Multivariable Pid Control Via Ilmis: Performances Assessment

Mathematical Problems in Engineering

Lungu

et al. 2018

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Section: The Quadruple-tank Processmentioning

confidence: 99%

Full and Reduced-Order Unknown Input Observer Design for Linear Time-Delay Systems with Multiple Delays

Warrad

Mathematical Problems in Engineering

Lungu

et al. 2018

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“…In the following, the SOF transformation of the PI controller of the delayed system (1) will be detailed. Using (18), the system (1) can be written as follows:̇(…”

Section: Pi Controller Design Via Ilmismentioning

confidence: 99%

“…On the other hand, iterative linear matrix inequalities (ILMIs) are known to be powerful tools to solve multivariable control problems. Particularly, ILMI approaches were already used to design PID controllers for LTI systems without delays [14][15][16][17][18]. The basic idea was based on transforming the PID controller into an equivalent static output feedback (SOF) stabilization one by augmenting, using some new state variables, the dimension of the controlled system.…”

Section: Introductionmentioning

confidence: 99%

MIMO PI Controllers for LTI Systems with Multiple Time Delays Based on ILMIs and Sensitivity Functions

Belhaj

Mathematical Problems in Engineering

2017

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In this paper, a MIMO PI design procedure is proposed for linear time invariant (LTI) systems with multiple time delays. The controller tuning is established in two stages and guarantees performances for set-point changes, disturbance variations, and parametric uncertainties. In the first stage, an iterative linear matrix inequality (ILMI) approach is extended to design PI controllers for systems with multiple time delays without performance guarantee, a priori. The second stage is devoted to improve the closed-loop performances by minimizing sensitivity functions. Simulations results carried out on the unstable distillation column, the stable industrial scale polymerization (ISP) reactor, and the non-minimum phase 4-tank benchmark prove the efficiency of the proposed approach. A comparative analysis with the conventional internal model control (IMC) approach, a multiloop IMC-PI approach, and a previous ILMI PID approach proves the superiority of the proposed approach compared to the related ones.

“…Finally, for random matrices 11 N and 21 N , matrices N, L,G and E can be found solving (46) and (47) and using (40)- (43).…”

Section: Seifeddine Ben Warrad and Olfa Boubaker Full Order Unknown mentioning

confidence: 99%

“…Using the equalities (44), the system (45) can be written as the two following systems: N , matrices N, L,G and E can be found solving (46) and ( 47) and using ( 40)- (43).…”

Section: Theoremmentioning

confidence: 99%

Full Order Unknown Inputs Observer for Multiple Time-Delay Systems

Warrad

International Journal on Smart Sensing and Intelligent Systems

2016

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Abstract-In this paper, a design of a full-order observer for linear time-invariant (LTI)multivariable systems with multiple time-delays and unknown inputs (UI) is proposed. The main idea is to reduce the problem of the unknown input observer (UIO) for systems with multiple time-delays to that of a standard one. To that purpose, the orthogonal collocation method is used to transform the infinite dimensional model of the delayed system described by a set of linear partial differential equations (PDEs) to a finite dimensional one described by a set of linear ordinary differential equations (ODEs). Even using an approximation method, the asymptotic stability of the UIO is well proven. The efficiency of the proposed algorithm is shown using the quadruple-tank benchmark. The two cases of minimum and non-minimum phase models are considered.