Abstract: This disclosure describes systems, methods, and apparatus for designing and using an H˜ controller. The controller can be used in an RF power generation system for providing multi-level pulsed waveforms to a plasma load, where robust controller design is desired. This can be achieved through a two phase optimization for the controller based on a first phase of H? loopshaping based on one or more first performance metrics, that acts as a sub-routine within a second phase or larger optimization loop that simulates the controller designed by the H? loopshaping and optimizes based on one or more second performance metrics that may include one or more of the first performance metrics.

Abstract: An example device comprises a reference model module, an adaptation law module, and an adaptive control module. The reference model module is configured to receive a setpoint input and a reference model input, and to generate a reference model output. The adaptation law module is configured to receive the reference model output from the reference model module, to perform a signum projection tensor operation based at least in part on the reference model output, and to generate a signum projection adaptation law output. The adaptive control module is configured to receive the adaptation law output from the adaptation law module, to receive the setpoint input, and to receive a sensor system output from a sensor system, and to generate an adaptive control signal.

Abstract: This disclosure describes systems, methods, and apparatus for generating a multi-level pulsed waveform using a DC section and a power amplifier. To improve DC section efficiency, a master state is used to determine when the rail voltage can be lowered, and to only allow a state assigned as the master state to lower the rail voltage. Selection of the master state is based on (1) any state having to raise the rail voltage to meet a power demand or (2) a state having the highest drive voltage as determined at the end of each pulse cycle. Further, to avoid challenges from integrator controller, drive voltage is carried over from a last state of one pulse cycle to a first state of a next pulse cycle and assignment of master state in the first state of each pulse cycle is not important and can be arbitrarily selected.