ME 372 – Dynamic Systems (3 Credit Hours)

Course Description: An introduction to the modeling, analysis, and control of dynamic systems. The course takes the student from initial modeling through analysis of the system response and finally into the control of the system. Specific systems include mechanical devices, electrical circuits, and electromechanical systems.

Course Instructors: This course is typically taught by the following instructors:

• Dr. Joey Parker
• Dr. Teik Lim
• Dr. Beth Todd

Sample Syllabus: A sample syllabus indicative of that typically used in the course can be found here.

Pre-Requisite Skills: Students entering this course are expected to have mastered the following skills:

• MATH 238 – Differential Equations
• Find the general form of the homogeneous solution to a linear, time invariant ordinary differential equation (ODE), including the roots of the characteristic equation;
• Find the general form and coefficients for the particular solution based on the specified input;
• Find the final solution using superposition of the homogeneous and particular solutions and the initial conditions.
• Write the general form for first order systems;
• Write the characteristic equation for a first order system given the general equation, given the system root, or given the time constant, t ;
• ESM 264 - Dynamics
• Draw a free body diagram (FBD) of both translational and rotational mechanical systems;
• Sum forces and torques from FBD;
• Compute relative velocities and accelerations for translational mechanical systems;
• ECE 320 – Electric Circuits
• Write the proper units for electrical elements, charges, etc.;
• Write Kirchoff’s Node and Current Laws for a circuit made of resistors, capacitors, and inductors;
• Derive equivalent circuits for resistors in series or in parallel;

Co-Requisite Skills: Students taking this course are expected to be enrolled (or to have taken) courses that teach students the following skills:

• ME 349 – Engineering Analysis
• Matrix formulation for simultaneous linear equations;
• General introduction to Matlabä ;
• Runge-Kutta solution of systems of 1st order equations;

Course Objectives: Students who successfully complete this course can be expected to:

• List appropriate assumptions for modeling a translational or rotational mechanical system made up of mass, spring, and damping elements; (a2)
• Develop state variable equations for translational, rotational (including gears and levers), and combined translational/rotational mechanical systems (e)
• Use Matlabä to find the time response of the state variable model system for arbitrary inputs; (k)
• Use Mapleä to reduce a set of simultaneous linear equations to a valid set of state variable equations; (k,n)
• Derive the state variable equations for an electrical circuit made of resistors, capacitors, inductors, and both ideal voltage and current sources; (e)
• Draw FBDs and write system equations for systems with combinations of linear and rotational mechanical elements and electro-mechanical elements such as a DC motor; (e)
• Determine from the system equations the damping ratio, undamped natural frequency, characteristic equation and the roots of a 2nd order system (e)
• Use Laplace Transform tables to transform a time function into the frequency domain or vice-versa, including the properties for derivatives, integrals, multiplication by e^-at, and multiplication by t to find additional transforms (m)
• Perform a partial fraction expansion on polynomials with real distinct poles, repeated poles, and complex poles; (m)
• Solve a system’s equations of motion (any order) using the ability of Mapleä to find Laplace Transforms and inverse Laplace Transforms; (k,n)
• Develop a transfer function from block diagrams or a set of state variable equations; (e)
• Determine the analytical frequency response (magnitude and phase) for first and second order transfer functions; (m)
• Use Matlabä to plot the frequency response (magnitude and phase) for higher order transfer functions; (k)
• Determine the system transfer function and the roots of the characteristic equation after "closing the loop" for a control system; (e)
• Explain the purpose and implementation of the following parts of the traditional PID controller: proportional, integral, and derivative term; (a)
• Determine the effect of PID controller gains on the following parts of the unit step response: peak overshoot, peak time, settling time, steady-state error. (e)

Sample Examinations: Examples of Examinations given in this course can be found here - Test #1 (PDF), Test #2 (PDF), Final Exam (PDF)

Downstream Users: This course serves as a pre-requisite to the following courses at The University of Alabama:

• ME 475 – Control Systems Analysis