Vibratory screening, sieving, and conveying processes are widely used in various industries. Among a great variety of vibration exciters, the unbalanced rotors are the most reliable, simple, and widespread ones. Due to the changeable operating conditions of vibratory equipment, in some cases, there occurs a necessity to control the disturbance (excitation) parameters of the corresponding drives. The primary purpose of this study is to substantiate the design parameters and analyze the dynamic characteristics of the vibratory screening conveyor based on the single-mass oscillatory system, and equipped with the controllable centrifugal exciter. The research methodology consists of several basic stages: developing the conveyor’s dynamic diagram and deducing the differential equations of the system’s motion; designing the machine’s 3D-model and defining its main geometrical and inertial parameters; numerical modeling of the system’s oscillations in the Mathematica software; simulating the conveyor’s operation in the SolidWorks software. The research results present the time dependencies of the conveyor’s working member kinematic parameters at different eccentricities of the unbalanced mass. The main scientific novelty of this research is substantiating the idea and possibilities of implementing the enhanced controllable centrifugal exciter for changing the disturbance (excitation) conditions of the vibratory screening and conveying machines. The proposed ideas and obtained results can be used by researchers and designers of similar equipment while developing control systems for regulating its operational efficiency (performance) in accordance with the changeable loading conditions or technological requirements.