Control Strategies for DC Motor Systems Driving Nonlinear Loads in Mechatronic Applications

DC motors are widely used in mechatronic systems; however, their performance degrades significantly in the presence of nonlinear mechanical loads, parameter variations and sensing uncertainties. This paper proposes three control strategies (i.e., PID, optimal, and hybrid controllers) for discrete-time DC motor systems to overcome the disturbances caused by nonlinear mechanical loads and parameter variations. Optimal control of nonlinear discrete-time systems is formally characterized by the Hamilton–Jacobi–Bellman (HJB) equation, whose analytical solution is generally intractable. To address this challenge, a learning-based optimal control strategy based on the Heuristic Dynamic Programming (HDP) framework is developed to approximate the HJB equation, supported by a formal convergence proof. For that purpose, Neural Networks (NNs) are employed to approximate both the cost function and the optimal control policy, enabling near-optimal performance with manageable computational complexity. Although the resulting optimal control achieves fast convergence, it may introduce overshoot and steady-state offset under nonlinear disturbances. To address this limitation, a hybrid control framework is proposed, where nonlinear optimal corrections are integrated with the robustness and adaptability of Proportional–Integral–Derivative (PID) control through error-dependent gating and gain-scheduling mechanisms. A structured evaluation framework is conducted, including nominal analysis, motor-parameter stress testing across nine nonlinear scenarios, controller-design sensitivity analysis, and stochastic measurement-noise assessment under filtered sensing conditions. Results demonstrate that the hybrid controller preserves transient speeds within 5–10% of the optimal controller while effectively eliminating overshoot and steady-state offset under nominal conditions. The hybrid design reduces the accumulated tracking error by more than 95% compared to the optimal controller, while incurring only negligible additional control effort. Under aggressive supply-sag disturbances, the hybrid controller significantly limits peak deviation and reduces accumulated tracking error by over 90%, while maintaining comparable control cost. Overall, the hybrid framework provides a convergence-proven and practically deployable control solution that combines near-optimal convergence speed with robust, overshoot-free performance for intelligent motion-control and robotics applications.