High quality multi-axis test facilities used for testing heavy loads and large structures of industrial equipment are usually simulated, designed and controlled based on reduced model equations neglecting the inertia properties of the actuators. The design and control of servo-pneumatic test facilities used for testing small and light structures must take into account extended test facility models including the various inertia properties of the actuators. In this paper (Part I) an extended test facility model is presented including the various inertia properties and joints of the actuators. These extended model equations are represented in a form well suited to be directly implemented in control algorithms based on exact linearization techniques for real time control. This is done by stepwise projecting the inertia properties of the various actuator housings and actuator pistons down to the common mass of the test table and payload. The resulting extended model equations have the same form as the reduced model equations. They only include more complex system matrices and vector functions. These compact model equations turn out to be suitable for an efficient nonlinear controller design of these test facilities. Computer simulations and associated laboratory experiments show the necessity to use extended model equations in case of testing small and light structures. In Part II of this paper [1] the inertia parameters of the planar test facility will be identified in laboratory experiments.