance isn't nearly as guaranteed as you'd like.

That's not meant as an indictment of observers: just that you need to be sure that your observer is robust.

Yea verily and Amen!

Depending on exactly why you need an integrator, it also works well to model your system as having a blind integrator that's generating an offset (in position, torque, etc. -- basically whatever you're killing with the integrator action that's what you model). That integrator then becomes the integrator in your PID controller, without needing to have two of them.

(grain-o-salt: I don't use observers a whole lot. Sometimes they're very handy, and then I use them. But if the system is SISO, or needs lots of nonlinearities, or has more significant poles than the needed order of the controller, I use other methods.)