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Licensed Unlicensed Requires Authentication Published by De Gruyter July 19, 2017

SSGM Based Multivariable Control of Unstable Non-Square Systems

Manickam Chidambaram and Dhanya Ram V ORCID logo


Davison (1976) proposed a method to design controllers for multivariable systems using the knowledge of only the Steady-State Gain Matrix (SSGM) of the system. In the present work, Davison's method is suitably modified to design controllers for unstable non-square multivariable systems. A single-stage multivariable PI controller is designed using the SSGM. Simulation results show that the overshoots of the closed loop responses are larger, hence a two-stage P-PI control system is proposed. For the proposed two- stage design (i) the system is first stabilized by a simple proportional controller matrix designed based on SSGM using modified Davison's method (1976). (ii) Diagonal PI controllers are designed for this stabilized system based on gain matrix. Simulation studies are carried out to compare the closed loop performance of the single stage multivariable PI control system with that of the two-stage control system (inner loop centralized P controllers and outer loop diagonal PI controllers). A method to identify the steady state gain matrix of a non-square multivariable (SSGM) unstable system under closed loop control is presented. The effect of disturbances and measurement noise on the identification of SSGM is also discussed.


Let A be a m × n matrix. For a non-square matrix, the inverse of ATA does not exist if m < n. The pseudoinverse can be defined as A=(ATA)1AT


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Received: 2017-5-16
Accepted: 2017-6-3
Published Online: 2017-7-19

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