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In this study, an analytical concept is explored in the simulation environment, and an unbalanced load detection technique is examined to determine its applicability. To continue the development process, a mathematical model for a horizontal washer is developed to comprehend the characteristics of an unbalanced load with respect to various sizes of balanced loads. The mathematical model is then divided into a regressor vector and an estimator vector. Finally, estimates of the unbalanced load, the unbalance location, and the rotational moment of inertia are compared to their references in the simulation environment.

This paper presents a mathematical modeling and simulation of a nonholonomic mobile robot for the low-level control regarding the parameter change using model-based design. The model-based design methodology has been a promising technique in automotive and home appliance industries to address and validate the algorithm development, code generation and its deployment on platform. To investigate the electrical and mechanical behavior of the mobile robot, nonlinear mathematical model is constructed and is added to the control loop with the estimator to identify the parameter change. The recursive least square algorithm is used to identify the inertia and the payload of the robot to adapt the dynamic behavior before applying control law. The performance of the model-based approach is investigated on the simulation environment considering the different payloads with DC motor's constraints to track the reference trajectory using PI controller.