The JDAM baseline guidance system uses and LQR PI controller. The LQR controller is tuned so that the convergence criteria focus on stability and actuator rates. By doing this it preserves the stability properties of state-feedback while eliminating the sensor hardware required to implement state feedback.
The projection feedback architecture is used to iterate through the LQR controller design to achieve the desired bandwidth.
This system was developed using wind tunnel data and gain scheduling. The open-loop plant and controller dynamic are determined by this equation
$$\dot{x}=Ax+B_1\Lambda(u+f(x_p))+B_2r(t)$$
Where \(x\) is the extended system state, \(u\) is the inner-loop commands, \(\Lambda\) is the control failures, \(f(x)\) are the moment uncertainties and \(r(t)\) are the guidance commands. The moment uncertainty equation is
the plant and controller equations are combined into an extended system state-space form. We can see how the individual system state \(x_p\) and the controller state \(x_C\) are combined.
[[JDAM Adaptive Control]] – upgrade
[[JDAM Dynamic Inversion CLAW]]
- AdaptiveFlightControl
[[Algebraic Riccati Equation]]
[[Gain Scheduling]]
[[JDAM]]
LQR-PI Controller
[[State-Space Model]]