Research on Fuzzy Proportional Integral Differential Control of Magnetic Drive Oil-free Scroll Compressor
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摘要:
磁悬浮直驱式无油涡旋压缩机采用电磁力非接触式驱动动涡盘运动. 针对压缩机系统非线性较强、PID (proportional-integral-differential)控制下轨迹跟踪误差较大的问题设计了一种模糊PID控制器,可以在线实时修正控制参数,提高轨迹跟踪效果. 首先,介绍了磁悬浮直驱式无油涡旋压缩机的结构和工作原理,建立电磁驱动力的数学模型和系统动力学模型,并进行系统稳定性分析;其次,添加模糊逻辑,进行模糊控制器设计;最后,在控制参数相同的情况下,将PID与模糊PID 2种控制下的阶跃响应与轨迹跟踪结果进行对比分析. 结果表明:相较于PID控制,模糊PID控制下,阶跃响应时的稳定时间减少0.461 s,稳态误差减小0.012 mm;轨迹跟踪时,
X 、Y 方向达到稳定跟踪的时间分别减少0.365、0.090 s;X 、Y 方向的最大轨迹跟踪误差分别减小0.043、0.060 mm,最大相对误差分别减小了50%、60%.Abstract:Magnetic drive oil-free scroll compressor (MDOFSC) adopts electromagnetic force to drive the orbiting scroll in a non-contact manner. The problems of strong nonlinearity in the compressor system and large trajectory tracking errors under proportional-integral-differential (PID) control were analyzed, and a fuzzy PID controller was designed to adjust control parameters online and improve trajectory tracking performance. Firstly, the structure and working principle of MDOFSC were introduced, and the mathematical model of electromagnetic drive and the system dynamics model were established; the system stability was analyzed. Secondly, fuzzy logic was added for fuzzy controller design; finally, the step response and trajectory tracking results under both PID and fuzzy PID control were compared under the same control parameters. The results show that under the fuzzy PID control, the stabilization time during the step response is reduced by 0.461 s, and the steady state error is reduced by 0.012 mm; the time to reach the stable tracking in the
X andY directions during the trajectory tracking is reduced by 0.365 s and 0.090 s, respectively, and the maximal trajectory tracking error in theX andY directions is reduced by 0.043 mm and 0.060 mm; the maximal relative error is reduced by 50% and 60%, respectively.-
Key words:
- magnetic drive /
- oil-free scroll compressor /
- fuzzy PID control /
- trajectory tracking
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表 1 系统参数
Table 1. System parameters
结构参数 数值 J/(kg•m2) 1.51 × 10−3 m/kg 1.7 kiX/(N•A−1) 150 kdX/(N•m−1) −75 × 10−3 kiY/(N•A−1) 180 kdY/(N•m−1) −57 × 10−3 kn/(N•mm−1) 4.544 c/(N•s•m−1) 40 × 103 H/m 0.0195 L/m 0.021 表 2 ΔKP模糊规则表
Table 2. Fuzzy control rules of ΔKP
e ce NB NM NS ZO PS PM PB NB PB PB PM PM PS ZO ZO NM PB PB PM PS PS ZO NS NS PM PM PM PS ZO NS NS ZO PM PM PS ZO NS NM NM PS PS PS ZO NS NS NM NM PM PS ZO NS NM NM NM NB PB ZO ZO NM NM NM NB NB 表 3 ΔKI模糊规则表
Table 3. Fuzzy control rules of ΔKI
e ce NB NM NS ZO PS PM PB NB NB NB NM NM PS NS ZO NM NB NB NM NS NS ZO ZO NS NB NM NS NS ZO PS PS ZO NM NM NS ZO PS PM PM PS NM NS ZO PS PS PM PB PM ZO ZO PS PS PM PB NB PB ZO ZO PS PM PM PB PB 表 4 ΔKD模糊规则表
Table 4. Fuzzy control rules of ΔKD
e ce NB NM NS ZO PS PM PB NB PS NS NB NB NB NM PS NM PS NS NB NM NM NS ZO NS ZO NS NM NM ZO NS ZO ZO ZO NS NS NM NB NS ZO PS PS PS ZO NS NS NM NM PM PS ZO NS NM NM NM NB PB ZO ZO NM NM NM NB NB -
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