In the past, resonant controllers were famous for tracking sinusoidal signals at higher accuracy. What is the progress or new control techniques to track sinusoidal signals?
I would use for this task robust control theory. Let r(t) be a sinusoid with amplitude ≤ 1. Consider the SISO system P(s). We want to find a controller K(s) (feedback connected with P) s.t. the error e(t) = r(t)-y(t) (y(t) is the output) has a small amplitude, let's say < eps. It was shown that this is equivalent with
||S||_inf < eps, (1)
where S:=1/(P+K) is the sensitivity function. So find an S(s) such that (1) holds (you can use Matlab for that; a Bode plot is sufficient) and then find K(s) from (1). You can check in Matlab that this actually works.
If you are dealing with MIMO plants, the idea is basically the same, but the computations are a bit more involved. See Matlab robust control toolbox or google it.
Cheers!
First of all you should specify a type of your system. If you are working with nonlinear systems, the answer is more complicated, or does not even exist.
However, for linear SISO system there are several solutions. One of them is the Robust one, specified by Florin. The good fact is that you obtain a single linear contoller. The drawback is that you do not obtain zero error, the H_inf controller is usually of a high-order and can be hard to compute for a wide range of frequencies.
Another solution, which I would like to propose, is Adaptive Control. The good fact is that it provides (theoreticaly) zero tracking error, is simple to compute and can be applied for a wide range of frequencies. The drawback is that it is usually assumed that you know a number of frequencies in your sinusoidal reference signals.
PS: All these approaches assume that you do not know a frequency of your signal. If you know, then even simpler solutions exist.
@Stanislav: System can be regarded as a linear SISO. Assume that the reference to be track is known(both amplitude and frequency). Possible control strategies to achieve perfect tracking of reference with zero steady state error are
1. Proportional Resonant Controllers
2. Sliding mode controller
3. Dead-beat controller
4. Repetitive controller
5. Adaptive controller
As you see, above controllers play an important role in providing solutions to the problem mentioned above. But what are the other possibilities that we can think of?
Hello!
Your methods are good, however, I wouldn't expect zero error for sliding control in a practical application. I believe you can also obtain good results with fuzzy-logic, NeuralNetworks and other modern techniques. But what is your goal? You want to solve a technical problem, or just collect a set of solutions?
PS: Is the plant known?
Hi,
I have a similar problem. I also need to track a sinusoidal reference. I tried using a feedforward control, it works "fine" but I always have a phase difference between my signals. And I know the frequency of my reference, I am the one defining it finally.
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