Pneumatic artificial muscles (PAMs) are a class of pneumatic drives that have received considerable attention for applications related to bio-inspired robotics. Nevertheless, servo control of PAMs is challenging due to the compressibility and nonlinear flow characteristics of air, hysteresis behaviour as well as uncertainties present. In this paper, positioning of an antagonistically paired PAM with mass flow rate of compressed air regulated by a 5/3-way proportional directional valve and driven by a dynamical adaptive backstepping-sliding mode control (DAB-SMC) scheme is investigated. Implemented for the first time on a PAM-driven actuating system, derivation of this model-based nonlinear control scheme is presented first followed by experimental evaluation. Positioning performance is studied using a sinusoidal trajectory with tracking frequencies of 0.05, 0.1, 0.2 and 0.5 Hz, and a multiple-step polynomial input having step sizes of 0.7 degrees, 1.4 degrees, 2.9 degrees and 5.7 degrees. Over various operating conditions, average root mean square error value of 0.16 degrees and steady-state error value of 0.04 degrees are achieved for position tracking and regulating, respectively. The adaptive LuGre friction observer embedded in the control scheme effectively compensates hysteresis behaviour of the PAMs and helps to improve the performance. The proposed DAB-SMC scheme outperforms the classical SMC scheme by 33% in accuracy. The control scheme has also demonstrated a robust performance towards the uncertainties including loading. In addition, a slight performance compromise in both tracking and regulating tasks was observed, when the 5/3-way proportional valve is replaced by cost-effective 2/2-way pulse width modulation controlled on-off valves.