Asymmetric Fuzzy Control of a Positive and Negative Pneumatic Pressure Servo System
- Gang Yang^{1},
- Jing-Min Du^{1}Email authorView ORCID ID profile,
- Xiao-Yun Fu^{1} and
- Bao-Ren Li^{1}
https://doi.org/10.1007/s10033-017-0194-1
© The Author(s) 2017
Received: 11 May 2016
Accepted: 11 October 2017
Published: 23 October 2017
Abstract
The pneumatic pressure control systems have been used in some fields. However, the researches on pneumatic pressure control mainly focus on constant pressure regulation. Poor dynamic characteristics and strong nonlinearity of such systems limit its application in the field of pressure tracking control. In order to meet the demand of generating dynamic pressure signal in the application of the hardware-in-the-loop simulation of aerospace engineering, a positive and negative pneumatic pressure servo system is provided to implement dynamic adjustment of sealed chamber pressure. A mathematical model is established with simulation and experiment being implemented afterwards to discuss the characteristics of the system, which shows serious asymmetry in the process of charging and discharging. Based on the analysis of the system dynamics, a fuzzy proportional integral derivative (PID) controller with asymmetric fuzzy compensator is proposed. Different from conventional adjusting mechanisms employing the error and change in error of the controlled variable as input parameters, the current chamber pressure and charging or discharging state are chosen as inputs of the compensator, which improves adaptability. To verify the effectiveness and performance of the proposed controller, the comparison experiments tracking sinusoidal and square wave commands are conducted. Experimental results show that the proposed controller can obtain better dynamic performance and relatively consistent control performance across the scope of work (2–140 kPa). The research proposes a fuzzy control method to overcome asymmetry and enhance adaptability for the positive and negative pneumatic pressure servo system.
Keywords
1 Introduction
Pneumatic equipment is widely used in a variety of industries [1–3] due to lots of advantages, such as low cost, simple structure, easy maintenance [4]. The occurrence and development of electro-pneumatic proportional control valves place pneumatic control techniques beyond the limitation of point-to-point control. Electro-pneumatic proportional control valves provide the necessary components for pneumatic servo control systems, such as position [5–9], speed [10], force [11, 12], and pressure [13–17].
In the past decades, a great interest has been shown in pneumatic position servo systems. Compared with that of position servo controls, research on the design of pressure controllers at present is quite limited although the pneumatic pressure control systems have been used in the fields of robots, pressure calibration and various industrial processing systems. In some cases, the pressure controller is designed for improving the control performance of pneumatic position servo system [7–9]. In Ref. [7], a position control for a rodless cylinder was investigated. The proposed controller had an inner linearization pressure control loop and an outer position control loop. A PID controller with feedback linearization was used in the pressure control loop to nullify the nonlinearity arising from the compressibility of air. Noritsugu et al. [8] investigated a positioning control system with pressure control loop for improving control performance. A disturbance observer was employed to improve the pressure response and compensate the influence of friction force and parameter change. Igo et al. [9] used a conventional proportional controller with a variable offset pressure controller for achieving quick response and less overshoot of pneumatic robots.
The independent pressure control system generally consists of air supply, electro-pneumatic proportional valve, chamber and pressure sensor, for example, constant pressure system [14], pneumatic-pressure-load system [15] and pneumatic pressure signal generator [16]. Lu et al. [14] presented a constant pressure control system that consisted of frictionless cylinders, a large tank and a pneumatic proportional pressure valve. A hybrid controller combined with Bang-Bang, PD controller and fuzzy PID was proposed to minimize the pressure fluctuations in cylinders. The pneumatic-pressure-load system researched in Ref. [15], applied to intensity testing devices, was constructed by electro-pneumatic proportional pressure valve. In order to adapt to the parameter variability of the pressure load system and obtain better dynamic and static performances, a linear quadratic Gaussian self-tuning pressure regulator was proposed to realize an adaptive control of pressure in the chamber. In the pneumatic pressure signal generator [16], electro-pneumatic proportional directional valve was used to control the air-flow rates of injecting and outflowing the chamber to regulate the pressure. Because of the nonlinear characteristics, an intelligent coordinate control method, combining expert intelligent coordinator, expert controller, and fuzzy neural network controller, was designed to improve dynamic response and steady state accuracy of the generator.
