# Steady-State Gain Identification and Control of Multivariable Unstable Systems

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1,464 citations

### "Steady-State Gain Identification an..." refers methods in this paper

...…various methods available for robustness analysis in multivariable systems (Morari and Zafiriou, 1989), the method based on the inverse of maximum singular value is one that is easy to use and to compare the different control system stabilities with (Maciejowski, 1989; Vijayakumar et al., 2012)....

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...First, for a process multiplicative input uncertainty as G(s)[IþDI(s)], the closed-loop system is stable if (Maciejowski, 1989): kDI ðjxÞk 1 r f½I þ GCðjxÞGðjxÞ 1GCðjxÞGðjxÞg ð25Þ where r is maximum singular value....

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...Methods of designing decentralized PI controllers for stable multiple-input multiple-output (MIMO) systems were reviewed by Luyben and Luyben (1997) and Maciejowski (1989)....

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### "Steady-State Gain Identification an..." refers methods in this paper

...The P controller is designed for each of the scalar transfer functions by the formula given by DePaor and O’Malley (1989):...

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...The P controller is designed for each of the scalar transfer functions by the formula given by DePaor and O’Malley (1989): KC ¼ ½ðs=LÞ0:5 =KP ðB2Þ Tanttu and Lieslehto’s method is used for designing the controller matrix for stabilizing the system....

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161 citations

### "Steady-State Gain Identification an..." refers background or methods in this paper

...Using this SSGM, the process is first stabilized by a simple P controller matrix (Davison, 1976): KC ¼ dK 1P ð3Þ where d is considered to be from 1.0 to 2.0....

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...The KC matrix is given by (Davison, 1976): KC ¼ d K 1P ð3Þ KI ¼ e K 1P ð4Þ For stable multivariable systems, Davison (1976) recommended a range of values of d from 0.1 to 0.4 and e is considered from 0.05 to 0.3....

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...Using this SSGM, the process is first stabilized by a simple P controller matrix (Davison, 1976): KC ¼ dK 1P ð19Þ where d is considered to be from 1.0 to 2.0....

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...Davison’s method (Davison, 1976) was modified to design single-stage multivariable PI controllers using only the steady-state gain matrix of the system....

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...The KC matrix is given by (Davison, 1976) Equation (3)....

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105 citations

### "Steady-State Gain Identification an..." refers background in this paper

...For unstable FOPTD systems, typical values for these two stability limits (KC,min and KC,max) are 1 and 6 (Chidambaram, 1998; Venkatashankar and Chidambaram, 1994)....

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