Dynamic performance of flow control valve using different models of system identification

Transcription

1 Dynamic performance of flow control valve using different models of system identification Ho Chang, Po-Kai Tzenog and Yun-Min Yeh Department of Mechanical Engineering, National Taipei University of Technology No. 1, Sec.3, Chung Hsiao E. Rd. Taipei 10608, Taiwan Tel: ext.2063 Fax: Abstract In this study, the dynamic characteristics of flow control valve was measured by using a self-developed square pressure wave generator (SPWG). Comprising a revolving shaft and a fixed ring, SPWG generates square pressure waves by the differential function of rotation between these two critical components. With the highly sensitive piezoelectric pressure sensor as the reference sensor, tests are conducted concurrently by using a flow control valve. Under the same experimental parameters, the dynamic characteristics of flow control valve is evaluated by using four kinds of system identification methods, namely ARX (Auto-Regressive with exogenous input model), ARMAX (Auto-Regressive moving Average with exogenous input model), OE (Output Error model) and BJ (Box-Jenkins model). The experimental results indicate that the dynamic performance of the tested flow control valve include resonance frequency, resonance peak and damping ratio, which are Hz, db and , respectively. Keywords: Flow control valve, output error model, resonance frequency, damping ratio 1. Introduction In recent years, the development of electronic control technology has produced enormous influence on hydraulic power system, making the parts of hydraulic power system develop towards small size, high-speed reaction and mechatronic integration in order to meet the need of industrial automation of the new generation [1-4]. Since flow control valve can steadily control the velocity of hydraulic actuator, it is an important hydraulic component in hydraulic system. In ideal situations, the flow rate emitted from flow control valve is merely controlled by the area of throttle valve, and is unrelated to load pressure and pressure change of system. Nevertheless, during the actual use, if there is any change happened to the pressure of system or the load pressure,the balancing position of the valve spindle in flow control valve changes accordingly. As known from the above, the dynamic performance of the flow control valve has extremely great influence on the accuracy of the control of hydraulic system. Most of the past studies of flow control valve took steady state into consideration, or simplified the 3-204

2 characteristic equation of flow control valve to be in a linear form for making analysis [6]. Nevertheless, the pressure of flow control valve often changed with time, and the change was usually very great. And the non-linear item in the dynamic characteristic equation of flow control valve changed to be a linear item only when the pressure change was small. This study uses the theory of pressure square wave as the foundation to find the dynamic performance of flow control valve. Its way is that a self-made square pressure wave generator (SPWG) is used to generate square pressure waves, which are then directly entered into the flow control valve of the hydraulic system. Four different system identification methods are used to analyze the dynamic equation of the flow control valve in hydraulic system, so as to understand the reaction performance of flow control valve, and find the most important dynamic performance of flow control valve, including resonance frequency, resonance peak and damping ratio. 2. Principles of flow control valve and system identification Flow control valve comprises a check valve and an adjustable throttle valve. The throttle valve inside the flow control valve can shrink the flow path of fluid to reduce the pressure and flow rate of fluid, as shown in Fig. 1. In the valve body, there is an adjusting screw to adjust the sectional area of flow path (size of orifice). Furthermore, the throttle valve is mainly used to adjust the velocity of hydraulic cylinder and control the flow velocity of fluid in the system. In general, before acquisition of dynamic performance of a system, we have to try to find the transfer function of its system. The study performs fast Forier transform for the output signal in time domain measured by pressure sensor. After the data of spectrum analysis are acquired, the data are finally adopted for making system identification. Then the transfer function of flow control valve can be acquired. In the system identification methods, time domain signals can be presented in parameterized models. The study adopts the models of ARX, ARMAX, OE and BJ to construct a system. The main difference of the various system identification methods is on the structure of model. For example, ARX and ARMAX model structures are of error type, whereas OE and BJ model structures are of output error type. Each type has its independent parameter system and disturbance model. The standard equation for the parameterized model of general time domain signals is expressed as equation (1): B( C( A ( y( u( e( ( 1) F( D( where A(, B(, C(, D( and F( are polymonials, q is the operating factor, y( is the output, u( is the input, and e( is the disturbance. The standard equation for the parameterized model of time domain is used to establish 4 different system identification methods

