LQR based improved discrete PID controller design via optimum selection of weighting matrices using fractional order integral performance index
Citations
75 citations
Cites background or methods from "LQR based improved discrete PID con..."
...Here, the points which are important for determining the controller gain alone are explained and the further detail can be referred in [10]....
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...Classical optimal control theory has evolved over decades to formulate the well known Linear Quadratic Regulators which minimizes the excursion in state trajectories of a system while requiring minimum controller effort [10]....
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...[10] have given a formulation for tuning the PID controller gains via LQR approach with guaranteed pole placement....
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70 citations
49 citations
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Cites methods from "LQR based improved discrete PID con..."
...Many techniques have been developed and still research is going on for better tuning of the PID controller using complex numerical optimization procedures [8,9]....
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46 citations
References
3,254 citations
"LQR based improved discrete PID con..." refers background in this paper
...Introduction Classical optimal control theory has evolved over d cades to formulate the well known Linear Quadratic Regulators which minimizes t he excursion in state trajectories of a system while requiring minimum controller effort [1]....
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2,098 citations
"LQR based improved discrete PID con..." refers background in this paper
...The basics of discrete time optimal quadratic regul ator is introduced here [27]....
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...Discrete Time Quadratic Regulator Theory Applied to Optimal Digital PID Controller Design It is well known that discrete time realization of PID controllers are now more preferred than their continuous time counterpart [1 3], [27] since the gains of a digital PID controller can be changed, switched or scheduled on line so as to control complicated time...
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1,361 citations
905 citations
"LQR based improved discrete PID con..." refers background in this paper
...For 1 Λ > , the values would be higher than that given by 1 Λ = due to the inherent nature of the memory effect pre sent in the fractional integral [29]-[32]....
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...8 also shows that the ITSE which is ba sed on a first order integration approaches towards a steady value monotonically as time increases whereas with a low order of fractional integration ( Λ ) the integration no longer remains monotonic funct ion which justifies the fact that the integrand in (31) is changing its shape over time [29], [32]....
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...[30] and Podlubny [32] have given the geometric il lustration of fractional order differentiation and integration in a lucid manner....
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...Thus if ( )v τ is the measured velocity of a body, then the wrong value of distance covered is given by the integral ( ) ( )10 0 t I v t v dτ τ= ∫ (29) whereas the real or actual distance passed is givenby ( ) ( ) ( )0 0 t I v t v dgα τ τ= ∫ (30) Gutierrez et al. [30] and Podlubny [32] have given the geometric illustration of fractional order differentiation and integration in a lucid manner....
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695 citations
"LQR based improved discrete PID con..." refers background in this paper
...The FO integral represents an area under a transformed function which is dependent on he time step and fractional order with changing limits [29]....
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...8 also shows that the ITSE which is ba sed on a first order integration approaches towards a steady value monotonically as time increases whereas with a low order of fractional integration ( Λ ) the integration no longer remains monotonic funct ion which justifies the fact that the integrand in (31) is changing its shape over time [29], [32]....
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...For 1 Λ > , the values would be higher than that given by 1 Λ = due to the inherent nature of the memory effect pre sent in the fractional integral [29]-[32]....
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...In Chapter 5 of [29], it has been illustrated in a detailed ma nner that for the FO integrals like that...
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...Fractional Order Integral Performance Indices and Their Impact on the LQR Based PID Design Fractional calculus is a 300 year’s old subject and has found wide application in many branches of engineering and science [29]-[31]....
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