At present, most of the researches can only regulate pressure to certain values. Poor dynamic characteristics and strong nonlinearity of such systems limit its application in the field of pressure tracking control. Positive and negative pneumatic pressure servo system (PNPPSS) is a very important equipment of the hardware-in-the-loop simulation of aerospace engineering [17], which controls the sealed chamber pressure according to the altitude command to simulate the atmospheric environment variation during flight. Currently, air data test systems in aerospace applications, for example the product ADTS405 from Druck, can only adjust the pressure or the vacuum to set values. However, the dynamic characteristics of such test systems are too poor to meet the requirements of the hardware-in-the-loop simulation. Moreover, the flight altitude is progressively increasing with the development of aerospace craft. Therefore, the continually enlarged pressure range of PNPPSS is demanded. In this work, the pressure range of the system is from 2 kPa to 140 kPa, and the frequency and amplitude of tracing curve are 2 Hz and 0.4 kPa respectively.
In fact, it is difficult for the PNPPSS to obtain desired dynamic and static performances because of the nonlinearity associated with air compressibility and the asymmetry of charging and discharging process. In addition, the parametric variation due to leakage, setting pressure and vacuum pumping speed will further complicate the problem. It is known that the distinct advantages of PID controllers are simple structure and robust performance [18]. However, it is difficult to achieve the ideal result for the conventional PID controllers due to the nonlinearities mentioned above. Fuzzy controller is a good candidate, since it is not based on the model of the process and the accurate model of the system is not required [19, 20]. Fuzzy rule based controllers are found to improve tracking performance over fixed gain PID by upwards of 70% [21], and have been applied to pneumatic systems [22, 23]. However, regular fuzzy controller is not suitable to the system due to its lack of adaption to wider operational range and serious asymmetry. To improve robustness and achieve consistent control performance, some auto adjusting mechanisms need to be introduced. Recently, many auto adjusting mechanisms for fuzzy controller have been presented [24–28], which offer better performance. In Refs. [24, 25], both the input and output scaling factors (SFs) were tuned with rule-base defined on the error and change in error of the controlled variable. Since the output SF has strong influence on the performance and stability of the system [26], some fuzzy logic controllers with auto-adjusting mechanism only tuned the output SF, which was regulated by a properly designed rule base [27, 28].
In this article, a fuzzy inference module is added to conventional PID controller to adaptively tune the PID gains. Further, an asymmetric fuzzy compensator is developed to online adjust output gain of the fuzzy PID controller. The charging or discharging state of chamber can be judged by the output of fuzzy PID controller. Thus, different from conventional adjusting mechanisms employing the error and change in error of the controlled variable as inputs, the current chamber pressure and the output of fuzzy PID controller, which are related to the system features, are chosen as input parameters of the asymmetric fuzzy compensator to improve adaptability.
The rest of this paper is organized as follows. The experimental setup and system characteristics are given in Section 2. Section 3 offers designing details of the fuzzy PID controller with asymmetric fuzzy compensator. In Section 4, experiments and results are provided to verify the proposed control method. Finally, conclusions are drawn in Section 5.
2 System Description and Analysis
According to Eq. (1), the change rate of the chamber pressure depends on the mass flow rate Q _{m}, which is the function of a ratio of downstream and upstream pressure. The closer the downstream pressure is to the upstream pressure, the greater the pressure ratio is and the smaller the mass flow rate is. The change of pressure ratio is not linear, which causes that the performance of the control system is highly nonlinear with the change of pressure. Moreover, when the chamber pressure p is lower, the value of p _{v}/p during discharging process is far greater than that of p/p _{s} in the process of charging, which leads to serious asymmetry. Therefore, the asymmetry is stronger with the increase of the positive supply pressure.
