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This paper aims to present the design and prototype of an inspection robot that can perform both horizontal and vertical locomotion in ferromagnetic pipelines. The proposed robot applies to a range from 5-inch (127 mm) diameter pipes to flat plates. The train-like robot is mainly composed of three sealed modules with omnidirectional driving wheels for longitudinal and transverse movements. Permanent magnets were designed to provide sufficient magnetic adhesion between the robot and the ferromagnetic surface of the pipes. The internal condition of the pipe can be monitored visually through cameras and sensors. Specific experimental conditions have been carried out to validate the robot’s capabilities, including maximum speed, payload capacity, and vertical climbing distance. The experimental results also show that the robot is capable of passing through a straight pipe and elbow fitting in both upward and downward directions.

The Hepatitis-B (HBV) epidemic's dynamic can be presented as a compartment model. Determining the HBV epidemic control strategy can be considered a nonlinear feedback control problem. The sliding mode controller (SMC) is an effective feedback control method for controlling the dynamical system under disturbances. Recently, the SMC based on fractional order calculus can provide preferable characteristics for a control system such as robustness and convergence rate. In this study, the HBV epidemic system's control policy is proposed using the fractional order sliding mode controller (FOSMC). The control policy with multiple measures including vaccination, isolation, and treatment is formulated to manipulate the susceptible and the infected subpopulations to the desired level. The Lyapunov-based approach is proven for stability analysis. The control policy is applied to the simulation example to verify the feasibility of the proposed FOSMC method. The simulation results are compared with those of the integer order SMC. By the proposed method, the results reveal that the susceptible and infected subpopulations are driven to the desired levels under disturbances with a higher convergence rate compared to that of the integer one. Moreover, the proposed FOSMC method can reduce the chattering occurrence which is the primary drawback of the SMC method.

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<span lang="EN-US">This article proposes the design of a sliding mode controller with a time-varying sliding surface for the plate heat exchanger. A time-varying sliding mode controller (TVSMC) combines the benefit of the control system’s robustness and convergence rate. Using Lyapunov stability theory, the stability of the designed controller is proved. In addition, the controller parameters of the designed controller are specified optimally via the dragonfly algorithm (DA). The input constraint’s effect is considered in the controller design process by applying the concept of the auxiliary system. The bounded disturbances are applied to investigate the robustness of the proposed techniques. Moreover, the quasi-sliding mode controller (QSMC) is developed as a benchmark to evaluate the convergence behavior of the proposed TVSMC technique. The simulation results demonstrate the proposed TVSMC with the optimal parameters provided by the DA algorithm (TVSMC+DA) can regulate the temperature to the desired level under bounded disturbances. When compared to the QSMC method, the TVSMC+DA performs significantly faster convergence speed and greater reduction in chattering occurrence. The results clearly indicate that the proposed controller can enhance convergence properties while being robust to disturbances.</span>

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