MESB 374 Modeling and Analysis of Dynamic System Introduction

1. MESB 374 Modeling and Analysis of Dynamic SystemIntroduction

2. v Increasing grade t - + + - Example Vehicle speed control Traction: input, excitation Gravitation: disturbance Inertia force Friction: damping 1 2 3 MODEL: linearization ANALYSIS: CONTROL: output input states

3. Remember these? Course Overview One of the most important and multi-disciplinary courses you’ll ever take Physics Kinematics Mathematics Time and frequency response analysis Engineering judgment Leveraging previous coursework and preparing for future coursework Mechanics, electrical, electromechanical Fluid-thermal Calculus, differential equations, complex algebra Measurements/instrumentation understanding Emphasize combination of theoretical and conceptual understanding i.e. Can you explain the basic concepts to other people?

4. Basic Concepts System A combination of components acting together to perform a specific objective Modeling A procedure to obtain a model describing important characteristics of system Analysis Investigation of performance of system, whose model is known, under specified conditions

5. Motivation for MESB 374Pervasiveness

6. Definitions Related to System Input A variable that excites a system Inputs are not always known beforehand Inputs are always responsible for problems in systems Output A variable that we observe and consider important Measurements/instrumentation Not necessary what we want to know State A variable that is used to describes the internal system dynamics A set of states can be used to fully describe system’s current situation. With two identical sets of initial values of states, performance of a system is the same Do you get all the states of system ?

7. Different Systems/System Descriptions Distributed System A System with infinitely many state variables Continuous elastic structures (beams, shells, and plates) Fluid systems (ocean and atmosphere) Can often be approximately described with lumped models (FEM, AMM) Lumped System A System with a finite number of state variables Lumped parameter/ discrete system Usually an artificial/modeling concept Continuous-time System All the signals are continuous in time Everything is defined at each instant time Also called Analog systems Discrete-time Systems Variables are only defined at discrete times Also called sampled data systems Hybrid System Continuous-time + discrete-time

8. More Different Systems/System Descriptions Time-varying System (in practice) The characteristics of system changes with time going time-varying parameters time-varying dynamics Time-invariant System (ideal) The features of system never ever changes Usually a good approximation for most engineering application A good starting point to obtain main features of system Relatively easy to analyze Linear System Equations describing system are linear Principle of superposition Nonlinear System Linearize it near a operating condition to obtain a linear approximation

9. Interdisciplinary and System Nature of MESB 374Analogous systems Models are the same regardless of the physical domain of interest We only need to understand how to analyze one model, but the results are applicable for four seemingly different types of physical systems! = = = y u

10. Verify Model Simulation Study Predict Performance Meet Performance Spec. Meet Performance Spec. Physical System Big Picture Develop Idea Model Modeling Not Good No OK Feedback/ Feedforward Control Design Analysis Design Not So great Good Yes Build Actual System and Verify Design Implement on Actual System Implementation Test GET PAID !! Yes No No Yes

11. Course Outline Introduction Components/ elements Connections/ interconnects Electrical Mechanical Thermal Electromech Hydraulic Input/output Vs. state-variable models Time-frequency tools of systems analysis Feedback and system design