The article is devoted to the urgent problem of improving the roadway cleaning efficiency. To achieve maximum cleaning efficiency, an optimal pressing force of the brush equipment to the surface being cleaned should be provided. A schematic diagram of a sweeping machine working process as a complex dynamic system was constructed including a basic machine, brush and running equipment, a hydraulic drive, a road surface, as well as a microrelief control device reflecting the effect of the microrelief on the vertical coordinate of the working equipment. A mathematical model of the working process of a sweeping machine is presented. The simulation was carried out using the MATLAB software, Simulink extension. As a result, the dependences of the vertical coordinates and the pressing force of the brush equipment were established. In most cases, the brush positioning control is provided by a standard hydraulic drive; however, when the dimensions of a pothole are large enough, the standard hydraulic pump does not guarantee the required speed of the control device so that the deviations of the vertical coordinate could be compensated. To improve the speed of the brush positioning control device, the standard hydraulic pump was supplemented with an additional pump switching on only at particular periods of time.