Weighted Multiobjective Metaheuristic Optimization of PID-SMC for a 2-DOF Manipulator under Torque Disturbances: MGO vs AHA

This paper investigates metaheuristic tuning of a PID-Sliding Mode Control (PID-SMC) structure for stepresponse of a 2-DOF planar robotic manipulator under additive torque disturbances. The controller parameter vector is optimized using two recent optimizers, the Mountain Gazelle Optimizer (MGO) and the Artificial Hummingbird Algorithm (AHA), and is benchmarked against Particle Swarm Optimization (PSO) and Ant Colony Optimization for Continuous Domains (ACOR). Optimization minimizes a scalar cost obtained by weighted-sum scalarization of multiple terms. All tuned controllers achieve stable step regulation for both joints; however, notable tradeoffs arise in overshoot and control activity. In the nominal case, MGO attains the best overall objective (Jθ=120.071643) and achieves the lowest Joint 2 overshoot (20.32 %) compared with PSO (42.90%), AHA (40.08%), and ACOR (28.75%). Under disturbance, tracking remains bounded for all methods, but the classical 2% settling-time metric becomes less informative due to the persistent excitation. The torque-norm plots reveal pronounced high-frequency switching ('chattering'), which is expected in discontinuous SMC implementations and is amplified by disturbance/noise. Overall, the comparative results support MGO as competitive tools for tuning PID-SMC controllers, while also highlighting the need for explicit chattering-mitigation mechanisms when implementing SMC in noisy/disturbed settings.