Y. Mutoh (Japan)

Pole Placement, Luenberger Observer, Linear Time Varying System, Discrete System

The pole placement feedback with the state observer is the well established framework for linear control systems. This structure is exactly the same for linear time-varying systems. However, different from the time-invariant case, calculation procedure to obtain the pole placement feed back gain or the observer gain is not straightforward. This paper gives a simple calculation method to design the pole placement feedback with the state observer for linear time varying discrete systems. For this purpose, the simple design method of the pole placement for linear time-varying discrete systems is pro posed. It is shown that the pole placement controller can be derived simply by ﬁnding some particular ”output signal” such that the relative degree from the input to this new out put is equal to the order of the system. Using this fact, the feedback gain vector can be calculated directly from plant parameters without transforming the system into any stan dard form. Then, this method is applied to the design of the observer, i.e., because of the duality of linear time-varying discrete system, the state observer can be derived by simple calculations.

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