A new optimal sliding mode controller design using scalar sign function

This paper presents a new optimal sliding mode controller using the scalar sign function method. A smooth, continuous-time scalar sign function is used to replace the discontinuous switching function in the design of a sliding mode controller. The proposed sliding mode controller is designed using an optimal Linear Quadratic Regulator (LQR) approach. The sliding surface of the system is designed using stable eigenvectors and the scalar sign function. Controller simulations are compared with another existing optimal sliding mode controller. To test the effectiveness of the proposed controller, the controller is implemented on an aluminum beam with piezoceramic sensor and actuator for vibration control. This paper includes the control design and stability analysis of the new optimal sliding mode controller, followed by simulation and experimental results. The simulation and experimental results show that the proposed approach is very effective. •Development of optimal sliding mode control using regional eigenvector assignment and scalar sign function.•Construction of sliding surface using the orthogonal matrix of the assigned eigenvector matrix.•Establishment of chattering reduction technique using the optimal linearization of the nonlinear switching function.•Implementation of the proposed method to a beam with piezoceramic sensor and actuator for vibration control.