Control Algorithms

4.4.1 Feedback Control Basics

• Open-loop vs closed-loop control
• Error signal, reference tracking, disturbance rejection
• Time-domain performance: rise time, overshoot, settling time, steady-state error
• Concept of gain and phase margins (stability robustness idea)

4.4.2 PID and Classical SISO Control

• P, PI, PD, and PID control structures
• Frequency-domain picture: low-frequency error vs high-frequency noise
• Tuning concepts (e.g. Ziegler–Nichols, loop shaping ideas)
• Lead–lag compensation (high-level)
• Saturation and basic anti-windup ideas

4.4.3 State-Space Control & Pole Placement

• State feedback law u = -Kx (concept only)
• Controllability (why it matters for pole placement)
• Pole placement design for desired dynamics
• Integral action via augmented state for zero steady-state error

4.4.4 Linear Quadratic Regulator (LQR)

• Quadratic cost function concept with Q and R
• Riccati equation leading to optimal gain (no derivations here)
• Interpreting Q and R as state and control weights
• Examples: attitude and orbit regulation problems

4.4.5 LQG / Output-Feedback Control

• Combining Kalman Filter with LQR (LQG structure)
• Separation principle (estimation and control design separately)
• Use in tracking with noisy measurements

4.4.6 Attitude Control Laws

• Attitude error representations (Euler angles, quaternions, rotation vectors)
• PD / PID attitude regulation and rate-damping control
• Quaternion feedback control ideas
• Control allocation to actuators: reaction wheels / CMGs, magnetorquers, thrusters

4.4.7 Digital Implementation & Constraints

• Continuous vs discrete-time controllers
• Sample time selection and zero-order hold concept
• Actuator rate and magnitude limits
• Command filters and rate limiting

4.4.8 Advanced / Nonlinear / Adaptive Control

• Feedback linearization and dynamic inversion (high-level idea)
• Model Reference Adaptive Control (MRAC)
• Neural-network-based adaptive control
• Robust control (e.g. H_∞, μ-synthesis) – pointer to Domain D

Detailed derivations and proofs for these topics can live in Domain D – Attitude Dynamics & Control (Advanced).