State-Adversarial Neuro-dynamic Nonlinear PIλDµ Control

Abstract Optimization and reinforcement-based algorithms that self-tune fractional order PID controllers have gained attention due to their enhanced set-point tracking and disturbance rejection capabilities for virtual inertia control problems. The proof of stability of fractional order PID controllers usually limits the fractional orders of |µ| and |λ| to between N −1 and N,N ∈ Z. However, this bound may be too restrictive owing to the loss of closed-loop performance and issues in training deep-learning networks that tune these strategies. In this study, a novel state-adversarial deep deterministic policy gradient nonlinear-fractional order PID (SA-DDPG-NFoPID) controller is constructed. We propose a framework for improper/proper fractional orders of µ and λ with relaxed bounds and sufficient conditions that guarantee stability under undisturbed scenarios i.t.s. of Lyapunov and separately is guaranteed to be Mittag-Leffler stable under disturbed conditions. The proposed technique is tested with 3 scenarios including a low-inertia microgrid with high penetration of renewables. The SA-DDPG-NFoPID controller exhibited the best performance in all test scenarios compared to recent control algorithms.