This paper proposes a control allocation framework where a feedback adaptive signal is designed for a group of redundant actuators and then it is adaptively allocated among all group members. In the adaptive control allocation structure, cooperative actuators are grouped and treated as an equivalent control effector. A state feedback adaptive control signal is designed for the equivalent effector and adaptively allocated to the member actuators. Two adaptive control allocation algorithms, guaranteeing closed-loop stability and asymptotic state tracking when partial and total loss of control effectiveness occur, are developed. Proper grouping of the actuators reduces the controller complexity without reducing their efficacy. The implementation and effectiveness of the strategies proposed is demonstrated in detail using several examples.
Actuator redundancy is highly desirable for fault-tolerant control. This redundancy yields multiple ways to implement the forces and moments prescribed by the controller. However, this freedom creates the need for properly allocating the control inputs among all individual actuators. While multiple actuator configurations do generate the desired forces and moments, some of them may yield unintended outcomes, for example, the effect of some control surface deflections counteracts the effect of other ones. Redundancy management is the need for properly allocating the control inputs among functionally redundant actuators when some of them may not be fully functional.
The purpose of control allocation is to distribute the control signals to the available actuators such that the desired moments and forces are efficiently generated. Traditional control allocation methods include explicit ganging [
Adaptive control, on the other hand, does not require knowing which controllers have failed nor the class or severity of the failure. This is due to its ability to change control parameters according to the existing flight condition. Due to parameter adaptation, it is also able to accommodate for parametric uncertainties in the vehicle dynamics. Substantial developments in adaptive control for actuator failures have been made in the last decade [
The lack of control allocation in the current direct adaptive control framework motivates this research effort. In this study, we aim at separating control generation from control allocation. In the adaptive control allocation framework, a key step is to combine redundant control surfaces similar to explicit ganging. For each group of combined actuators, we design an adaptive control signal, which is then allocated among group members by an adaptive gain. If no failure occurs, a nonadaptive control allocation scheme set in advance is enforced. In the presence of uncertainty of actuator failure, the adaptive flight controller modifies the allocation of input accordingly.
The structure of the adaptive control allocation framework is illustrated in Figure
Aircraft pitch control with adaptive control allocation.
One advantage of this adaptive control allocation structure is the ease in solving problems such as the counteracting actuation. To remedy this problem, the signs of the adaptive allocation gains
In this paper, we develop the mathematical foundation of this adaptive control allocation structure for a single group of actuators. Two adaptive control allocation algorithms are presented for both loss of effectiveness and constant-magnitude actuator failures. Technical issues such as design conditions, adaptive law designs, and stability analysis are addressed. The proposed schemes are shown to guarantee stability and asymptotic state tracking in the presence of unknown failures. Simulation-based examples are used to demonstrate the strategy proposed.
The paper is organized as follows. Section
Consider the linear time-invariant (LTI) system
The control signal
The control input
For the adaptive control, the desired closed-loop dynamics is given by
There exist constant
The control objective is to design the virtual control signal
The plant model matching condition in Assumption
When a failure occurs, the allocation gain will be adaptively adjusted to accommodate for failure, but
With the plant and control in (
From the closed-loop dynamics in (
Based on the error dynamics in (
The properties of the adaptive control allocation scheme can be summarized in the following theorem whose proof is presented in the appendix.
For the system in (
From the definition of
Two case studies based on linearized aircraft models are presented next.
Consider the linearized lateral dynamic model of a large transport aircraft flying in a steady wings-level cruise condition with
The nominal allocation gain vector is selected as
The nominal controller is designed based on the LQR approach for
For this example, the reference model is chosen as the closed-loop dynamics with the above LQR controller, that is,
We will consider the 80% loss in control effectiveness:
The following cases will be studied. Case Case
The time history of the system state under failure and the desired state is shown in Figure
Time history of plant state (solid) and reference model state (dashed) (Case
Figure
Time history of control signals and actuator outputs (Case
The adaptive parameters are shown in Figure
Time history of controller parameters (Case
Time history of allocation gains (Case
The system state and desired state are shown in Figure
In this simulation case, we have achieved similar results to Case
Time history of plant state (solid) and reference model state (dashed) (Case
Time history of control signals and actuator outputs (Case
Time history of allocation gains (Case
In this section, we apply the control allocation strategy to the NASA Generic Transport Model (GTM). The NASA GTM is a high-fidelity model of the NASA AirSTAR UAV testbed [
For this simulation study, we trim and linearize the GTM at a wings-level flight for an aerodynamic speed of 92.09 knots. The same states and controls of (
As in the previous example, the aircraft is commanded to turn right from the initial wings-level horizontal flight. The turn starts at 10 seconds and at steady state the heading angle will increase 60 degrees.
