Energy Saving in Feed Drive Systems Using Sliding-Mode-Based Contouring Control With a Nonlinear Sliding Surface

Reduction of contour error, which is defined as the shortest distance between the actual position of the cutting tool and the reference trajectory, is an essential requirement in machining by multiaxis feed drive systems. In addition, because these machines operate all the time in industrial applications all over the world, reduction of the consumed energy in these machines contributes to environmental, natural resources, and energy problems. This paper presents a novel sliding mode contouring controller with a nonlinear sliding surface to improve the machining accuracy of the biaxial feed drive systems. Because the contour error is more important than the tracking error with respect to each feed drive axis, the contour error component is included in the proposed sliding surface. The advantage of including the contour error in the proposed sliding surface is that the damping ratio of the system changes from its initial low value to final high value as the contour error changes from high value to small value and vice versa. Hence, the proposed algorithm allows a closed-loop system to simultaneously achieve low energy consumption and small settling time, resulting in a smaller error. By using the proposed method, experimental results for a biaxial feed drive system show a significant performance improvement in terms of the contour error. In addition, the proposed approach reduces the control input variance by about 41.2 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$%$</tex> </formula> and 14.9 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$%$</tex></formula> for <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">x </tex></formula> - and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">y</tex></formula> -axis, respectively, and consumed energy by about 23.7 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$%$</tex></formula> and 5.5 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$%$</tex> </formula> for the respective axis from the conventional method with a linear sliding surface.