High-Order Filtered PID Controller Tuning Based on Magnitude Optimum

Abstract

The paper presents a tuning method for PID controllers with higher-order derivatives and higher-order controller filters (HO-PID), where the controller and filter orders can be arbitrarily chosen by the user. The controller and filter parameters are tuned according to the magnitude optimum criteria and the specified noise gain of the controller. The advantages of the proposed approach are twofold. First, all parameters can be obtained from the process transfer function or from the measured input and output time responses of the process as the steady-state changes. Second, the a priori defined controller noise gain limits the amount of HO-PID output noise. Therefore, the method can be successfully applied in practice. The work shows that the HO-PID controllers can significantly improve the control performance of various process models compared to the standard PID controllers. Of course, the increased efficiency is limited by the selected noise gain. The proposed tuning method is illustrated on several process models and compared with two other tuning methods for higher-order controllers.

The Fuzzy Logic in the Problems of Test Control of a Bypass Turbojet Engine Gas Generator

“…Thus, notwithstanding that in automatic control theory the synthesis of a controller using conventional methods is performed in a strictly formal way, in practice, such synthesis largely depends both on the properties of the control object and on the experience of the designer. This has been confirmed by a large number of publications devoted to the synthesis of such controllers [20][21][22][23][24][25]. Therefore, it can be assumed that if the synthesis and adjustment of the controller coefficients is a formalized procedure and not a creative process, then such a number of publications would be unjustified.…”

“…An overview is provided in [20] of the various types of PID controllers that are commonly used in industrial automation, and their advantages and disadvantages were considered. The study by [21] presented the setting of the speed controller of a DC motor based on the modified Ziegler-Nichols method, and [22] investigated a modification of the Ziegler-Nichols method to set a digital PID controller.…”

The Regulation of an Electric Oven and an Inverted Pendulum

“…For the development of the PID regulator, Equation ( 4) is considered, which describes the behavior of the internal heat of the electric oven. Then Equation ( 9) is defined as the PID regulator [1,2], where e = r − y is the error, r is the set point, and y is the output.…”

“…There are several kinds of controls: proportional integral derivative (PID) controls are studied in [1,2], model-based controls are discussed in [3,4], and disturbance rejection controls are designed in [5,6]. For these controls, there are two types of objective-tracking, which involves the following of a time-varying set point, and regulation, which involves the following of a constant set point.…”

“…2 + 36, 960c + 6272b)s 4 + (6272bc4 + 73, 920c 2 + 28, 000c +36, 960b)s 3 + (36, 960bc 4 + 56, 000c 2 + 28, 000b)s 2 + (28, 000bc 4 )s and D(s) = 6272cs 5 + (12, 544c 2 + 36, 960c + 6272b + 15, 680)s 4 + (6272bc 4 + 73, 920c 2 + 28, 000c + 36, 960b+ 2.0314 ×…”