We let the left aileron lose 90% of its effectiveness at 12 seconds. The failure magnitude and its onset time instant are unknown to the controller. The control objective is for the aircraft to achieve an accurate turn in the presence of the failure.
The simulation results are shown in Figures
The longitudinal states are shown in Figure
Figures
Figure
Time history of lateral states (solid) and reference model states (dashed).
Time history of longitudinal states.
Ground track of the aircraft.
Time history of virtual control signal and actuator inputs.
Time history of actuator deflections.
Time history of allocation gains and adaptive parameters.
When constant failures occur, the control signal can be rewritten as [
The plant dynamics can then be rewritten as
For adaptive control of constant actuator failures, sufficient built-in actuation redundancy is required. The redundancy condition is described in the following assumption.
The rank of
The rank condition characterizes the redundancy of actuation which is necessary for a successful constant failure compensation. This rank condition suggests that the system remains controllable after a failure, and the effect of the constant failure can be properly matched and canceled by the allocated control signals through other columns of
Consider the nominal controller structure
Next we will show that the controller in (
Based on the rank condition in Assumption
For
With (
Due to the uncertain nature of the failures, the controller parameters must be adjusted. Consider the adaptive control allocation scheme
For this adaptive control scheme design, we define
With (
From the error dynamics in (
The following theorem summarizes the properties of the adaptive control allocation scheme and the proof is provided in the Appendix:
The adaptive control allocation scheme in (
Consider the longitudinal LTI model of the NASA GTM given by
The nominal allocation gain
Similar to the simulation study in Section
The left outboard elevator is stuck at −5 degrees after 1 second, that is,
The results are shown in Figures
Time history of plant state (solid) and reference model state (dashed).
Time history of control signals and actuator outputs.
Here we apply the adaptive control scheme to the nonlinear NASA GTM.
For adaptive control design, we consider a LTI model for a wings levelled flight having a 3 deg angle of attack at trim. Similar to the linear simulation study, we study the compensation for constant elevator failures and will consider multiple elevator failures in which both the lateral and longitudinal are active. The state and control vectors are given by
A set of commands that aim to make the aircraft climb at 4-degree pitch angle is applied at 5 seconds. The nominal parameters and reference inputs are obtained as in the linear simulation example.
The right outboard elevator is locked at 10 degrees at 10 seconds and the right inboard elevator at 5 degrees at 20 seconds. The control objective is to maintain the climbing flight in the presence of these failures.
The simulation results are shown in Figures
The lateral states are shown in Figure
Figure
Time history of longitudinal states (solid) and reference model states (dashed).
Time history of lateral states (solid) and reference model states (dashed).
Flight trajectory, ground track, and altitude of the aircraft.
Time history of lumped and allocated elevators and elevator deflections.
Time history of the inputs and outputs of ailerons, rudders, and engines.
Time history of control allocation gains.
Time history of selected adaptive controller parameters.
A novel adaptive control allocation framework is proposed herein. The adaptive allocation scheme includes an adaptive control signal and a control allocation unit with adaptively updated allocation gains. Two adaptive control allocation algorithms have been proposed for the compensation of uncertain failures. The proposed algorithms have been shown to guarantee closed-loop stability and asymptotic state tracking. It has also been shown that the proposed adaptive control allocation framework reduces the controller complexity with proper grouping of the actuators. In this framework, the control signal to be adaptively allocated can be actuated by nonadaptive controllers. The simulation results demonstrate the performance of the proposed algorithms and their applicability to aircraft flight control. Some future research topics in this direction include the extension of the adaptive control allocation framework to systems with multiple groups of actuators and the strict enforcement of a pure allocation, that is, exactly enforcing the designed control signal with
When a failure occurs, the control effectiveness matrix
In Section
We can further obtain that
This work was supported by the NRA NNX08AC62A of the IRAC project of NASA. The authors would like to thank Drs. Suresh M. Joshi and Sean P. Kenny at the NASA Langley Research Center for their valuable comments.