Abstract
The continuous stirred tank reactor (CSTR) tends to reveal unstable severe nonlinear behavior when the operating level changes. As investigated in an earlier work, the hard nonlinearity nature of the CSTR originates from multiple probable sets of states for the same reaction in the same CSTR under identical ongoing inlet conditions. The previous work concluded, and this paper will discuss, that nonlinear processes with dynamic trajectories will involve a degrading control performance whenever the measured process variable evolves away from the designed level of the desired output trajectory. In this work, this problem will be examined for temperature tracking control on a CSTR with an adaptive fuzzy gain-scheduling proportional-integral-derivative (AFGS-PID) controller scheduled for a dynamic output trajectory. It will be proven that the AFGS-PID has better tracking performance than the fuzzy gain scheduling (FGS-PID) and conventional PID. Although all three controllers demonstrate the same level of control efforts, AFGS-PID has the smallest IAE and ISE. The lowest settling time being exhibited by AFGS-PID also proves that the intended regulator can rapidly track the desired coolant jacket temperature. A Lyapunov analysis is presented to prove the stability of the closed-loop and support the simulated result in the comparative study.
Highlights
The literature shows that the adaptive control design has been used in industrial cases in which there is a little theoretical information regarding the process dynamics
An adaptive fuzzy gain-scheduling proportional-integral-derivative controller, or AFGS-PID controller approach, is proposed as a benchmark nonlinear model of a continuous stirred tank reactor (CSTR), which depends on the exogenous scheduling trajectory
The control input appears for the second derivative of the output; the relative degree of the third-order CSTR model is 2, which is less than the system order
Summary
The literature shows that the adaptive control design has been used in industrial cases in which there is a little theoretical information regarding the process dynamics. An adaptive fuzzy gain-scheduling proportional-integral-derivative controller, or AFGS-PID controller approach, is proposed as a benchmark nonlinear model of a CSTR, which depends on the exogenous scheduling trajectory. This process comprises nonlinear dynamics with several stable and unstable equilibrium points and may resort to detect unstable nonlinear behavior when the nonmonotonic operating trajectory changes [25]–[27]. To manage the nonlinear control issue by examining the localized, simplified plant approximations, the control approach examined here uses some general opinions of the gain scheduling formalism, which manages linearized nonlinear models along the operating points or reference trajectories [28], [29].
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