In this paper, a mathematical model of cancer treatment, in the form of a system of ordinary differential equations, by chemotherapy and radiotherapy where there is metastasis from a primary to a secondary site has been proposed and analyzed. The interaction between immune cells and cancer cells has been examined, and the chemotherapy agent has been considered as a predator on both normal and cancer cells. The metastasis may be time delayed. For better investigation of the treatment process and based on physical investigation, the immanent effects of inputs on cancer dynamic have been investigated. It is supposed that the interaction between NK cells and tumor cells changes during the chemotherapy. Thisnovel approach is useful not only to gain a broad understanding of the specific system dynamics but also to guide the development of combination therapies. The analysis is carried out both analytically (where possible) and numerically. By considering such immanent effects, the tumor-free equilibrium point will be stable at the end of treatment, and the tumor can not recur again, and the patient will totally recover. So, the present analysis suggests that a proper treatment method should change the dynamics of the cancer instead of only reducing the population of cancer cells.

The proportional-integral-derivative controller is widely used in various industrial applications. But, in many noisy problems the strong methods are needed to optimize the proportional-integral-derivative parameters. In this paper, a novel method is introduced for adjusting the proportional-integral-derivative parameters through the model predictive control and generalized type-2 fuzzy-logic systems. The rules of suggested fuzzy system are online adjusted and the parameters of proportional-integral-derivative are tuned based on the fuzzy model such that a cost function to be minimized. The designed controller is applied on continuous stirred tank reactor and the performance is compared with other traditional approaches. The main advantages are that the accuracy is improved by online modeling and optimization and a predictive scheme is added to the conventional proportional-integral-derivative controller.

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The two challenges facing human life are water and energy. Reverse osmosis (RO) desalination systems are popular owning to their unique advantages. However, robust performance and power supply are the two main challenges in this desalination system. This power is used to drive an induction motor that rotates a centrifugal pump to apply the required back pressure to the RO membrane.To solve these two challenges, a complete RO system powered by a photovoltaic (PV) system was considered, and for each subsystem, a robust controller was designed based on their dynamic models. A fuzzy controller optimized by the invasive weed algorithm (IWA) was designed to track the maximum power in the photovoltaic subsystem under different environmental conditions. A fuzzy-PID controller was used to control the motor-pump subsystem. Furthermore, it is focused on designing a robust controller with the ability to compensate for large set-point changes, reject external disturbances, and cope with parametric uncertainties, such as variations in feed water salinity. Hence, state-dependent Riccati equation control (SDRE) was used to control the reverse osmosis system. The simulation results for different scenarios show that the proposed controller performs well under different operating conditions and can remove the effects of disturbances on the system.