# 유리차수 미분을 이용한 위치제어기 구현

• 강정욱 (신라대학교 수학교육과) ;
• 전용호 (중원대학교 항공정비학과)
• Accepted : 2019.02.15
• Published : 2019.02.28
• 278 6

#### Abstract

This study aims to apply the mathematical method of fractional order derivatives to the controller that controls the system response. In general, the Laplace transform of the PID controller has an exponent of the integer order of s. The derivative of the fractional order has a fractional exponent of s when it is transformed by Laplace transform. Therefore, this controller proposes a design method with the result of discrete time conversion. Because controllers with fractional exponents of s are not easy to design. This controller is applied to a standard secondary system and its performance is examined. Then, it applies to solenoid valve which is widely used in industrial field. A Luenberger's observer was designed to estimate the disturbance state and the observed state was applied to the fractional order controller. As a result, uniform and precise control performance was obtained. It was confirmed that the position error of the steady state is within 0.1 [%] and the rising time is within about 0.03 [s].

#### File

그림 1. 전향보상 PID 제어기 Fig. 1 Forward PID controller

그림 2. 이항계수차수 3 에서 6의 유리차수 미분기 Fig. 2 The Fractional Derivative controller when binomial coefficient order is 3 to 6

그림 3. α에 대한 유리차수 미분기 Fig. 3 The Fractional Derivative controller when α is 0.31 to 0.91

그림 4. 유리차수미분기의 이득 $K^{\alpha}_d$ Fig. 4 The Fractional Derivative controller when the gain $K^{\alpha}_d$ is 50 to 1000

그림 5. 유리차수미분기를 포함하는 PID 제어기 Fig. 5 The PID controller with fractional derivative

그림 6. 솔레노이드 밸브의 위치제어 Fig. 6 The position control of the Solenoid valve

#### Acknowledgement

Supported by : 한국연구재단

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