With the recent sophistication of industry, a lot of complicated and elaborate control techniques have been developed and widely used in various industrial processes. An existing PID controller with adjustable parameters of proportional gain, integral gain, and derivative gain can be relatively easily operated by onsite engineers due to its simple structure, and thus has been widely used.
However, tuning the parameters of a controller so that a linear PID (L-PID) controller can have appropriate control performance is not easy. If the gain of a controller is increased to shorten the response time, overshoot increases, nonlinear saturation motion of the control valve is induced, and the control system becomes unstable. On the other hand, if the gain of a controller is decreased to reduce overshoot, the response time becomes longer, and thus satisfactory control performance cannot be obtained.
To maintain a constant desired water level of the water tank system examined in this study, the inflow rate needs to be adjusted by appropriately controlling the valve installed at the inflow pipeline considering the outflow rate. For an inflow valve, a servo valve operated by a motor is generally used, and the valve has a large time constant and thus has a slow response characteristics for the changes in the set point. Accordingly, it includes the fundamental limitation of a linear PID controller mentioned earlier.
To improve this, various studies that implement the gain of controller introducing a nonlinear element into a structure of linear PID controller have been performed. In most cases, a method in which an error is used after scaling nonlinearly and a method in which the gain of a controller is implemented as a nonlinear function have been studied.
In this study, a nonlinear PI (N-PI) controller that introduced nonlinear proportional gain and nonlinear integral gain into a structure of linear PI controller depending on the changes in the error was proposed. In the case of the proportional gain and integral gain of the N-PI controller, a simple nonlinear function was used so that they could change during operation depending on the changes in the size of the error. For the nonlinear proportional gain, the value was nonlinearly controlled so that it would become large when the error was large and would become small when the error was small after the response had reached a steady state. For the nonlinear integral gain, when the absolute value of the error was large, the integral gain value was decreased to prepare for the occurrence of overshoot and the superiority of the N-PI controller to linear PID controllers despite the absence of derivative control was demonstrated by comparing its response characteristics with those of the existing methods: the Z-N tuning method, the IMC tuning method, and the C-C tuning method. and when the absolute value of the error was small, the integral gain value was increased to reduce the steady-state error. The water tank selected as the control target was mathematically modeled, and the parameters were obtained through experiments at a water level of 5 cm, 10 cm, and 15 cm, respectively.
To examine the performance of the N-PI controller proposed in this study, simulation was performed by applying the proposed controller to a water tank system