## 5 Simulations and Results
### Performance Evaluation and Discussion
The superior performance of the RLCA over the LQI controller is attributed to its adaptive gain modulation and structured control strategy. Unlike the fixed-gain LQI, which applies uniform control gains irrespective of varying system conditions, the RLCA dynamically adjusts its control response based on real-time state errors. This adaptability enables it to achieve improved tracking accuracy, faster convergence, and better disturbance rejection. One of the primary advantages of the RLCA is its ability to effectively mitigate overshoot while enhancing convergence speed. This is achieved through the interplay of its three constituent control terms: \begin{table}
\begin{tabular}{l l l l l} \hline \hline \multirow{2}{*}{**Experiment**} & \multicolumn{2}{c}{**Performance Index**} & \multicolumn{2}{c}{**Control Procedure**} \\ \cline{2-5}  & **Symbol** & **Unit** & **LQI** & **RLCA** \\ \hline \multirow{3}{*}{A} & \(RMSE_{\theta}\) & deg. & 0.017 & 0.013 \\  & OS & deg. & 0.246 & 0.027 \\  & \(T_{\text{ref}}\) & sec. & 0.516 & 0.296 \\ \hline \multirow{3}{*}{B} & \(RMSE_{\theta}\) & deg. & 0.127 & 0.026 \\  & OS & deg. & 1.537 & 0.217 \\  & \(T_{\text{ref}}\) & sec. & 0.514 & 0.288 \\ \hline \multirow{3}{*}{C} & \(RMSE_{\theta}\) & deg. & 0.027 & 0.019 \\  & OS & deg. & 0.255 & 0.020 \\  & \(T_{\text{ref}}\) & sec. & 0.524 & 0.252 \\  & \(M_{\text{park}}\) & deg. & 0.63 & 0.31 \\  & \(T_{\text{ref}}\) & sec. & 0.305 & 0.211 \\ \hline \multirow{3}{*}{D} & \(RMSE_{\theta}\) & deg. & 0.023 & 0.017 \\  & OS & deg. & 0.247 & 0.025 \\  & \(T_{\text{ref}}\) & sec. & 0.520 & 0.204 \\  & \(M_{\text{park}}^{\text{park}}\) & deg. & 0.333 & 0.145 \\  & \(T_{\text{ref}}\) & sec. & 1.292 & 0.815 \\ \hline \multirow{3}{*}{E} & \(RMSE_{\theta}\) & deg. & 0.028 & 0.015 \\  & OS & deg. & 0.250 & 0.010 \\  & \(T_{\text{ref}}\) & sec. & 0.517 & 0.288 \\  & \(M_{\text{park}}^{\text{park}}\) & deg. & 0.735 & 0.270 \\  & \(T_{\text{ref}}\) & sec. & 0.427 & 0.403 \\ \hline \multirow{3}{*}{F} & \(RMSE_{\theta}\) & deg. & 0.263 & 0.081 \\  & OS & deg. & 1.193 & 0.046 \\ \cline{1-1}  & \(T_{\text{ref}}\) & sec. & 0.496 & 0.302 \\ \cline{1-1}  & \(T_{\text{ref}}\) & deg. & 2.958 & 1.709 \\ \cline{1-1}  & \(T_{\text{ref}}\) & sec. & 0.344 & 0.235 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of experimental results. * _Dissipative control component:_ Under small error conditions, the dissipative term ensures controlled energy dissipation, preventing excessive control input fluctuations that could lead to oscillations or overshoot. This mechanism exponentially attenuates the applied control action as the system state approaches equilibrium, ensuring a smooth and stable convergence. * _Model-reference tracking component:_ The RLCA employs an LQI-derived model-reference tracking term, which acts as a baseline controller under nominal conditions. By maintaining alignment with the LQI control law when disturbances are absent, the RLCA preserves steady-state accuracy while minimizing unnecessary control effort. This ensures that the system operates optimally without excessive control actions that could compromise stability. * _Anti-dissipative control component:_ In contrast to the LQI controller, which lacks a real-time adaptive response to exogenous perturbations, the RLCA leverages an anti-dissipative term informed by the phase of the system's state error. This term intensifies control actions under large error conditions, ensuring rapid disturbance rejection. The inclusion of an error cube polynomial further amplifies corrective control inputs when the system deviates significantly from the reference trajectory, accelerating transient recovery while maintaining stability. These control components are self-regulated via HSF-based adaptive weight functions, allowing smooth transitions between different control phases while minimizing chattering and actuator stress.