3 The study designs the experimental platform of a hydraulic system, and uses SPWG to replace electromagnetic valve. Figure 2 shows the platform of hydraulic system. When hydraulic source is connected with SPWG to give output of square pressure waves, such a square pressure wave signal is measured by the highly sensitive piezoelectric pressure sensor. After that, the square pressure waves flow to the flow control valve. Then another piezoelectric pressure sensor is used to measure the square pressure wave signal flown out of the flow control valve. This square wave signal is in time domain, such as the rise time, overshoot, etc. After that, the time domain of square wave signal is captured through the spectrum analyzer, and transferred to the frequency domain. Finally, the data of spectrum analyzer are adopted for making system identification. Then the study constructs a mathematical model of flow control valve, and analyzes the dynamic characteristics of flow control valve. Computer FFT System identification Amplifier Amplifier DC motor Pressure square wave generator Spectrum analyer Pressure sensor Flow control. valve Pressure sensor DC power supply Fig. 1. Schematic diagram of internal structure of flow control valve. Fig. 2. Schematic diagram of the system test procedures. Fig. 3. Square wave response of reference pressure sensor at the frequency of 250Hz. 3. Experimental results and discussion First, the time domain of square pressure wave response at different frequencies can be tested. As shown in Fig. 3, when the square pressure wave response frequency is 250Hz, its noise is very small and the wave shape looks very square. Hence, the square wave data acquired under this condition are the sources of data for analysis. It also implies that the input source of flow control valve comes from the square waves generated by SPWG, and the rise time is quite short. Figure 4 is the square wave response diagram of the flow control valve at frequency of 250 Hz. The figure shows that the rise time is longer, and smaller damping is caused. Besides, it shows that the flow passing through the flow control valve is more stable, and the disturbance is less. Finally, the input and output signals acquired from the time domain diagram of square wave response are handled by different system identification methods so as to acquire the transfer function of flow control valve, and also the various dynamic characteristics like resonance frequency, resonance peak and damping ratio. By using the 4 system identification methods, the input and output data are employed to build up models, such as ARX input model, ARMAX input model, OE model and BJ model, 3-206

4 so as to construct more accurate transfer function [7]. After calculation, the error functions for 4 different system identification methods can be achieved respectively. Among them, the error function of ARX system identification method is , and its modeled shape is shown in Fig. 5. In Fig. 5, the solid line shows the actual output value, and the dotted line shows the simulated output value. The error function of ARMAX system identification method is , and its modeled shape is shown in Fig. 6. The error function of OE system identification method is , and its modeled shape is shown in Fig. 7. The error function of BJ system identification method is , and its modeled shape is shown in Fig. 8. Comparing the results of Figs. 5~8, among these 4 different system identification methods, the output simulated from OE system identification method is closest to the actual output. Hence, the study adopts the fourth order system modeled from OE system identification method to make subsequent calculation. Fig. 4. Square wave response of flow control valve at the frequency of 250Hz. Fig. 5. Comparison between simulated ARX system identification results (dotted line) of flow control valve. Fig. 6. Comparison between simulated ARMAX system identification results (dotted line) of flow control valve. Fig. 7. Comparison between simulated OE system identification results (dotted line) of flow control valve. Fig. 8. Comparison between simulated BJ system identification results (dotted line) of flow control valve. Fig. 9. The root locus curve of OE system identification results. After comparison of different system identification methods, the transfer function of flow control valve can be acquired. The transfer function is then transferred from Z domain to S domain, and a root locus can be drawn, as shown in Fig. 9. As known from Fig. 9, both the 3-207

5 pole point and zero point lie on the left half side. When the gain value increases from zero to infinity, the range of root locus is also on the left half side. Hence, the system is judged to be stable [8]. Equation (2) is the transfer function from Z domain to S domain. After calculation, the acquired resonance frequency ( ) of flow control valve is Hz, the resonance peak (M pw ) is db, and the damping ratio is S S S T(s)=.. (2) S 4321S S S The system dynamic characteristics of flow control valve acquired through the system identification method can be the important design parameters for the designers of flow control valve, and can be provided as a reference for users of flow control valve in designing hydraulic system. r 4. Conclusion Among the various system identification methods, the error function of OE system identification method is It is more accurate than the systems simulated by other identification methods. Some significant dynamic characteristics of the system of flow control valve modeled by OE system identification method have been successfully achieved, including: the resonance frequency ( ) is Hz, the resonance peak (M pw ) is db, and the damping ratio is r References 1. T. Miyajima, T. Fujita, K. Sakaki, K. Kawashima, and T. Kagawa. Development of a digital control system for high-performance pneumatic servo valve. Precision Engineering. 2007, 31, pp J. Kim, H. Kido, R.H. Rangel, and M.J. Madou. Passive flow switching valves on a centrifugal microfluidic platform. Sensors and Actuators, B: Chemical. 2008, 128, pp N.T. Nguyen, X. Huang, and T.K. Chuan. MEMS-micropumps: A review. Journal of Fluids Engineering, Transactions of the ASME. 2002, 124, pp N.T. Nguyen, and T.Q. Truong. A fully polymeric micropump with piezoelectric actuator, Sensors and Actuators, B: Chemical. 2004, 97, pp T. Leephakpreeda. Flow-sensorless control valve: Neural computing approach, Flow Measurement and Instrumentation, 14, 2003, pp J.S. Stecki. Hydraulic system analysis - computer aided analysis of a bidirectional, pressure-compensated, flow control valve. The BFPR Journal. 1986, 14, pp Paul P.J. Bosch, Alexander C. Klauw. Modeling, Identification, and Simulation of Dynamical Systems Richard C. Dorf, Robert H. Bishop. Modern Control Systems