Decentralized fractional-order PIλ control applied to a TITO distillation column: a comparative study with PID and MPC

Abstract

This paper investigates the use of fractional-order PIλ (FO-PI) controllers and compares their performance with classical integer-order PID (IO-PID) and fractional-order PID (FO-PID) controllers for a two-input, two-output (TITO) distillation column. Additionally, a comparative study between FO-PI and model predictive control (MPC) is conducted on the same multivariable system. While fractional control in multivariable systems has been explored, evaluations of global performance metrics—such as integral square error (ISE), integral absolute value of error (IAE), integral time weighted absolute error (ITAE), integral time weighted square error (ITSE), and integral of manipulated variables (IU)—compared to IO-PID and MPC are still scarce. This work addresses this gap by examining these metrics alongside the steps necessary for fractional control design, including Laplace numerical inversion and controller tuning. The results demonstrate that the FO-PI controller shows superior performance compared to FO/IO-PID and MPC controllers. The global relative gain indexes show improvements, with FO-PI achieving gains of 36.9% to 59.9% compared to FO/IO-PID, and a reduction of 19% to 44.1% in global index compared to MPC. The distillation column dynamics were modeled using transfer functions, allowing for a detailed comparison of control strategies. The studies conducted in this work indicate that fractional-order controllers (FO-PI) show promise in controlling the dynamics of the TITO distillation column, as evidenced by simulations and comparison with integer-order (IO-PID) and fractional-order (FO-PID) control strategies, as well as with MPC control. The study highlights the potential benefits of using fractional controllers for a classical multivariable system, allowing to advance the state of the art of this type of control approach.