Optimal control that minimises a quadratic cost.
LQR chooses K to minimise J=∫(xᵀQx+uᵀRu)dt; solution u=-Kx with K=R⁻¹BᵀP from the algebraic Riccati equation. Guarantees stability and good margins (≥60° PM). Tuning Q (state penalty) vs R (control effort) trades performance and effort. LQG adds a Kalman filter.
An LQR balances an inverted pendulum with minimal effort.
LQR gives an optimal state feedback by balancing state error and control effort, which leads to systematic designs for many systems.
Optimal control that minimises a quadratic cost.
LQR gives an optimal state feedback by balancing state error and control effort, which leads to systematic designs for many systems.
Weighted sums of the state deviations and the control effort, so the designer chooses weights to set the trade-off.
It gives guaranteed stability margins for the nominal model and a systematic method to find the gain.
Typical applications include designing a controller for a self-balancing robot that balances speed and effort, tuning an aircraft pitch controller with a quadratic cost and choosing weights for an active suspension that trades comfort and body motion.
Study "Observers" first (topic 62 of 101 in Signals, Control & Comms). It covers the groundwork this topic builds on.
Riccati equation. Q and R weighting. Optimality.
An LQR balances an inverted pendulum with minimal effort.
The next topic is "Digital control", which builds directly on this one.
It is classed as Intermediate in Signals, Control & Comms (topic 63 of 101). It is an intermediate topic. Work through the beginner topics in Signals, Control & Comms first.
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