I describe how intelligent scientific computing techniques are used in automating the difficult task of analyzing and synthesizing complex control systems. My research has developed a novel design methodology for the synthesis of automatic controllers, together with a suite of computational tools that automatically analyze and design controllers for high-performance, global control of nonlinear systems. These programs combine powerful numerical and symbolic computations with artificial intelligence representation and reasoning mechanisms. They embody deep knowledge of nonlinear dynamics and control theory and actively exploit special properties of the domains to attain otherwise impossible performance. They formalize implicit working knowledge of professional control engineers in computational terms and use the formalized knowledge to autonomously explore the design space. The two major programs in the suite of tools--MAPS and Phase Space Navigator--work together to visualize and model the phase-space geometry and topology of a given system, use a novel technique of "flow pipes" to plan global reference trajectories in phase space, and navigate the system along the planned trajectories. The flow-pipe technique parses a continuous phase space of a dynamical system, consisting of an infinite number of individual trajectories, into a discrete collection of equivalence classes that a computer can efficiently reason about. The programs have been demonstrated on a real engineering problem--the automatic design of a high-quality controller for a magnetic levitation system.