Fault Tolerant Control of Drone Interceptors Using Command Filtered Backstepping and Fault Weighting Dynamic Control Allocation
He Kong
Shihua Li
Round 1
Reviewer 1 Report
This paper is concerned with fault tolerant control for drone interceptors with fixed wings and reaction jets subject to actuator faults. The proposed fault tolerant control system consists of two parts, a nonlinear virtual control law, and a dynamic control allocator. The virtual control law with a parameter update law is designed by command-filtered backstepping to deal with system uncertainty and quantization error. The fault weighting dynamic control allocation algorithm is developed to distribute the virtual control signal to the actuators on the drone interceptor. As a result, when an actuator fault occurs, the proposed fault weighting dynamic control allocation scheme can redistribute the control signals to the remaining actuators. The authors have also verified the effectiveness of the proposed algorithm via numerical simulation.
Overall, I found the considered question interesting and important. In general, the submission is well-written and easy to follow. I only have some minor suggestions for the authors to consider.
A major comment I have is that the difficulty of the considered problem and the novelty of the proposed framework is not well explained. It was mentioned in the Abstract that the drone interceptors have both continuous and discrete actuators, which pose a challenge to the control system design. But what is the main challenge exactly is not sufficiently discussed in the Abstract or Introduction. Hence, the reader cannot comprehend the difficulty of the considered problem or the novelty of the proposed method. I encourage the authors to elaborate more on the above in the Abstract and Introduction.
Author Response
Thank you for your suggestion. We have added the explanation in the introduction:
For the interceptor with aerodynamic surfaces and reaction jets, each pulse thrust has only two states of working and non-working. The thrust cannot be adjusted, and it cannot be stopped after starting until the work is completed, which has obvious discrete and nonlinear working characteristics. At the same time, the aerodynamic control system changes continuously. Therefore, the controller design of the whole is a challenging problem. In order to deal with this hybrid system and actuator fault tolerance problem, a fault weighting dynamic control allocation algorithm is proposed.
Reviewer 2 Report
In this paper, a fault tolerant control strategy for drone interceptors with fixed wings and reaction jets is proposed. The proposed fault weighting dynamic control allocation is novel and has good performance. Even in the presence of quantization errors and actuator faults, the proposed autopilot system tracks acceleration commands fast and smoothly. The detailed review comments are as follows
(1) In this paper, the agility of the interceptor is enhanced by using reaction control system. The authors should indicate how much the force of one pulse thrust is. In the simulation section, the aerodynamic coefficients need to be given.
(2) After the introduction of the reaction system, the phenomenon of non-minimum phase of the system disappeared, what is the benefit of this for the interceptor.
(3) Equation 20 does not appear in Ref.14. Please check whether the citation of Equation 20 in the paper is correct.
(4) Some ‘figure’ in the paper are in bold, and some are not bold. Please confirm the paper submission template requirements and maintain a unified style.
Author Response
(1) In this paper, the agility of the interceptor is enhanced by using reaction control system. The authors should indicate how much the force of one pulse thrust is. In the simulation section, the aerodynamic coefficients need to be given.
Reply: Thank you for your comments. One pulse thrust can produce a force of 2500N. The aerodynamic coefficients are obtained from Ref[16]. We have added these to the simulation section.
(2) After the introduction of the reaction system, the phenomenon of non-minimum phase of the system disappeared, what is the benefit of this for the interceptor.
Reply: Thank you for your comments. Tail Control Interceptor is a non-minimum phase system. The acceleration response delay is large, and the rise time of acceleration response is 0.9s. The introduction of the reaction system effectively compensates for this delay, significantly improving the speed of maneuver tracking. We have added these to the simulation analysis.
(3) Equation 20 does not appear in Ref.14. Please check whether the citation of Equation 20 in the paper is correct.
Reply: Thank you for your comments. The Ref. is 16. We have corrected the error.
(4) Some ‘figure’ in the paper are in bold, and some are not bold. Please confirm the paper submission template requirements and maintain a unified style.
Reply: Thank you for your comments. We have revised these formats.
Reviewer 3 Report
In this paper, a virtual control law with parameter updating law is designed to deal with the uncertainty and quantization error of the system. On this basis, a fault weighted dynamic control allocation algorithm is proposed to distribute virtual control signals to each actuator according to the fault diagnosis result, thus realizing fault tolerant control.
The English writing of this article is good and the structure is reasonable, but the following issues deserve attention:
1. Since matrix Bv in Eq. (13) is the identity matrix I, which is not used in the subsequent design, what is the significance of the division of matrix Bu? If you want to show the relationship between the virtual control law and the actual control law in the fault-free case, you can add a few extra words to explain it.
2. The fault weighted dynamic control distribution scheme proposed in this paper needs to solve the optimization problem shown in Eq. (18) online. Considering that the control cycle is very short, there may be insufficient computing power in reality. Has the relevant improvement plan been considered in the follow-up research?
3. In this paper, a limit is set for the amplitude of the actual control input u , so whether the virtual control law v designed later can ensure that the actual actuator can realize it?
4. In the simulation verification, the description of the fault is missing, and the type, size and occurrence time of the fault in the simulation are not given. In addition, W1, W2, and W3 are the core parameters of FWDCA algorithm in this paper. You can add a specific reason for choosing these values.
Author Response
- Since matrix Bv in Eq. (13) is the identity matrix I, which is not used in the subsequent design, what is the significance of the division of matrix Bu? If you want to show the relationship between the virtual control law and the actual control law in the fault-free case, you can add a few extra words to explain it.
Reply: Thank you for your comments. It is a coincidence that Bv=I. After the transformation of the control allocation, the original system has four control inputs changed to two virtual inputs. The advantage is that it is convenient to deal with system redundancy and fault tolerance issues. We have added the explanations after Eq. (13).
- The fault weighted dynamic control distribution scheme proposed in this paper needs to solve the optimization problem shown in Eq. (18) online. Considering that the control cycle is very short, there may be insufficient computing power in reality. Has the relevant improvement plan been considered in the follow-up research?
Reply: Thank you for your comments. According to Ref.23, in the case of unsaturated conditions, the dynamic control allocation algorithm has an analytical solution, the response time of the system can be guaranteed. In the follow-up research, we will consider the control saturation problem, quadratic programming algorithm and intelligent algorithm can be considered to solve the control allocation problem.
- In this paper, a limit is set for the amplitude of the actual control input u , so whether the virtual control law v designed later can ensure that the actual actuator can realize it?
Reply: Thank you for your comments. The reaction control force of the interceptor is large enough. In fact, if we do not consider the consumption of the reaction pulse thrust, the output of the reaction control system can directly act as normal accelerations, so the response speed is almost without delay. We only need to adjust the appropriate parameters and allocate more control to the reaction force system to ensure that the system will not be saturated, but at the same time we need to balance the consumption of the reaction force system. We have added the explanation to section 3.1.
- In the simulation verification, the description of the fault is missing, and the type, size and occurrence time of the fault in the simulation are not given. In addition, W1, W2, and W3 are the core parameters of FWDCA algorithm in this paper. You can add a specific reason for choosing these values.
Reply: Thank you for your comments. In the simulation, we consider the damage of the aerodynamic control surfaces and the reaction control system failure due to the interactions between the airflow and the reaction jets. We have added the description to the simulation section.
The three weighting matrices play important roles in the control allocation algorithm. A large W1 ensures the corresponding actuator converge fast to its desired position; A large W2 makes the actuator move slowly; And a large W3 prevent the actuator consuming too much energy. We have given the description in Remark 1.
