Dynamometer Simulation

This program simulates an electric dynamometer with a PID controller.

An absorption dynamometer, also known as a" dyno", is a device that measures the instantaneous rotational speed and torque of an engine, motor, or any rotating prime mover while acting as a load. This is accomplished by using various methods to brake the tested motor. Electric dynamometers use another DC motor (a load motor) as a generator and couple it with the test motor to produce an opposing torque that resists the motion. The graphical representation of the dynamometer is illustrated below.

We want to control the torque of the test motor by adjusting R_l. The system is modeled using the fundamental principles, and the state-space representation of the system model is shown below.

$$ \left\lbrack \begin{matrix} \dot{i_t } \\ \dot{\omega} \\ \dot{i_l } \end{matrix}\right\rbrack =\left\lbrack \begin{matrix} {-R}_t/L_t & {-K}_{\text{emf},t}/L_t & 0\\ K_{T,t} /I & -c/I & -{nK}_{T,l} /I\\ 0 & {nK}_{\text{emf},l} /L_l & {-R}_l(t) /L_l \end{matrix}\right\rbrack \left\lbrack \begin{matrix} i_t \\ \omega \\ i_l \end{matrix}\right\rbrack +\left\lbrack \begin{matrix} 1/L_t \\ 0\\ 0 \end{matrix}\right\rbrack \left\lbrack \begin{matrix} V_{\text{in}} \end{matrix}\right\rbrack $$

The objective is to simulate the system's closed-loop response to investigate the behavior. The tricky part is that $R_l(t)$ is not a standard input like a voltage or current source but rather a property of the system. This makes the system a time-variant system and hard to analyze with the Control System Toolbox of MATLAB. Fortunately, the system is linear, and the closed-loop response is simulated with the ode15s function. The block diagram of the system can be seen below.