This work deals with the design of a nonlinear control and estimation strategy for a very low frequency (VLF) test generator which is used for a mobile onsite testing of high-voltage cables. A suitable control of the test generator is required to meet the high demands on the quality and accuracy of the VLF test voltage. First, a detailed mathematical model of the test generator is developed, which describes all the non-ideal characteristics of the system. Based on this detailed model, a reduced model of the test generator and an envelope model are derived. Both simplified models reproduce the main characteristics of the test generator very well and are thus suitable for systems analysis and controller design. In the systems analysis, optimal control inputs are determined in such a way that the power losses during the testing operation are minimized and the high requirements regarding the quality of the test voltage are fulfilled. This knowledge gained from the analysis is directly used in the development of the controller. It is shown that the required quality of the test voltage can only be achieved if, in addition to a suitable nonlinear controller design, several system parameters are optimized. Since the capacitance of the test cable is generally unknown before the testing, the controller is extended by an appropriate estimator for the cable capacitance. The achievable control performance is validated in simulations and measurements on a VLF test generator prototype for test voltages up to 200 kV rms. Finally, an alternative hardware design of the prototype is presented, which further improves the quality of the test voltage and increases the value of the maximum cable capacitance to be tested.