Physical-System-Modeling for Controls Engineering

For the subject Control Engineering

1. Physical System Modeling Foundations for Control Engineering

2. What is System Modeling? System modeling is the mathematical representation of physical systems to understand their behavior and predict responses to inputs. It's essential for designing effective control systems across all engineering disciplines. Definition Mathematical representation of physical phenomena Purpose Predict system behavior and design controls Application Foundation for all control engineering

3. Types of Physical Systems Physical systems span multiple engineering domains, each with unique characteristics and modeling approaches. Mechanical Motion, forces, and dynamics Electrical Voltage, current, and circuits Thermal Heat transfer and temperature Fluid Flow and pressure dynamics Electro-Mechanical Combined electrical and mechanical

4. Key System Terminologies System Properties Lumped vs. Distributed: Concentrated vs. spatially spread parameters Linear vs. Nonlinear: Proportional vs. complex relationships Time-Invariant vs. Variant: Constant vs. changing characteristics System Components Input: External stimulus or command Process: System transformation Output: System response Feedback: Output information for control

5. Fundamental Modeling Principles All physical system models are built on universal laws and conservation principles that govern physical phenomena. 01 Newton's Laws Govern translational and rotational motion dynamics 02 Kirchhoff's Laws Define voltage and current relationships in circuits 03 Conservation Laws Energy and mass conservation across all domains 04 Domain Analogies Force–voltage and force–current relationships

6. Translational Mechanical Systems Translational systems involve linear motion and are modeled using three primary elements: mass, springs, and dampers. Mass Inertia element resisting acceleration Spring Elastic element storing potential energy Damper Viscous friction dissipating energy

7. Rotational Mechanical Systems Rotational systems involve angular motion and torque, modeled using moment of inertia, torsional springs, and rotational dampers. Key Elements Moment of Inertia (rotational mass) Torsional Spring (angular stiffness) Rotational Damper (angular friction) Coupled Systems Translational and rotational motion often interact, requiring integrated modeling approaches for accurate system representation.

8. Modeling Assumptions & Simplifications Practical system modeling requires strategic assumptions to balance accuracy with mathematical tractability. Neglect Small Effects Ignore minor forces and parameters that don't significantly impact system behavior Linearization Approximate nonlinear relationships as linear around operating points Lumped Parameters Treat distributed properties as concentrated elements for simplicity

9. Block Diagram Representation Block diagrams provide visual representation of system structure, showing how components interact through inputs, outputs, and feedback paths. Block diagrams enable engineers to visualize system dynamics, identify feedback mechanisms, and design control strategies systematically.

10. From Theory to Practice System modeling bridges theoretical principles and real-world applications through experimental validation and iterative refinement. Experimental Determination Measure damping and stiffness constants through testing Model Verification Validate torque–angular velocity relationships experimentally System Refinement Adjust models based on measured data for accuracy Control Design Apply validated models to design effective control systems