Design of Level Control in A 10 L Pure Capacitive Tank: Stability Analysis and Dynamic Simulation

Abstract

The open loop experiment of a 10 L pure capacitive tank has been successfully done in laboratory. The square tank connected with a pump was designed for investigation in laboratory, and the water was chosen as a fluid with its input volumetric rate of f_i(t) [cm³/min]. The output volumetric rate of f_o(t) can be adjusted by changing the pump voltage of v_pu(t) [volt]. The open loop experiment has given the steady state parameters, and it could then be used for calculating the dynamic parameters. This study has proposed the level control configuration of a 10 L pure capacitive tank system; liquid level in the tank h(t) was kept constant by manipulating the pump voltage of v_pu(t); and the input water volumetric rate of f_i(t) was considered as a disturbance. The P-only-control was implemented to control the level. Purposes of this study are to analyze the stability of the closed loop responses and to do the closed loop dynamic simulation. The closed loop mathematical model was solved analytically with Laplace Transform, and Routh-Hurwitz criterion was chosen to analyze the stability. Since the closed loop model was found in the 2^nd order system, the response depended on the value of the damping coefficient (ζ), in which it was really affected by the controller gain (K_c). In order to examine the control configuration, the input water volumetric rate disturbance (with amount of ±14%) was made based on step function. Based on the stability analysis, a stable response would be achieved if the controller gain is negative (K_c<0) and the damping coefficient is positive (ζ>0). Based on the dynamic simulation, the controller gain was recommended in between -117.36 [volt/cm] and -1.17 [volt/cm] and the damping coefficient in between 0 and 1. This study also revealed that by tuning an appropriate controller gain, the fastest and the stable response would be achieved.