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With the price decreasing of the pneumatic proportional valve and the high performance micro controller, the simple structure and high tracking performance pneumatic servo system demonstrates more application potential in many fields. However, most existing control methods with high tracking performance need to know the model information and to use pressure sensor. This limits the application of the pneumatic servo system. An adaptive backstepping slide mode control method is proposed for pneumatic position servo system. The proposed method designs adaptive slide mode controller using backstepping design technique. The controller parameter adaptive law is derived from Lyapunov analysis to guarantee the stability of the system. A theorem is testified to show that the state of closed-loop system is uniformly bounded, and the closed-loop system is stable. The advantages of the proposed method include that system dynamic model parameters are not required for the controller design, uncertain parameters bounds are not need, and the bulk and expensive pressure sensor is not needed as well. Experimental results show that the designed controller can achieve better tracking performance, as compared with some existing methods. REN Haipeng, born in 1975, is currently a professor at Xi'an University of Technology, China. He received his PhD degree from Xi'an University of Technology, China, in 2003. His research field includes nonlinear system control, complex networks and communication with nonlinear dynamics. FAN Juntao, born in 1991, is currently a master candidate at Xi'an University of Technology, China. His research interest is pneumatic servo system control technology．

The performance of the pneumatic elements and the micro-controller steadily increases as the price of them decreases. This trend promotes high performance tracking control research on pneumatic servo systems. However, it is very difficult to obtain exact model parameters, which is one of the main obstacles to design a high performance controller. Moreover, in some application cases, the control direction is undetermined because of the possible false or incorrect valve outlets connection. At the same time, the inaccuracy of the proportional valve zero points also degrades the tracking performance of pneumatic servo systems. In this paper, an adaptive backstepping control approach is proposed for a pneumatic position servo system considering unknown model parameters, unknown control direction, and inaccurate valve zero points. The proposed method combines the Nussbaum function and backstepping technique to design a position tracking controller of a pneumatic servo system with the aforementioned uncertainties. By using the Lyapunov method, the designed controller is proved to be stable, and the tracking error asymptotically converges to zero. The experimental results demonstrate the effectiveness and the superiority of the proposed approach as compared with some existing methods, even for negative direction case for which the other methods fail. The performance of the proposed controller is further improved by considering the proportional valve zero points. INDEX TERMSPneumatic system, unknown model parameters, inaccurate proportional valve zero point, Nussbaum function, unknown control direction.