Abstract
In this paper the new methods concerning the energy-based minimization of the perfect control inputs is presented. For that reason the multivariable integer- and fractional-order models are applied which can be used for describing a various real world processes. Up to now, the classical approaches have been used in forms of minimum-norm/least squares inverses. Notwithstanding, the above-mentioned tool do not guarantee the optimal control corresponding to optimal input energy. Therefore the new class of inversebased methods has been introduced, in particular the new σ - and H -inverse of nonsquare parameter and polynomial matrices. Thus a proposed solution remarkably outperforms the typical ones in systems where the control runs can be understood in terms of different physical quantities, for example heat and mass transfer, electricity etc. A simulation study performed in Matlab/Simulink environment confirms the big potential of the new energy-based approaches.
Highlights
The issues involving the stability and robustness of MV/perfect control for Linear time-invariant (LTI) MIMO integer-order discrete-time systems in state-space framework become the field of intense scientific research [1,2,3,4,5,6,7]
Application the unique T-inverse produce only one inverse model control (IMC) system, it cannot be used to wide class of cases where the control inputs remain unstable under perfect control law
To overcome such obstacle there is a need for finding nonunique right inverse letting us generate an infinite set of IMC systems, amongst which we can look for stable and robust ones
Summary
The issues involving the stability and robustness of MV/perfect control for LTI MIMO integer-order discrete-time systems in state-space framework become the field of intense scientific research [1,2,3,4,5,6,7]. Application the unique T-inverse produce only one inverse model control (IMC) system, it cannot be used to wide class of cases where the control inputs remain unstable under perfect control law. To overcome such obstacle there is a need for finding nonunique right inverse letting us generate an infinite set of IMC systems, amongst which we can look for stable and robust ones. The method of employment fractional model is based on entering slight modification into the order α of wellknown Grünwald–Letnikov discrete-time fractional difference operator Δα of non-integer order α [10,11], which for classical perfect control systems is equal to α=1. The new method is mainly dedicated to nonsquare systems i.e. systems having different number of input and output variables
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