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Avionics & Control

The electronic systems that enable modern flight: navigation, communication, flight control, and mission management. From analog autopilots to digital fly-by-wire systems, avionics represent the nervous system of every aircraft and spacecraft.

Key Facts

  • Fly-by-wire replaces mechanical flight controls with electronic signals, enabling unstable aircraft designs with better performance
  • Inertial Navigation Systems (INS) use accelerometers and gyroscopes to track position without external references
  • GPS provides position accuracy to within meters; differential GPS can achieve centimeter-level precision
  • The glass cockpit replaces analog instruments with digital displays, reducing pilot workload
  • Autopilot systems use PID controllers to maintain altitude, heading, and speed
  • Triple or quad-redundant systems ensure no single failure can compromise flight safety
  • Data buses (ARINC 429, MIL-STD-1553) standardize avionics communication between systems
  • Modern avionics suites integrate radar, TCAS, EGPWS, and weather systems for situational awareness

Fundamental Equations

PID Controller

u(t)=Kpe(t)+Kiโˆซ0te(ฯ„)โ€‰dฯ„+Kdde(t)dtu(t) = K_p e(t) + K_i \int_0^t e(\tau)\,d\tau + K_d \frac{de(t)}{dt}

The fundamental feedback control law used in autopilot systems, combining proportional, integral, and derivative action.

Transfer Function

G(s)=Y(s)U(s)=Kฯ„s+1G(s) = \frac{Y(s)}{U(s)} = \frac{K}{\tau s + 1}

First-order system transfer function in the Laplace domain, relating output to input.

INS Position Update

rโƒ—(t)=rโƒ—0+โˆซ0tvโƒ—(ฯ„)โ€‰dฯ„\vec{r}(t) = \vec{r}_0 + \int_0^t \vec{v}(\tau)\,d\tau

Position computed by integrating velocity from accelerometer measurements over time.

GPS Pseudorange

ฯi=cโ‹…(trxโˆ’ttx,i)=ri+cโ‹…ฮดt\rho_i = c \cdot (t_{rx} - t_{tx,i}) = r_i + c \cdot \delta t

Measured range to GPS satellite i, including clock bias error ฮดt.

Nyquist Stability Criterion

Z=N+PZ = N + P

Relates number of unstable closed-loop poles (Z) to open-loop poles (P) and encirclements (N) of the critical point.

State Space Model

xโƒ—ห™=Axโƒ—+Buโƒ—,yโƒ—=Cxโƒ—+Duโƒ—\dot{\vec{x}} = A\vec{x} + B\vec{u}, \quad \vec{y} = C\vec{x} + D\vec{u}

Standard state-space representation for linear time-invariant systems used in modern flight control design.

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