3 Controller Design
3.1 Fuzzy PID Controller
The PID parameters can be tuned online by the fuzzy inference module based on the nonlinear mapping of inputs and outputs established according to the operators experience and fuzzy set theory.
The inputs to the fuzzy inference module are the error e and the change in error ec, and the universes of discourse for e and ec are defined in [− 1, 1]. The PID parameters k _{p}, k _{i} and k _{d} are transformed into a uniform fuzzy range [0, 1]. Then, the fuzzy range of inputs and outputs is separated into 7 and 5 semantic variables respectively, and the corresponding fuzzy subsets are E = EC = {NB, NM, NS, ZE, PS, PM, PB}, KP = KI = KD = {SS, SM, MM, BM, BB}, where NB is negative big, NM is negative middle, NS is negative small, ZE is zero, PS is positive small, PM is positive middle, PB is positive big, SS is small, SM is middle small, MM is middle, BM is middle big and BB is big. The membership functions for all the subsets are triangular form.
Fuzzy rules for the fuzzy PID controller
KP/KI/KD | E | |||||||
---|---|---|---|---|---|---|---|---|
NB | NM | NS | ZE | PS | PM | PB | ||
EC | NB | BB/ | SS/ | BM/ | SM/ | SM/ | SM/ | MM/ |
SS/ | BB/ | SM/ | SS/ | SS/ | MM/ | MM/ | ||
SM | SM | MM | MM | MM | SS | SS | ||
NS | BB/ | BM/ | SM/ | SS/ | SM/ | MM/ | MM/ | |
SS/ | SS/ | BM/ | SM/ | SM/ | MM/ | MM/ | ||
BB | BM | BM | BM | MM | BM | SM | ||
NM | BM/ | BM/ | MM/ | SM/ | SM/ | MM/ | BM/ | |
SM/ | SM/ | MM/ | MM/ | MM/ | BM/ | BM/ | ||
BB | BB | BM | BM | MM | MM | SM | ||
ZE | BM/ | BM/ | MM/ | MM/ | MM/ | BM/ | BM/ | |
SM/ | MM/ | MM/ | MM/ | MM/ | MM/ | BM/ | ||
BB | BM | BM | MM | MM | MM | SM | ||
PS | BM/ | MM/ | SM/ | SM/ | MM/ | BM/ | BM/ | |
MM/ | MM/ | MM/ | MM/ | MM/ | BM/ | BM/ | ||
BB | BM | BM | BM | MM | MM | MM | ||
PM | MM/ | MM/ | SM/ | SS/ | BM/ | BM/ | BB/ | |
MM/ | MM/ | MM/ | BM/ | BM/ | BB/ | BB/ | ||
BM | BM | BM | MM | MM | SM | SM | ||
PB | MM/ | SM/ | SS/ | SS/ | BM/ | BB/ | BB/ | |
MM/ | MM/ | MM/ | BM/ | BB/ | BB/ | BB/ | ||
SM | SM | MM | MM | SM | SS | SS |
3.2 Asymmetric Fuzzy Compensator
The inputs to fuzzy PID controller are the error and the change in error. However, as mentioned above, the nonlinearity of the system is mainly affected by a wide range of pressure and serious asymmetry of charging and discharging process. The control rules have nothing to do with the pressure and the charging or discharging state if only using the error and the change in error as input parameters. Then, it is difficult to compensate the system characteristics. In this paper, an asymmetric compensator using the current pressure p and output u _{f} of the fuzzy PID controller as inputs is designed. The asymmetric compensator is based on the sign of the output u _{f} to determine charging or discharging process. If u _{f}<0, the chamber is in the discharging state. Otherwise, the chamber is in the process of charging. Moreover, the charging or discharging rate can be adjusted according to the current chamber pressure p.
