GATE EY key terms

A frequency-domain test that determines closed-loop stability by counting encirclements of the point -1 by the open-loop transfer function's polar plot, relating encirclements to open-loop right-half-plane poles.

An algebraic method that counts right-half-plane roots of a polynomial by inspecting sign changes in the first column of the Routh array, avoiding explicit root computation.

The factor by which open-loop gain can be increased before a closed-loop system reaches marginal stability, read as the vertical distance from the magnitude curve to 0 dB at the phase crossover frequency.

The additional phase lag, measured in degrees, that can be applied at the gain crossover frequency before the closed-loop system becomes unstable; a direct indicator of relative stability and damping.

A pair of logarithmic frequency-response graphs showing magnitude in decibels and phase in degrees versus frequency, used to assess stability margins and to design cascade compensators.

The polynomial equation obtained by setting the denominator of a closed-loop transfer function to zero; its roots are the closed-loop poles that determine stability and transient response.

The path traced in the complex s-plane by closed-loop poles as a single parameter, usually proportional gain, varies from zero to infinity, revealing how gain shifts dynamic behaviour.

A location on the real axis of the s-plane where two branches of a root locus meet and depart into the complex plane, found where the derivative of gain with respect to position vanishes.

A model of a dynamic system as first-order vector differential equations x-dot = Ax + Bu and y = Cx + Du, exposing internal states rather than only input-output behaviour.

A property meaning an input can drive the state from any initial condition to any final state in finite time; tested by the rank of the controllability matrix built from A and B.

A property meaning the initial state can be reconstructed from knowledge of inputs and outputs over finite time; tested by the rank of the observability matrix built from A and C.

The discrete-time counterpart of the Laplace transform, mapping a sequence to a function of complex variable z; used to analyse stability and response of sampled-data and digital control systems.

A tabular algebraic procedure that determines whether all roots of a discrete-time characteristic polynomial lie inside the unit circle, without explicitly solving for the roots.

An integral transform converting a time-domain function into the complex frequency domain, turning linear differential equations into algebraic equations that are easier to solve and analyse.

The ratio of the Laplace transform of output to that of input under zero initial conditions, characterising a linear time-invariant system completely for input-output purposes.

A feedback controller combining proportional, integral, and derivative actions on the error signal; the integral removes steady-state offset while the derivative adds damping and speeds response.

The residual difference between reference input and output as time tends to infinity; its value depends on system type and on the standard input applied, such as step or ramp.

The number of pure integrators (poles at the origin) in the open-loop transfer function, which fixes whether steady-state error to a step, ramp, or parabolic input is finite or infinite.

The identity expressing a complex exponential as cosine plus imaginary sine of the same angle, underpinning phasor analysis, Fourier series, and complex representations of sinusoids.

A complex number representing the amplitude and phase of a sinusoid at a fixed frequency, allowing steady-state AC circuit equations to be solved algebraically rather than with differential equations.

The complex ratio of phasor voltage to phasor current in an AC circuit, combining resistance with reactance from inductors and capacitors and depending on signal frequency.

A condition in which an AC circuit's inductive and capacitive reactances cancel, making impedance purely resistive and current or voltage amplitudes reach an extremum at a specific frequency.

A dimensionless measure of energy stored versus energy dissipated per cycle in a resonant circuit; higher values mean a sharper, narrower resonance peak and slower decay.

A linear two-terminal network can be replaced by a single voltage source in series with a resistance, determined by the open-circuit voltage and the equivalent resistance seen with sources deactivated.

A linear two-terminal network can be replaced by a current source in parallel with a resistance, the dual of Thevenin's equivalent and related to it by source transformation.

In linear circuits with multiple independent sources, the total response equals the algebraic sum of responses computed with each source acting alone while others are deactivated.

Four coupled equations relating electric and magnetic fields to charge and current distributions, governing electromagnetic wave propagation, induction, and the behaviour of all classical electromagnetic phenomena.

The cross product of electric and magnetic field intensities, giving power flow per unit area in an electromagnetic field; its time average yields the radiated power density.

The distance into a conductor at which current density falls to 1/e of its surface value, shrinking with increasing frequency and causing high-frequency current to crowd near the surface.

A thermodynamic relation giving the slope of a phase boundary in the pressure-temperature plane as latent heat divided by temperature times the change in molar volume.

The partial molar Gibbs free energy of a component, measuring how the free energy of a system changes when that component's amount changes at fixed temperature and pressure.

A thermodynamic potential defined as enthalpy minus temperature times entropy; its decrease at constant temperature and pressure sets the spontaneous direction of a process.

The relation stating that degrees of freedom equal components minus phases plus two, for a system in equilibrium where temperature and pressure are both variable.

A state function measuring the dispersal of energy in a system; it increases for spontaneous processes in an isolated system and is defined via reversible heat exchange divided by temperature.

The principle that entropy of an isolated system never decreases, establishing the direction of spontaneous change and forbidding complete conversion of heat into work in a cyclic engine.

The maximum possible efficiency of a heat engine operating between two reservoirs, equal to one minus the ratio of cold to hot absolute temperatures, independent of the working substance.

A model of enzyme-catalysed reaction rate as a function of substrate concentration, giving a rectangular hyperbola with parameters maximum velocity and the Michaelis constant.

A double-reciprocal linearisation of the Michaelis-Menten equation whose intercepts and slope yield the Michaelis constant and maximum velocity, and whose pattern reveals inhibition type.