Loop Bandwidth Optimization and Dynamic Performance Improvement of Digitally Controlled High Voltage Power Supply
Digital control of high voltage power supplies offers advantages including flexibility, advanced control algorithms, and integration with system management. The control loop bandwidth, the frequency range over which the control effectively rejects disturbances and tracks commands, determines the dynamic performance including transient response and disturbance rejection. Optimization of the loop bandwidth in digital control must account for the discrete time nature of the control, the sampling and computation delays, and the stability constraints.
Digital control systems sample the output at discrete intervals, compute the control action, and update the control output. The sampling period introduces a delay that affects the phase margin of the control loop. The computation time between sampling and output update adds additional delay. These delays reduce the achievable bandwidth compared to continuous time control, as the phase lag from delay reduces the phase margin at crossover.
The control loop bandwidth is the frequency where the loop gain crosses unity. Below this frequency, the control effectively rejects disturbances and tracks reference changes. Above this frequency, the loop has little effect and the output responds to disturbances according to the open loop characteristics. Higher bandwidth enables rejection of higher frequency disturbances and faster response to reference changes.
Stability requirements constrain the achievable bandwidth. The phase margin at crossover, the difference between the loop phase and negative 180 degrees, must be positive to ensure stability. Adequate phase margin, typically 45 degrees or more, provides robustness against variations in loop parameters. The gain margin, the factor by which the gain can increase before instability, must also be adequate. The delays in digital control reduce the phase margin, limiting the crossover frequency for a given phase margin requirement.
Controller design for digital control uses discrete time control theory. The proportional integral derivative controller is commonly used, with the integral term providing zero steady state error for constant references and the derivative term providing phase lead for stability. The controller parameters are tuned to achieve the desired crossover frequency and phase margin. More advanced controllers including lead lag compensators and state feedback can provide better performance.
Anti windup strategies prevent integrator windup during saturation. When the control output saturates, the integrator continues to integrate the error, potentially winding up to large values. When the saturation clears, the wound up integrator causes large overshoot or slow recovery. Anti windup modifies the integrator state during saturation to prevent this behavior, improving the transient response.
Feedforward control can improve the transient response to reference changes. The feedforward path computes a control action based on the reference and its derivatives, bypassing the feedback loop to provide immediate response. The feedforward action handles the predictable part of the response, while the feedback handles disturbances and modeling errors. Feedforward can achieve faster response than feedback alone.
Disturbance observer techniques estimate disturbances from the measured output and the control action, enabling feedforward of the estimated disturbance to cancel its effect. The disturbance observer effectively increases the loop gain at frequencies where the observer is accurate, improving disturbance rejection without requiring high bandwidth feedback. The observer bandwidth determines the frequency range of effective disturbance rejection.
Digital implementation considerations include quantization effects, sampling jitter, and computation precision. Quantization of the measured output and the control action introduces quantization noise and can cause limit cycles. Sampling jitter varies the effective sampling period, introducing phase modulation. Finite precision arithmetic can cause overflow or underflow. These effects must be considered in the design to ensure that the digital implementation achieves the designed performance.
Testing and validation of the digital control performance measure the transient response, the disturbance rejection, and the stability margins. Step response tests characterize the response to reference changes. Load transient tests characterize the disturbance rejection. Frequency response tests measure the loop gain and phase, identifying the crossover frequency and margins. The tests verify that the design meets the performance requirements and validate the digital implementation.
