This paper addresses the finite-time tracking problem for the double-layer Peltier system. Peltier is a semiconductor thermoelectrical transform device. It is widely used in the thermal tactile reappearance area. To expand temperature differences, Peltier is usually used in the form of double layers. There are some uncertain factors such as state coupling, external disturbance, and parameter perturbation in double-layer Peltier. Therefore, it is of great theoretical and practical significance to design a controller with superior performance. To this end, a compound continuous integral terminal sliding mode control strategy is proposed here. Firstly, finite-time disturbance observers are designed for feedforward compensation and evaluating the external disturbances. Secondly, the strong robustness of the sliding mode control enhances the disturbance rejection of the system. The continuous integral sliding mode makes the input continuous and weakens the chattering. Also, the terminal sliding mode improves the convergence speed of the system on the sliding surface significantly. The performance of the proposed method is analyzed through Lyapunov stability analysis, simulations, and experiments. Compared to nonsmooth finite-time control, the continuous integral terminal sliding mode control achieves rapid temperature stability and better disturbance rejection under the same condition of finite-time convergence.
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