Adaptive Control of Very-Flexible Aircraft in Simulink
This package is used to simulate the control of the longitudinal dynamics of a 3-wing very-flexible aircraft (VFA), using MATLAB and Simulink. The required functions for the simulation are encapuslated in the class "SimVFA". The script "RunVFASim" provides the necessary input to instantiate the simulation class, run a simulation, and plot some basic output. The main choice to be made is to use a first-order actuator model and associated adaptive controller, or the more complex second-order actuator model and associated adaptive controller.
The simulations demonstrate how adaptive control is able to cope with uncertainties in the actuator and/or vehicle dynamics. Simulations (when uncertanity is on) demonstrate how "degraded" actuators (slow and lower than normal effectiveness) cause problems with fixed-gain controllers, which can be avoided with the use of adaptive control. To see this, both uncertainty and adaptation can be turned off to see the baseline LQR controller, and uncertainty can be turned on to see the LQR controller struggle with uncertain dynamics.
The VFA model (see attached rendering) consists of three rigid wing sections of equal size, which are hinged together such that a dihedral angle can form between the wing sections. The simulation uses a nonlinear VFA model as the plant, with controllers based on linearizations of the (nominal version of the) model at different dihedral angles. The adaptive controller is designed according to the method described in the paper "Adaptive Control for a Class of Multi-Input Multi-Output Plants with Arbitrary Relative Degree" by Zheng (Max) Qu et al. These simulation files originate with Max's work, but have been continued by Ben Thomsen and other lab members since Max's graduation.
The main steps of the simulation process are:
- Trim the nominal nonlinear VFA model (without actuator dynamics) at different dihedral angles (find the inputs and states such that states are not changing) and compute linearized state-space representation
- Introduce uncertainties and actuator dynamics
- For each trim point:
- Augment linearized system with actuator dynamics and integral error for command tracking
- Add ficticious inputs to "square-up" the system - to provide strictly-positive real (SPR) properties necessary for adaptive control design
- Compute baseline LQR feedback matrix (K), CRM feedback matrix (L), along with ouptut-mixing matrix (S) and transformed coordinates according to method in paper
- Set initial conditions, choose adaptation rates and related gains for simulation, define command trajectory, and run simulation
Outer Aileron, Center Elevator
With first-order actuator model (Relative-degree 2):
Airspeed, Angle of Attack, Pitch Angle, Pitch Rate, Dihedral, Dihedral Rate, Outer Aileron Deflection, Center Elevator Deflection, Dihedral Integral Error, Vert Accel Integral Error
With second-order actuator model (Relative-degree 3):
Airspeed, Angle of Attack, Pitch Angle, Pitch Rate, Dihedral, Dihedral Rate, Outer Aileron Deflection, Center Elevator Deflection, Outer Aileron Rate, Center Elevator Rate, Dihedral Integral Error, Vert Accel Integral Error
Pitch Rate, Dihedral Integral Error, Vertical Accel Integral Error
Dihedral Angle, Vertical Accel.
Goal is for outputs z to track command r (some notation uses z_cmd)
The use of this simulation package requires the Control System Toolbox and Simulink Control Design
"Adaptive Control for a Class of Multi-Input Multi-Output Plants with Arbitrary Relative Degree"
"Adaptive Output-Feedback Control and Applications to Very Flexible Aircraft" (http://hdl.handle.net/1721.1/104223)
"Modeling for Control of Very Flexible Aircraft" (https://doi.org/10.2514/6.2011-6202)
"Squaring-Up Method in the Presence of Transmission Zeros" (https://arxiv.org/abs/1310.1439v2)
"Robust and Adaptive Control - with Aerospace Applications" (https://doi.org/10.1007/978-1-4471-4396-3)