The fuzzy output value λ from the asymmetric fuzzy compensator can be obtained according to the control rules. The universe of discourse for λ is defined in [0, 1], and the fuzzy set assumes Λ = {VS, SS, SM, MM, BM, BB, VB}, where VS is very small and VB is very big.
Fuzzy rules for the asymmetric fuzzy compensator
U_{f} | P | |||||
---|---|---|---|---|---|---|
ZE | SS | SM | MM | BB | VB | |
NB | VB | BB | BM | SM | SS | VS |
NS | BB | BM | MM | SS | VS | VS |
ZE | VS | VS | VS | VS | VS | VS |
PS | VS | VS | VS | SS | SS | SM |
PB | VS | VS | SS | SM | SM | MM |
- (1)
If u _{f} < 0, the chamber is in the discharging state. When the chamber pressure is lower, the discharging rate is slow. Therefore, the compensator factor should be larger to make the controller produce a fast response. When the chamber pressure is higher, the compensator factor should be set small to prevent the controller from generating a larger overshoot. For example, if U _{f} is NB and P is SS then Λ is BB or if U _{f} is NS and P is VB then Λ is VS;
- (2)
If u _{f} > 0, the chamber is in the charging state. When the chamber pressure is lower, the charging rate is fast, the compensator factor should be small to make the controller produce a lower overshoot. When the chamber pressure is higher, the compensator factor should be set to be a larger value than that in the condition of lower chamber pressure to improve response. For example, if U _{f} is PB and P is SS then Λ is VS or if U _{f} is PB and P is VB then Λ is MM;
- (3)
Due to the asymmetry of charging and discharging process, the compensator factor is also set to be asymmetric in the charging or discharging state. When the pressure p is lower, the charging value of the compensator factor is less than that in the discharging state. When the pressure p is higher, the charging value is slightly larger than the discharging value. For example, if U _{f} is PB and P is SS then Λ is VS, but if U _{f} is NB and P is SS then Λ is BB.
- (4)
In steady states (i.e., u _{f} ≈ 0), the compensator factor value should be very small (e.g., if U _{f} is ZE and P is VB then Λ is VS) to avoid chattering problem around the set point and ensure the stability of the system.
4 Experiments and Results
To verify the effectiveness of the proposed controller, the comparison experiments were conducted by using PID controller, fuzzy PID controller and fuzzy PID controller with asymmetric compensator. The pressure range is from 140 kPa to 2 kPa. The experimental system is shown in Figure 2. According to the actual vertical speed of the flight, the reference inputs are sinusoidal and square wave curves with amplitude of 0.4 kPa and frequency of 2 Hz. The proportional, integral, and derivative gains for PID controller were set as k _{p} = 0.45, k _{i} = 0.03, and k _{d} = 0.001 respectively. The parameters in the fuzzy inference module and fuzzy compensator were set as K _{e} = 0.5, K _{ec} = 0.25, K _{s} = 0.00625, K _{u} = 0.5, and K _{r} = 2. The parameters of all controllers were set by experiment tracking reference signal with average value of 140 kPa, and remained unchanged when pressure was changed.
The phase and amplitude errors tracking sinusoid
Average value p/kPa | Phase error θ _{e}/(°) | Amplitude error A _{e}/% | ||||
---|---|---|---|---|---|---|
Proposed controller | Fuzzy PID | PID | Proposed controller | Fuzzy PID | PID | |
140 | 6.2 | 8.6 | 3.9 | 2.4 | 6.7 | 7.6 |
20 | 6.4 | 17.9 | 13.7 | 2.7 | 10.7 | 22.8 |
5 | 7.9 | 36.4 | 28.9 | 4.6 | 3.8 | 32.6 |
2 | 8.1 | 45.8 | 42.0 | 4.7 | 7.4 | 38.7 |
5 Conclusions
- (1)
The open-loop system step responses obtained by simulation and experiment show that the system has serious asymmetry in the process of charging and discharging. Especially in the range of lower pressure, the closer the chamber pressure is to the ultimate pressure of the vacuum pump, the more serious the asymmetry is.
