Designing LQG controller for non-minimum phase LTI systems using fractional order zero-pole partial canceller

This paper proposes a practical approach to designing a linear quadratic regulator (LQR), Kalman filter, andlinear quadratic gaussian (LQG) regulator/controller for fractional-order systems, which have an order between zeroand one (in Caputo sense). For this purpose, it is shown that the cost function of the LQR is convex with respect to thestate feedback gains, and consequently, the optimal state feedback gains of the LQR and the gains of the Kalman filtercan be calculated using a gradient-based numerical algorithm. Different fractional-order LQR and Kalman filterdesign problems have been solved using the propounded method. Considering the fact that in non-minimum phasesystems, the undesirable effect of right-hand zeros cannot be reduced by right-hand poles of the controller since resultsin internal instability. The proposed convexity-based numerical method with fractional partial zero-pole cancellerapplied for designing LQG controller to achieve more effective control of non-minimum phase systems.

کلیدواژه ها:

fractional-order zero-pole cancellation ، non-minimum phase system ، linear quadratic regulator ، Kalman filter ، convex problem.