Decentralized PID control for nonlinear multivariable systems using decoupler

Document Type : Research Paper


Department of Instrumentation and Control Systems Engineering, PSG College of Technology, Coimbatore, India.


Interactions between input and output variables are a prevalent challenge in the design of multi-loop controllers for multivariable processes, and they can be a major stumbling block to obtaining good overall performance of a multi loop control system. The deconstructed dynamic interaction analysis is proposed to solve this limitation by decomposing the multi loop control system into a series of n independent SISO systems, each with its own PID controller. The multivariable decoupler and multi loop PID controller is applied to Two Tank Conical Interacting System (TTCIS). This TTCIS is chosen as benchmark problem used by many researchers. Firstly, the Mathematical modelling of TTCIS is derived using First principal model. The non-linear system is linearized using Jacobian matrix and decomposed into multiple SISO systems. The controller design for the process is then obtained, and an RGA matrix is constructed to minimise the interaction effects. To demonstrate the efficiency of the suggested strategy, simulation results using TTCIS are provided.


[1] B.W. Bequette, Process Control Modelling, Design and Simulation, Prentice Hall, USA, 2003.
[2] P.J. Campo and M. Morari, Achievable closed-loop properties of systems under decentralized control: conditions
involving the steady-state gain, IEEE Trans. Automat. Control 39 (1994) 932–943.
[3] S.K. Lakshmanaprabu, U. Sabura Banu and C. Bharanitharan, Linear quadratic gaussian control for two interacting conical tank process, Int. J. Comput. Appl. (2014) 35–39.
[4] T. Pushpaveni, S. Srinivasulu Raju, N. Archana and M. Chandana, Modeling and controlling of conical tank
system using adaptive controllers and performance comparison with conventional PID, Int. J. Sci. Engine. Res. 4
(2013) 629–635.
[5] V.R. Ravi and T. Thyagarajan, A decentralized PID controller for interacting non linear systems, IEEE Pub.
(2011) 297–302.
[6] G. Stephanopoulos, Chemical Process Control, Prentice Hall of India, New Delhi, 1990.
[7] F. Vazquez and F. Morilla, Tuning decentralized PID controllers for MIMO systems with decouplers, IFAC Pub.
(2002) 349–354.
[8] T.N.L. Vu and M. Lee, Independent design of multi-loop PI/PID controllers for multi-delay processes, Int. J.
Elect. Info. Engine. 3(12) (2009) 1586–1591.
Volume 12, Special Issue
December 2021
Pages 1529-1539
  • Receive Date: 09 August 2021
  • Revise Date: 20 October 2021
  • Accept Date: 16 November 2021