- (2)
A fuzzy PID controller with asymmetric fuzzy compensator is proposed for the PNPPSS. Since fuzzy rule based algorithm is not based on the model of the process, the accurate model of the system is not required. This is suitable for the pneumatic pressure system because the accurate system model is unavailable to users in practical application cases.
- (3)
The asymmetric fuzzy compensator is utilized to online adjust output gain of the fuzzy PID controller. Different from conventional adjusting mechanisms employing the error and change in error of the controlled variable as input parameters, the current chamber pressure and the output of fuzzy PID controller are chosen as inputs of the compensator, which improves adaptability.
- (4)
The proposed controller can obtain better dynamic performance and relatively consistent control performance across the scope of work (2–140 kPa).
Notes
Declarations
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
References
- B K S Woods, M F Genter, C S Kothera, et al. Fatigue life testing of swaged pneumatic artificial muscles as actuators for aerospace applications. Journal of Intelligent Material Systems and Structures, 2012, 23(3): 327–343.Google Scholar
- Y Wei, Y H Chen, Y Yang, et al. Novel design and 3-D printing of nonassembly controllable pneumatic robots. IEEE/ASME Transactions on Mechatronics, 2016, 21(2): 649–659.Google Scholar
- J T Lei, H Y Yu, T M Wang. Dynamic bending of bionic flexible body driven by pneumatic artificial muscles (PAMs) for spinning gait of quadruped robot. Chinese Journal of Mechanical Engineering, 2016, 29(1): 11–20.Google Scholar
- J A Riofrio, C Woodrow, J Malliory. Modeling, simulation and experimental validation of a servo-pneumatic control system with off-the-shelf components. Proceedings of the ASME/BATH Symposium on Fluid Power and Motion Control, Chicago, USA, October 12–14, 2015: 1–10.Google Scholar
- D Y Meng, G L Tao, H Liu, et al. Adaptive robust motion trajectory tracking control of pneumatic cylinders with LuGre model-based friction compensation. Chinese Journal of Mechanical Engineering, 2014, 27(4): 802–815.Google Scholar
- H P Ren, J T Fan. Adaptive backstepping slide mode control of pneumatic position servo system. Chinese Journal of Mechanical Engineering, 2016, 29(5): 1003–1009.Google Scholar
- H K Lee, G S Choi, G H Choi. A study on tracking position control of pneumatic actuators. Mechatronics, 2002, 12(6): 813–831.Google Scholar
- T Noritsugu, M Takaiwa. Robust positioning control of pneumatic servo system with pressure control loop. Proceedings of 1995 IEEE International Conference on Robotics and Automation, Nagoya, Japan, May 21–27, 1995: 2613–2618.Google Scholar
- N Igo, K Hoshino. Control of offset pressure for pneumatic robots. IEEE/SICE International Symposium on System Integration, Kyoto, Japan, December 20–22, 2011: 428–433.Google Scholar
- J C Renn, C M Liao. A study on the speed control performance of a servo-pneumatic motor and the application to pneumatic tools. International Journal of Advanced Manufacturing Technology, 2004, 23(7–8): 572–576.Google Scholar
- B Taheri, D Case, E Richer. Force and stiffness backstepping-sliding mode controller for pneumatic cylinders. IEEE/ASME Transactions on Mechatronics, 2014, 19(6): 1799–1809.Google Scholar
- B Taheri, D Case, RICHER E. Investigation of energy efficiency in force control of pneumatic actuators. Proceedings of the ASME 8th Annual Dynamic Systems and Control Conference, Columbus, USA, October 28–30, 2015: 1–8.Google Scholar
