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Design of Multivariable PID Controllers: A Comparative Study


Shabeena Memon and Arbab Nighat Kalhoro


Vol. 21  No. 8  pp. 212-218


The Proportional Integral Derivative (PID) controller is the most popular industrial controller and more than 90% process industries use this controller. During the past 50 years, numerous good tuning methods have been proposed for Single Input Single Output Systems. However, design of PI/PID controllers for multivariable processes is a challenge for the researchers. A comparative study of three PID controllers design methods has been carried-out. These methods include the DS (Direct Synthesis) method, IMC (Internal model Control) method and ETF (Effective Transfer Function) method. MIMO PID controllers are designed for a number of 2×2, 3×3 and 4×4 process models with multiple delays. The performance of the three methods has been evaluated through simulation studies in Matlab/Simulink environment. After extensive simulation studies, it is found that the Effective Transfer Function (ETF) Method produces better output responses among two methods. In this work, only decentralized methods of PID controllers have been studied and investigated.


Direct Synthesis, Internal Model Control, Effective Transfer Function, MIMO Controller, relative gain array, multivariable processes.