ولی اله غفاری

The pursuit of time-optimal performance is a fundamental objective for high-speed robotic and mechatronic systems, where minimizing settling-time directly enhances throughput and operational efficiency. Despite its importance, deriving exact solutions for practical systems remains a formidable challenge. Existing methodologies, which predominantly rely on numerical optimization or simplified plant models, often yield suboptimal results; they fail to provide guarantees of global optimality and frequently prove inadequate when confronting realistic system constraints such as actuator saturation. To address this critical gap, this paper introduces an analytical framework for synthesizing time-optimal control laws for a class of second-order systems. The proposed method is based on phase portrait analysis, a powerful geometric approach that facilitates the direct derivation of the exact switching curve. This curve is the critical element that defines the globally optimal, bang-bang controller. The final control law is presented in a closed-form expression, thereby enabling computationally efficient and straightforward implementation. Simulation results validate the theoretical framework, demonstrating that the proposed controller consistently achieves the theoretical performance by tracking the optimal trajectory perfectly.