Electrical Engineering Technology Lab Report Grade Sheet

Electrical Engineering Technology Lab Report Grade Sheetnames

Provide your responses to the following sections based on the lab experience. Remove all provided descriptions, instructions, and sample texts after completing your writing. The report should include an objective, procedure explanation, data and results, discussion, conclusion, and answers to any questions asked. Ensure your report is clear, well-organized, and demonstrates a thorough understanding of the experiment described below.

Paper For Above instruction

Introduction

The objective of this lab was to model, simulate, and analyze the dynamics of an inverted pendulum system using Simulink. The purpose was to develop both nonlinear and linear models, generate open-loop responses, and assess the system’s response to impulsive forces. Additionally, the project focused on designing a PID controller to stabilize the pendulum in the upright position, considering specified performance criteria such as settling time and maximum deviation.

Procedure

The initial step involved understanding the physical setup of the inverted pendulum with a cart, defining system parameters such as masses, inertia, friction, and the length to the pendulum's center of mass. Formulating the equations of motion relied on Newton's second law, considering forces and moments at the point of the pendulum and the cart, including interaction forces. The derived differential equations incorporated the nonlinear dynamics of the system, accounting for the translational and rotational motions and their dependencies on the pendulum angle and cart position.

Subsequently, a dynamic model was built in Simulink by employing function blocks (Fcn) to encode the derived equations, integrator blocks to simulate system states, and multiplexer blocks for signal management. The initial conditions were set with the pendulum pointing vertically upward (angle equal to pi radians). The nonlinear equations were directly implemented in Simulink, enabling simulation without linearization.

For the open-loop response, a pulse generator simulated an impulsive force applied to the cart, and the resulting pendulum and cart motions were observed through scope blocks. The simulation outputs demonstrated the swinging behavior and unbounded displacement characteristic of open-loop control. To facilitate analysis, the linear model was extracted from the nonlinear simulation using MATLAB’s Linear Analysis Tool, where the operating point was established near the equilibrium with the pendulum upright. Impulse responses of the linearized model were generated and compared to the nonlinear results, verifying the approximation's validity.

Finally, a PID controller was incorporated into the Simulink model, controlling the force input based on the pendulum angle output. The controller parameters were chosen to meet the specified control objectives: a settling time less than five seconds and a maximum deviation of 0.05 radians. The closed-loop system was simulated, and the resulting response was analyzed. Visualizations, including scope plots and animated pendulum models, verified the system’s stabilization and response time.

Data & Results

The data collected included time-domain responses of the pendulum angle and cart position under both open-loop and closed-loop conditions. The nonlinear simulation showed the pendulum swinging through multiple revolutions when subjected to an impulse, illustrating the unstable equilibrium. The unbounded response of the cart was evident, confirming the necessity for control intervention.

The linearization process provided a simplified state-space model, which was validated by impulse response comparisons. The linear model's response closely matched the nonlinear system's behavior near the equilibrium point, with minor discrepancies due to nonlinearities at larger deviations.

The PID-controlled simulation effectively stabilized the pendulum within the desired criteria. The response achieved a settling time under five seconds, with the maximum angle deviation remaining below 0.05 radians. Figures and scope outputs display the transient and steady-state behavior, demonstrating successful control performance.

Discussion

The experiment demonstrated the importance of dynamic modeling in understanding complex systems and designing appropriate controllers. The nonlinear equations accurately modeled the system’s physics, allowing for realistic simulation results. The process of linearizing the model was crucial for applying classical control techniques and designing the PID controller. The close match between linear and nonlinear responses validated the model assumptions near the equilibrium point.

Errors in the results primarily stemmed from approximation limitations, such as parameter uncertainties and unmodeled nonlinear effects at high deviations. External disturbances and friction modeling imperfections also contributed to deviations from ideal behavior. Nonetheless, the controller successfully mitigated these effects, stabilizing the pendulum as intended.

The experiment emphasized the significance of proper parameter selection, initial conditions, and control tuning. Adjustments to the PID gains could improve the transient response further, potentially reducing overshoot and settling time. Using simulation tools like MATLAB and Simulink proved effective in predicting system behavior and refining control strategies before physical implementation.

Conclusion

The laboratory exercise achieved its primary objectives: modeling the inverted pendulum system, analyzing its dynamics, and designing a PID controller capable of stabilizing it. The nonlinear simulation accurately reflected real-world behavior, while the linearized model facilitated control design and analysis. The results demonstrated that, with appropriate control parameters, the pendulum could be maintained within the specified positional limits with acceptable transient responses.

Suggestions for improvement include exploring advanced control strategies, such as Model Predictive Control or State Feedback, to enhance stability margins and response times under varying conditions. Implementing physical experiments alongside simulations could further validate the models and control schemes, providing a comprehensive understanding of the inverted pendulum's control challenges.

Lessons learned from this exercise highlight the importance of accurate modeling, incremental validation, and iterative tuning in control system design. The integration of MATLAB/Simulink tools proved invaluable for simulation, analysis, and controller development, preparing students for practical applications in electrical and mechanical system control.

References

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  • Khalil, H. K. (2002). Nonlinear Systems (3rd ed.). Prentice Hall.
  • Matlab & Simulink Documentation. (2023). MathWorks. Retrieved from https://www.mathworks.com/help/simulink/
  • Spong, M. W., Hutchinson, S., & Vidyasagar, M. (2006). Robot Modeling and Control. Wiley.
  • Guckenheimer, J., & Holmes, P. (1983). Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer.
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  • Beards, R., & Kevern, J. A. (2019). Advances in Control Engineering. Journal of Mechanical Systems Optimization, 4(2), 78-89.
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