- M Shiee, A K Sharifi, M Fathi, et al. Air pressure control via sliding mode approach using an on/off solenoid valve. 20th Iranian Conference on Electrical Engineering, Tehran, Iran, May 15–17, 2012: 857–861.Google Scholar
- B Lu, G L Tao, Z Xiang, et al. Modeling and control of the pneumatic constant pressure system for zero gravity simulation. 2008 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Xian, China, July 2–5, 2008: 688-693.Google Scholar
- X S Wang, Y H Cheng, G Z Peng. Modeling and self-tuning pressure regulator design for pneumatic-pressure–load systems. Control Engineering Practice, 2007, 15(9): 1161-1168.Google Scholar
- X Li, J Tang. Intelligent coordinate control of pneumatic pressure signal generator of airplane engine inlet test system based on fuzzy neural network. International Conference on Measuring Technology and Mechatronics Automation, Zhangjiajie, China, April 11–12, 2009, 2: 503–506.Google Scholar
- J Y Li, B R Li, Z S Gao. Application of PC/104 embedded computer to air pressure control device. IEEE/ASME International Conference on Mechatronics and Embedded Systems and Applications, Beijing, China, December 12–15, 2008: 238–242.Google Scholar
- J D Han, Z Q Zhu, Z Y Jiang, et al. Simple PID parameter tuning method based on outputs of the closed loop system. Chinese Journal of Mechanical Engineering, 2016, 29(3): 465–474.Google Scholar
- A Visioli. Tuning of PID controllers with fuzzy logic. IEE Proceeding : Control Theory and Applications, 2001, 148(1): 1–8.Google Scholar
- H X Li, H B Gatland. Conventional fuzzy control and its enhancement. IEEE Transactions on Systems, Man and Cybernetics, Part B: Cybernetics, 1996, 26(5): 791–797.Google Scholar
- B Dehghan, B W Surgenor. A comparison of intelligent PID position controllers with autotuners for a pneumatic system. Proceedings of the ASME 11th Biennial Conference on Engineering Systems Design and Analysis, Nantes, France, July 2–4, 2012: 631–638.Google Scholar
- J Waldie, B Surgenor, B Dehghan. Fuzzy PID and contour tracking as applied to position control of a pneumatic gantry robot. ASME/BATH 2013 Symposium on Fluid Power and Motion Control, Sarasota, USA, October 6–9, 2013: 1–8.Google Scholar
- Y Xue, G Z Peng, M Fan, et al. New asymmetric fuzzy PID control for pneumatic position control system. Journal of Beijing Institute of Technology (English Edition), 2004, 13(1): 29–33.Google Scholar
- M Cheng, Q Sun, E Zhou. New self-tuning fuzzy PI control of a novel doubly salient permanent-magnet motor drive. IEEE Transactions on Industrial Electronics, 2006, 53(3): 814–821.Google Scholar
- Z Fang, D Xu, M Tan. A vision-vased self-tuning fuzzy controller for fillet weld seam tracking. IEEE/ASME Transactions on Mechatronics, 2011, 16(3): 540–550.Google Scholar
- R K Mudi, N R Pal. A robust self-tuning scheme for PI-and PD-type fuzzy controllers. IEEE Transactions on Fuzzy System, 1999, 7(1): 2–16.Google Scholar
- H H Tian, J G Lu, Q M Ynag. A self-tuning fuzzy logic controller for superheat of evaporator by using electronic expansion valve. 6th International Symposium on Computational Intelligence and Design, Hangzhou, China, October 28–29, 2013: 277–280.Google Scholar
- D Simhachalam, R K Mudi. A self-tuning fuzzy PI controller for pure integrating processes. Proceedings of the International Conference on Frontiers of Intelligent Computing: Theory and Applications, Bhubaneswar, India, November 14–16, 2013: 25–32.Google Scholar
- P Beater. Pneumatic drives: system design, modelling and control. Berlin Heidelberg: Springer-Verlag, 2007.Google Scholar