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This paper presents a penalty-based sliding mode control (SMC) law for flexible bar system, which uses shape memory alloy (SMA) as actuator. SMA actuators are lightweight, compact and flexible which facilitate their integration into flexible structures. The proposed control law manipulates SMA current to exert the necessary force for deflecting the flexible bar into the desired state. Numerical simulations demonstrate that this new method can control the one-input, multi-output under-actuated system of the flexible bar efficiently. The mathematical model of the flexible system is obtained using physical discretization. The bar is modeled as a combination of rigid rods connected by joints without elasticity and friction. This model demonstrates the flexibility of the system in an effective way. The numerical simulation illustrates the feasibility of the proposed model for analyzing the oscillations of the system and the effectivness of proposed control algorithms.

Deflection Sliding Mode Control of a Flexible Bar Using a Shape Memory Alloy Actuator with an Uncertainty Model