Instead of using knowledge-based controllers, which need a lot of experience and experimental data to form a reliable knowledge base, a model-based controller is proposed in this article based on a sliding mode control method to control the brake cylinder pressures of an electropneumatic brake on subway trains. The complicated structure of the electropneumatic brake is simplified, and an order-reduced nonlinear model of the plant is built. An equivalently continuous technique based on pulse width modulation is used to deal with the discontinuity of the plant model, which is derived from the discontinuous nature of On/Off valves. The nonlinear sliding mode controller is designed for air charging and discharging periods, respectively. Measures such as continuous approximation and control dead zone are introduced into the controller to improve control performance. This article concerns mainly about the theoretical part of the whole research. Plant parameter identification and controller tests are performed in a sequel article.