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OPTIMAL CONTROL
[Part 5] Tuning and Practical of LQR
Linear quadratic regulator
Designing an effective Linear Quadratic Regulator (LQR) involves not only solving the Algebraic Riccati Equation (ARE) but also appropriately tuning the weighting matrices Q and R to achieve desired performance and robustness. This section delves into the tuning process, practical considerations, and common pitfalls to avoid.
Tuning the Weighting Matrices Q and R
The matrices Q and R in the cost function:
play a crucial role in shaping the controller’s behavior.
State Weighting Matrix Q
Magnitude: Higher values in Q penalize deviations in corresponding states more heavily, leading to a stronger emphasis on keeping those states close to zero.
Diagonal vs. Off-Diagonal Elements: Diagonal elements of Q correspond to individual state penalties, while off-diagonal elements can be used to couple the state penalties, though they are often set to zero for simplicity.
Scaling: Ensure Q is appropriately scaled to reflect the relative importance of each state variable. For example, if certain states should be controlled more tightly, their corresponding diagonal entries should be…
