Renewable energy generation is increasingly important due to serious energy issues. A Doubly Salient Permanent Magnet Generator (DSPMG) can be an interesting candidate for tidal stream renewable energy systems. However, the special structure makes the system nonlinear and strongly coupled even after Park transformation and involves a larger torque ripple. Previous research mainly focused on model-based control for this machine, which is very sensitive to the parameters. Thus, to control the complex systems stably and accurately, two model-free control algorithms, Active Disturbance Rejection-Based Iterative Learning Control (ADRILC) and Active Disturbance Rejection Control–Iterative Learning Control (ADRC–ILC), are proposed for the current and speed control loops of a DSPMG-based Tidal Stream Turbine (TST), respectively. ADRC–ILC uses ADRC to deal with the external non-periodic speed ripple and adopts ILC to reduce the internal periodic speed ripple. ADRILC employs an iterative method to improve the ESO for the enhancement of the convergence rate of ILC. Considering the variable tidal speed, when the speed is above the rated value, Maximum Power Point Tracking (MPPT) must be changed to a power limitation strategy for limiting the generator power to the rated value and extending the system operating range. Thus, Optimal Tip Speed Ratio (OTSR)-based MPPT (for a low tidal current speed) and Leading Angle Flux-Weakening Control (LAFWC) (for a high tidal current speed) strategies are also proposed. According to the simulation results, the proposed ADRC–ILC + ADRILC has the lowest torque ripple, the highest control accuracy, as well as a good current tracking capability and strong robustness. At the rated speed, the proposed method reduces the torque ripple by more than 20% and the speed error by about 80% compared with PI control: the current difference is limited in 2A. The LAFWC proposed for an excessive tidal current speed is effective in conserving the electromagnetic power and increasing the generator speed.