Generalized Minimum Variance Control for Water Distribution System

Silva, Magno Jose Gomes; Araújo, Clivaldo Silva de; Bezerra, Saulo de Tarso Marques; Souto, Cícero da Rocha; Silva, Simplício Arnaud; Gomes, Heber Pimentel

doi:10.1109/tla.2015.7069088

Cited by 13 publications

(2 citation statements)

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“…Remark 7: Accordingly, due to the lack of analytical results in this field, the pseudo-optimal well-known unique MP inverse (9) has commonly been used in the IMC-oriented scheme design processes [20], [30], [32].…”

Section: Energy Problem Formulationmentioning

confidence: 99%

“…The family of IMC-related algorithms constitutes the wellknown and broadly explored stochastic minimum variance (MV) and deterministic perfect control (PC) formulas strictly dedicated to the plants defined in both the transfer function [12], [13], [14], and state-space frameworks [4], [15], [16]. The special peculiarities of such unified control law, i.e., the maximum-speed/maximum-accuracy and robust maintenance, make it desirable in many industrial real-life implementations, for example, in the quadruple tank process [9], wireless autopilot of a quadcopter [17], control of a satellite system [18], power system control [19], water distribution system [20], linear/nonlinear servo control systems [21], [22], nonlinear pendulum system [23], and refrigeration device [24]. However, the main disadvantage associated with the high energy expenditure of the control input signals frequently prevents practical applications of the discussed control strategy.…”

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confidence: 99%

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Application of Generalized Inverses in the Minimum-Energy Perfect Control Theory

Feliks

Hunek

Stanimirović

2023

IEEE Trans. Syst. Man Cybern, Syst.

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Application of generalized inverses in solving the inverse model control (IMC)-oriented minimum-energy perfect control design (PCD) problem for linear time-invariant multi-input/multi-output systems governed by the discrete-time d-state-space structure is presented in this article. For this reason, an appropriate class of polynomial generalized inverses is investigated. Moreover, it can be stated that the nonunique right σ -inverse, based on properly selected so-called degrees of freedom (DOFs), outperforms the well-known unique Moore-Penrose (MP) minimum-norm right T-inverse in terms of the energy consumption of perfect control (PC) input signals. However, the analytical confirmation of such an intriguing statement has only been established for the special class of the single-delayed plants with a zero reference value. Moreover, because of the complexity of the IMC, the objects with a time delay d > 1 having a nonzero setpoint have never been analytically explored in regard to the PC energy context until now. Thus, the newly introduced analytical methods defined in this article allow us to designate the proper forms of σ -inverse-related DOFs that guarantee the minimum-energy PCD for the entire set of LTI multivariable nonsquare systems with the delay d ≥ 1. Moreover, the new original results, supported by numerical examples, strongly contest the well-established control and systems theory canons related to the optimal minimum-energy-originated peculiarity of the MP pseudoinverse.

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Section: Energy Problem Formulationmentioning

confidence: 99%