Daronmont Technologies
Question
Asked 17th Mar, 2015
Why it is the deadbeat controller considered not robust?
I has been written in literature that deadbeat controller is not robust with perturbations. But i could never find any mathematical or logical proof for this statement. Can somebody explain this? Related literature link would be appreciated.
Popular answers (1)
Deadbeat control is a very optimistic and aggressive approach, particularly for short sampling periods. By "optimistic" I mean that it aims to obtain a zero tracking error in M time steps where M is the order of the plant. By "aggressive" I mean that this usually requires very large control commands (i.e. plant inputs), typically of opposing signs. Furthermore, even when the plant is known precisely, you may end up with oscillatory closed-loop behaviour, in the intra-sample response, due to (stable) poles near z = -1, even though the plant output may look fine at the sample times!
Like many other controller design techniques that utilize a plant model (e.g. linear-state-space with observer, internal model control, smith predictor, polynomial design), you need to be realistic and not "ask too much" of your controller (i.e. closed-loop poles too close to the origin, from the right, in the z plane). As an aggressive control strategy will hurt you if your plant model is not perfect - with a highly under-damped closed-loop system at best and an unstable system at worst. Although these problems can often be lessened somewhat, by incorporating a low-pass filter into your controller, e.g. with repeated poles on the real axis (at 0<z<1, but closer to 1 for more smoothing).
Don't worry about proofs, you will see these effects if you play around with Simulink for a an hour or two.
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All Answers (2)
TAAC Aerospace Technologies
Deadbeat controller is related with eliminating system poles which means the nominator of controller is denominator of the system, in practical there is always a modelling mistake or parameter perturbation that changes the actual system. Therefore the mathematical controller will not work properly.
In mathematical controller design it can be seen i suppose, or in simulink you can see the difference.
Hope this helps.
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Daronmont Technologies
Deadbeat control is a very optimistic and aggressive approach, particularly for short sampling periods. By "optimistic" I mean that it aims to obtain a zero tracking error in M time steps where M is the order of the plant. By "aggressive" I mean that this usually requires very large control commands (i.e. plant inputs), typically of opposing signs. Furthermore, even when the plant is known precisely, you may end up with oscillatory closed-loop behaviour, in the intra-sample response, due to (stable) poles near z = -1, even though the plant output may look fine at the sample times!
Like many other controller design techniques that utilize a plant model (e.g. linear-state-space with observer, internal model control, smith predictor, polynomial design), you need to be realistic and not "ask too much" of your controller (i.e. closed-loop poles too close to the origin, from the right, in the z plane). As an aggressive control strategy will hurt you if your plant model is not perfect - with a highly under-damped closed-loop system at best and an unstable system at worst. Although these problems can often be lessened somewhat, by incorporating a low-pass filter into your controller, e.g. with repeated poles on the real axis (at 0<z<1, but closer to 1 for more smoothing).
Don't worry about proofs, you will see these effects if you play around with Simulink for a an hour or two.
3 Recommendations
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