Cascaded PID-LQR control for trajectory tracking in a 3-DOF robotic arm system: Modeling and simulation

Robotic arm trajectory tracking control is challenging due to multi-joint coupling, nonlinear dynamics, and external disturbances. Conventional PID controllers achieve high tracking accuracy but tend to produce excessive control effort and large current peaks, whereas standalone LQR controllers provide smoother actuation at the cost of slower convergence and larger tracking error. To exploit the complementary strengths of both methods, this paper proposes a cascaded PID-LQR control strategy for a 3-DOF robotic arm driven by separately excited DC motors. The robotic arm kinematics are modeled using the modified Denavit–Hartenberg method with a weighted inverse-kinematics criterion for preferred joint-solution selection. A linear state-space model of the DC motor is derived, upon which an inner-loop LQR controller performs optimal state regulation while an outer-loop PID controller generates a bounded reference correction to enhance tracking capability and disturbance rejection. Comparative simulations are conducted on the MWORKS platform under nominal conditions, external disturbance, measurement noise, and parameter uncertainty. Under external disturbance, the proposed controller reduces the tracking RMSE by 48.63% and the settling time by 93.93% compared with LQR-only, while reducing the control effort by 52.41%, the peak armature current by 82.89%, and the voltage total variation by 84.44% compared with PID-only. Consistent improvements are observed across all tested conditions, confirming the effectiveness and robustness of the proposed method.