ME 4030 Final Oral Exam Study Guide Flashcards

Vocabulary-style flashcards covering foundational to advanced concepts in control systems theory, following the ME 4030 course schedule.

Control system

An arrangement of components that directs or regulates a process so its output behaves in a desired way by comparing actual performance with desired behavior.

Open-loop system

A system that chooses its input without measuring the actual output, meaning it cannot automatically correct for disturbances or modeling errors.

Closed-loop system

A system that measures the output, compares it with a reference, and changes the input based on the error to improve accuracy and disturbance resistance.

Plant

The physical process being controlled, such as a motor, aircraft, or chemical process, where dynamics map actuator input to measured output.

Controller

A component that uses the reference and measured output to calculate the command sent to the actuator to meet stability and performance requirements.

Actuator

A device that converts the controller's low-power command into a physical action on the plant, often limited by saturation and non-instantaneous dynamics.

Sensor

A component that measures the controlled output or state and converts it into a signal usable by the controller; its noise and delay affect loop performance.

Error signal

The difference between the desired reference and the feedback measurement, commonly expressed as $e(t) = r(t) - y_m(t)$.

Negative feedback

Feedback that acts to reduce deviations from the reference, generally used to improve regulation, robustness, and stability.

Positive feedback

Feedback that reinforces deviations and tends to drive poles toward instability, used intentionally in devices like electronic oscillators or Schmitt triggers.

Laplace Transform

A mathematical tool that converts linear differential equations into algebraic equations in $s$, turning differentiation into multiplication by $s$.

Transfer function

A model describing the external input-output behavior of a linear time-invariant (LTI) system, defined under the assumption of zero initial conditions.

s-variable

A complex variable $s = \text{sigma} + j\text{omega}$ representing exponential modes $e^{st}$, where the real part determines decay/growth and the imaginary part determines oscillation frequency.

Poles

Natural modes of the system that determine stability and basic transient response; they are the roots of the characteristic equation (denominator of the transfer function).

Zeros

Roots of the numerator of a transfer function that shape how inputs excite natural modes, affecting factors like overshoot and phase.

Initial Value Theorem

A theorem used to determine the value of a time signal immediately after time zero from its Laplace transform by examining high-frequency behavior.

Final Value Theorem

A theorem giving the long-term value of a signal from its Laplace transform; it fails if the signal does not settle or if poles of $sY(s)$ lie in the right-half plane.

Dominant poles

Poles closest to the imaginary axis that decay most slowly and therefore govern the visible settling and transient behavior of the system.

Rise time

A practical measure of response speed, representing the time required for output to move from a low percentage to a high percentage of its final value (commonly $10\%$ to $90\%$).

Settling time

The time required for a system response to enter and remain within a specified band (often $2\%$ or $5\%$) around the final value.

Stability

A property where bounded disturbances or inputs do not grow without limit; for continuous-time LTI systems, this requires all closed-loop poles to be in the left-half plane.

Marginally stable

A state where a system has simple poles on the imaginary axis, resulting in sustained oscillations or constant modes that neither decay nor grow.

Routh's Criterion

An algebraic method for determining how many roots of a polynomial lie in the right-half plane, left-half plane, or imaginary axis without explicitly calculating the roots.

Damping ratio

A parameter describing how strongly a system suppresses oscillation; low values lead to ringing/overshoot while high values return smoothly but more slowly.

Proportional control

A control method that commands an input proportional to the present error; it increases response speed but often cannot eliminate steady-state error on its own.

Integral control

A control method that accumulates error over time to provide infinite gain at zero frequency, effectively eliminating steady-state error for constant inputs.

Derivative control

A control method that responds to the rate of change of error to anticipate output movement, adding damping and reducing overshoot.

System Type

The number of pure integrators (open-loop poles at the origin) in $G(s)H(s)$, which determines the system's ability to track polynomial reference inputs.

Step input

A command that suddenly changes to a new constant value, such as a thermostat being adjusted from $70$ to $72$ degrees.

Ramp input

A command that increases at a constant rate, representing a target moving with constant velocity.

Parabolic input

A command with a linearly increasing slope, corresponding to constant acceleration in a position command.

Root Locus

A graphical map showing how closed-loop poles move in the complex plane as a scalar loop gain varies from zero to infinity.

Breakaway point

A location where two or more real closed-loop poles meet and then leave the real axis, marking a transition between nonoscillatory and complex oscillatory modes.

Lead compensation

A controller design that adds positive phase to increase bandwidth and move dominant poles farther left, generally speeding up the system.

Lag compensation

A controller design that increases low-frequency gain relative to crossover to improve steady-state error without significantly changing the transient response poles.

Bode Plots

A frequency response representation using logarithmic frequency axes to display magnitude (in decibels) and phase (in degrees).

Bandwidth

The frequency range over which a closed-loop system follows inputs effectively; it involves a tradeoff between tracking speed and noise transmission.

Nyquist Criterion

A method that assesses closed-loop stability by tracking how the complex value $L(j\text{omega})$ winds around the critical point $-1$ as frequency sweeps.

Gain margin

A measure of robustness estimating how much the loop gain can increase before the closed-loop system reaches the stability boundary.

Phase margin

An estimate of how much additional phase lag (e.g., from time delay) can be tolerated at the gain crossover frequency before reaching instability.

Time delay

A nonrational component that adds linear phase lag with frequency while leaving magnitude unchanged, which can turn corrective feedback into reinforcing feedback.

State

A minimal set of variables whose current values and future inputs determine the system's future behavior, representing stored information or energy.

Controllability

A system property meaning an appropriate input can move the state from any initial condition to any desired final state in finite time.

Observability

A system property meaning the internal state can be uniquely reconstructed from the known input and measured output over a finite interval.

Robustness

The ability of a system to remain stable and perform acceptably despite uncertainty, disturbances, noise, and parameter changes.