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Engineering - ENGR 430

Systems and Control

• Partial fraction expansion of transfer functions involving real distinct, real multiple, complex roots and combinations of the above (done by hand).
• Laplace transforms of systems in the time domain and inverse Laplace transforms of systems in the frequency domain.
• Model simple mechanical translational, mechanical rotational, electrical and electromechanical systems (systems involving motors) and derive their transfer functions in the frequency domain.
• Model systems with inverting and non-inverting amplifiers and derive their transfer functions.
• Convert mechanical to electrical equivalent circuits or analogs (series approach).
• Model simple mechanical translational, mechanical rotational, electrical and electromechanical systems (systems involving motors), selecting state variables, and derive their state space equations.
• Convert a transfer function to a set of state space equations.
• Convert a set of state space equations to a transfer function.
• Convert a transfer function to an nth order Ordinary Differential Equation (ODE).
• Convert an nth order ODE to a set of state space equations.
• Convert a set of state space equations to an nth order ODE.
• Sketch the step response of first order systems.
• Analyze first order systems and determine their rise time, settling time,
• Sketch the step response of second order systems for various damping ratios.
• Analyze underdamped, second order systems and determine their rise time, settling time, damping ratio, peak time, percent overshoot.
• Determine the effect that pole displacement on the complex plane has on underdamped, second order systems.
• Determine the system response when additional poles (other than the dominant poles) are present.
• Determine the system response when additional zeros (other than the zero found on the original transfer function) are present.
• Draw and manipulate block diagrams (reduction in order to derive the transfer function). Work can be done using tables or mathematics.
• Reduce block diagram in order to determine the system’s transient response.
• Draw signal flow graphs.
• Use Mason’s rule to calculate the transfer function from a signal flow graph.
• Draw signal flow graphs of state equations and any other ODEs with constant coefficients.
• Determine system stability via the Routh-Hurwitz Criterion.
• Apply the Routh-Hurwitz Criterion in special cases.
• Design systems using the Routh-Hurwitz Criterion.
• Determine steady state errors for unity feedback systems.
• Derive static error constants and system types.
• Determine steady state error specifications.
• Calculate steady state error for disturbances and non-unity feedback systems.
• Sketch a complete root locus by hand. Find the breakaway/breakin points, jw crossings, angles of departure, angles of arrival, location of asymptotes.
• Draw a complete root locus on the computer using Matlab.
• Interpret Root Locus plots based on their properties.
• Design linear compensators for controlling dynamics systems based on specific requirements.

Prepared by Drs. Nikos Kiritsis & Therrill Valentine