A study on a new criterion for minimum-energy perfect control in the state-space framework

Abstract

In this article, an advanced study concerning the energy cost of the perfect control algorithm is provided. An application of different nonunique matrix inverses into perfect control law has resulted in remarkable influence on both control and state signals. Following the newly obtained issues, covering the minimum-energy behavior, a new related criterion is proposed here. Based on deterministic norm we can, in a simple way, estimate the crucial energy performance. Simulation examples made in MATLAB/Simulink environment show the high potential of a new approach considered in the article.

Perfect Control for Continuous-Time LTI State-Space Systems: The Nonzero Reference Case Study

“…In fact, the perfect control law ensures the globally lowest value of the mentioned norm. This obvious property is also confirmed here, since the control error tends to zero for any t > dt → 0 [14]. Remark 6: The employment of B R and C R in our investigation exhausts successfully the set of right-invertible plants (CB) R .…”

“…In such BIBO/BIBS paradigms, only the auto-regressive parts of the system dynamics are taken into consideration, with the well-known criterion covering connection between closed-loop poles and discussed the stability feature. Studies concerning the discrete-time perfect control systems have shown, that the state-feedback matrix K used in this control design is crucial in the context of obtaining the different closed-loop poles [14]. For example, the application of nonunique matrix inverses can lead to the different control properties with various closed-loop system matrix [11].…”

“…For instance, the inverse-based pole-free perfect control for discrete-time state-space system has already been delivered in such a way [11]. Notwithstanding, the inverse problem has nonunique solutions mainly for plants having plural numbers of inputs and outputs [12]- [14]. This phenomenon is employed during design of IMC robust MIMO strategies [7], [15].…”

“…Notwithstanding, most of the mentioned peculiarities have been used in the discrete-time manner, as the perfect control is well known for such system framework (for example see Ref. [14] in the context of new energy-based criterion dedicated to discrete-time perfect control law). What could have been foreseen, the discussed control law obtained for discrete-time systems applied to the continuous-time plant resulted in the odd responses of the steady-state values, but different from the reference ones.…”

A New Stability Theory for Grünwald–Letnikov Inverse Model Control in the Multivariable LTI Fractional-Order Framework

“…The issues regarding the stability and robustness of MV/perfect control for LTI MIMO integer-order discrete-time systems in state-space domain are subject to increasingly intensive scientific exploration [20,21]. The search for various methods is being conducted in particular to obtain new classes of right inverses.…”