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ajout cascaded_loop

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Nolan Reynier Nomer 2026-05-14 15:27:12 +02:00
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@ -279,7 +279,7 @@ assistance based on system dynamics.
microcontroller.
The initial idea was to make this tile \textit{pluggable} into our
carrier board, similar to an Arduino shield. This would allow :
carrier board, similar to an Arduino shield. This would allow:
\begin{itemize}
\item Easy replacement of the computing core without re-soldering.
\item Modular upgrades of the microcontroller.
@ -525,6 +525,53 @@ where $e_{\text{ref}} = \SI{-0.5}{\meter}$ represents the desired equilibrium of
\subsection{Control Architecture Exploration}
Beyond the standard PI control structure simulated in the previous sections, this project explores a more sophisticated
control law: the Cascaded Loop Architecture. This approach is envisioned as a high-level software enhancement to meet
the robustness and safety requirements inherent to electric cargo mobility. This means that our control law includes two
feedback loops that use two different physical parameters.
The selected cascaded structure is a well-established industry standard, particularly in high-performance motion control
and robotics. Similar architectures are widely employed in Automated Guided Vehicles (AGVs) and platooning systems,
where a “follower” unit must synchronize its dynamics with a “leader” unit through precise feedback loops.
The proposed approach decomposes the complex task of “cart following” into manageable sub-tasks by nesting control
loops:
\begin{itemize}
\item Outer loop: Position control layer.
Using a linear encoder or distance sensor mounted on the trailer’s hitch, the system measures the relative
displacement (error) between the bicycle and the cargo cart. This error is processed by a Proportional (P)
Controller. The primary goal of this stage is to translate physical distance into a target velocity setpoint. By
saturating the output of this loop, we can prevent the cargo cart from ever exceeding the bicycle’s speed, thereby
ensuring it never “pushes” the cyclist.
\item Inner loop: Velocity control layer.
The velocity setpoint generated by the outer loop is fed into this internal layer, the inner loop is responsible for
commanding the motor torque directly to compensate for immediate mechanical disturbances. Because this loop operates
at a higher frequency, it can reject disturbances such as sudden changes in rolling resistance or friction, before
they significantly impact the overall position error.
\end{itemize}
\begin{figure}[!h]
\centering
\includegraphics[width=\linewidth]{./Figures/Schema_Autom_PIR.pdf}
\caption{Cascaded control architecture for the bicycle-cargo system.}
\label{fig:cascaded-loop}
\end{figure}
Fig.~\ref{fig:cascaded-loop} illustrates the cascade architecture for the dynamics of the cargo bike.
An outer Proportional Controller $K_{p,x}$ converts the position error $e_x = x_{\text{ref}} - x$ into a velocity
reference $v_{\text{ref}}$, which serves as the set-point for the inner loop.
The inner Proportional Controller $K_{p,v}$ then transforms the velocity error $e_v = v_{\text{ref}} - v$ into a
torque reference $\tau_{\text{ref}}$.
This command is processed by the motor/actuator block, which delivers the actual torque $\tau$.
The model of the plant maps this torque to velocity $v$, and the integrator $1/s$ reconstructs the position $x$.
The adoption of a cascaded loop architecture offers decisive advantages but comes with disadvantages. This precision
introduces increased complexity: the multiplication of tuning parameters and the requirement for high-resolution
feedback sensors, such as encoders, raise hardware costs and must come with high-performance software. These technical
constraints represent a significant challenge and may raise other issues.
% ******************************** RESULTS **************************************************************************
@ -592,7 +639,7 @@ cargo cart. The motor current measured during these experiments is shown in Fig.
\begin{figure}[!h]
\centering
\includegraphics[width=\linewidth]{./Figures/Motor_currents.png}
\includegraphics[width=\linewidth]{./Figures/Motor_currents.pdf}
\caption{Measured motor current under three loading conditions.}
\label{fig:motor-currents}
\end{figure}