A novel adaptive SMC strategy for sustained oscillations in nonlinear sandwich systems based on stable limit cycle approach

This paper deals with the problem of creating stable oscillations in the class of nonlinear sandwich systems with dead-zone nonlinearity and unknown disturbances by creating the stable limit cycle. Due to the presence of the non-smooth dead-zone nonlinearity in the middle of the separate subsystems in the sandwich systems' structure, the control synthesis of such systems is complex. In this paper, to deal with the complexities, the control design process is implemented in two steps and a robust adaptive controller is presented by utilizing the sliding mode control (SMC) method. To achieve the control purpose through the SMC, a novel sliding surface is introduced regarding the structure of the admissible limit cycle, which is associated with some characteristics such as frequency, shape, and the amplitude of the desired sustained output oscillations. Simultaneously, the adaptive scheme is employed through the controller design process to extract the proper adaptive laws to estimate the upper bounds of unknown terms. The proposed method guarantees that the admissible limit cycle is generated in the phase plane of the controlled system and consequently verifies that the desired sustained oscillation (with the prescribed properties) is produced at the system's output. It also ensures that all variables in the resulting closed-loop system keep bounded. Finally, to show the effectiveness of the presented method, the given approach is applied to a practical system, and simulation results are given.