Fictitious Reference Tuning of the Feed-Forward Controller in a Two-Degree-of-Freedom Control System

Abstract

: In this paper, we provide a new effective tuning method to obtain the optimal parameter of the feed-forward controller in a two-degree-of-freedom (2DOF) control system for the purpose of achieving the desired response without using a mathematical model of a plant. The first author proposed "fictitious reference iterative tuning" (which is abbreviated to FRIT) as an effective method for the tuning of parameters of a controller by using only one-shot experimental data instead of using mathematical models of a plant. Here, we extend FRIT to the tuning of the feed-forward controller in a 2DOF control system and develop the off-line computation so as to be done by the least squares method. For these purposes, we introduce a new cost function consisting of the fictitious reference and the actual data (since we do not have to do iterative computation in the least squares method, we call the proposed method here as "fictitious reference tuning"). Since the new cost function is quadratically-parameterized, it is possible to analyze how far the obtained parameter is apart from the desired one. Thus, we then derive a pre-filter which is applied to the actual data so as to guarantee that the obtained parameter is close to the desired one. We also show that the proposed method is applicable to the case in which the initial experiment is performed in the conventional 1DOF control system. Finally, we illustrate experimental results in order to show the utility and the validity of the proposed method.

Direct controller parameter tuning for systems with backlash

“…In contrast, virtual reference feedback tuning (VRFT) proposed in [2] and fictitious reference iterative tuning (FRIT) proposed in [3] are performed based on input and output data obtained from only a one-shot experiment, which means that VRFT and FRIT are more practical than IFT. Moreover, although FRIT and VRFT are based on a similar idea, FRIT is more intuitively understandable and simple than VRFT as stated in [4]. For these reasons, FRIT has received much attention recently as a practical and useful method, and its extended methods have been studied (see, e.g., [5,6]).…”

Fictitious Reference Iterative Tuning-Based Two-Degrees-of-Freedom Method for Permanent Magnet Synchronous Motor Speed Control Using FPGA for a High-Frequency SiC MOSFET InverterMOSFET Inverter

“…Recently, FRIT, which can be used to obtain optimal controller parameters using the input and output data from one-shot experimental data, has been studied by several researchers [8][9][10][11][12][13][14][15][16][17]. The data are used to determine the plant dynamics without knowing the mathematical model of the plant [13].…”

“…These researchers studied tuning methods using FRIT in a one-degree-of-freedom control system. Kaneko et al [12][13][14][15] proposed the use of the FRIT method for tuning of the feedforward controller in a 2DOF control system. The FRIT method is now the focus of research for many control systems researchers.…”

Quadrotor tuning for attitude control based on PID controller using fictitious reference iterative tuning (FRIT)

“…H.Hjalmarsson et al [3] developed iterative feedback tuning (IFT), M.C.Campi et al [4] proposed virtual reference feedback tuning (VRFT) and Kaneko et al [5] proposed fictitious reference iterative tuning (FRIT). Among these methods, FRIT is more intuitively understandable, simple and practical 1 http://store.3drobotics.com/products/apm-2-6-kit-1 2 http://store.3drobotics.com/products/3dr-pixhawk 3 http://store.openpilot.org/5-flight-controllers 4 http://www.hobbyking.com/hobbyking/store/ 26588 multiwii pro flight controller w mtk gps module.html 5 http://www.hobbyking.com/hobbyking/store/ 54299 hobbyking kk2 1 5 multi rotor lcd flight control board with 6050mpu and atmel 644pa.html 6 http://copter.ardupilot.com/wiki/tuning/ 7 http://wiki.openpilot.org/display/Doc/Stabilization+Tuning++Multirotor than IFT and VRFT because it requires only one-shot first experimental input-output data to compute optimal control parameters and is suitable for close-loop system tuning [6]. This paper proposes a method for quadrotor tuning, which normally takes time and experience.…”