A formal representation of cloud models for mapping between qualitative and quantitative knowledge is presented in this paper.The algorithms for producing the cloud drops are given to describe fuzziness and randomness contained in linguistic concepts. The uncertainty reasoning mechanism is proposed with such cloud models, while several qualitative rules are activated simultaneously.The cloud theory has been successfully applied to balance one-, two- and three-link inverted pendulum systems driven by single motor showing different balancing patterns and some robustness. This intelligent control technique can be used in control of robots and flying objects in space. Moreover, it may have universal significance in revealing the transformation law between qualitative and quantitative knowledge.