Model and Sensor Based Nonlinear Adaptive Flight Control with Online System Identification

Abstract

Consensus exists that many loss-of-control (LOC) in flight accidents caused by severe aircraft damage or system failure could be prevented if flight performance could be recovered using the valid and remaining control authorities. However, the safe maneuverability of a post-failure aircraft will inevitably be reduced due to the malfunction. Non-conventional control strategies which rely on modern control techniques and computational power are essential to control systems in post-failure flight conditions to extract the most from the reduced, remaining aircraft control authorities and restore the flight performance of an aircraft or achieve a safe landing. One such non-conventional control strategy is called active fault tolerant flight control (FTFC), which is designed to detect changes in an aircraft's dynamics caused by structural, actuator, or sensor failure and accommodate the damage or failure using an adaptive reconfiguration mechanism. The active FTFC technique is able to deal with unanticipated and multiple simultaneous failures. The overall architecture of an active FTFC system ideally should consist of a fault detection and diagnosis (FDD) module, a state reconstruction unit, a reconfigurable control component, a control allocation unit and a flight envelope protection (FEP) unit. Generally speaking, FTFC systems can be classified into two types: model-based FTFC systems and model-free FTFC systems, according to whether any of the system's components require an aerodynamic model at their core or not. A model-based FTFC system contains an aerodynamic model identification (AMI) module, which supplies an accurate aircraft model to an indirect adaptive nonlinear controller in the reconfigurable control block, to a dynamic flight envelope determination algorithm in an FEP unit, or to an FDD unit. An aerodynamic model identification approach using a physical, interpretable modeling structure can detect and even quantify structural failures occurring in the aircraft structure or one of the control surfaces by monitoring changes in stability derivatives and control derivatives. There are many candidate control approaches which can achieve reconfiguration when designing a reconfigurable flight controller. These reconfigurable control methods may rely on many different reconfiguration mechanisms ranging from switching, model following, matching to adaptive compensation. These methods include nonlinear adaptive control which achieves reconfiguration through compensation, and this method is receiving increasing attention in the flight control aerospace research community. Nonlinear adaptive control is divided into direct adaptive control and indirect adaptive control, the difference is that the latter requires an online system model. Indirect adaptive control is also called model-based or modular adaptive control, which has some advantages over the direct adaptive control and other model-free control methods. One advantage is that a modular control approach has the potential to yield a more efficient controller which requires less control effort. Such an efficient controller can be achieved by maintaining useful damping terms of an identified system model in the closed-loop system. This is attributed to the good properties of many control design techniques such as backstepping such that the dynamics of an original system can be chosen to be canceled or maintained during a controller design process. Modular adaptive control also has an inherited shortcoming, it can only guarantee input-to-state stability, i.e. modular adaptive control cannot guarantee the stability of the overall closed-loop system because its stability proof relies on the certainty equivalence principle. The weakness of the certainty equivalence principle, i.e., convergence problem of the model parameters, can be improved by enhancing model accuracy or reliability, to do this, it becomes critical to develop advanced, powerful aerodynamic model identification approaches capable of capturing changes in flight dynamics either during a high maneuvering flight mission or a post-failure condition. Flight envelope protection is a necessary technique that should be applied by controller designers to prevent LOC incidents, taking into account highly maneuvering flight tasks and/or highly perturbed flight conditions due to the ongoing failure. An FEP component should provide a pilot with a safe flight envelope and pose constraints on the reference commands fed to an internal controller to make the commands achievable. An aerodynamic model that is valid over an entire flight envelope plays a crucial role in full-envelope modular adaptive control and flight envelope protection. A globally valid model is required for modular adaptive control to enable the designed controller to work properly in a large operating range. Once estimated, the global model in a model-based adaptive control method can be stored for later re-use when the same flight condition is revisited. Except being needed by a model-based controller, an accurate aerodynamic model is also required for flight envelope protection. Naturally, the estimated aerodynamic model has to be valid for the current aircraft configuration over the entire flight envelope to enable an evolution algorithm to estimate the boundary of the safe flight envelope for the current flight condition. However, only a limited number of model identification approaches are suited for estimating a globally valid aerodynamic model, and each existing possible candidate has variant shortcomings or limitations which make it hard to apply directly to identify an aircraft model. For example, neural networks usually yield a nontransparent model structure which is hard to interpret using physical knowledge of the system, and they commonly encounter a convergence problem. Most kernel methods fall into the nonparametric type of methods, which by nature need as many kernels as the data points under evaluation. It should be kept in mind that only equation-error type model identification methods were investigated in the work reported here. The assumption was made that a sufficiently accurate estimation of aircraft states was available. An alternate method to the modular adaptive reconfigurable control approach is the acceleration measurements-based incremental nonlinear control (AMINC) method. An accurate estimation of an aircraft is hard to achieve during a high maneuvering moment or at a transient period when the flight performance is highly perturbed due to aircraft failure. Incremental nonlinear controllers such as incremental nonlinear dynamic inversion (INDI), incremental backstepping (IBKS) and sensor-based backstepping (SBB) are suited for reconfigurable flight control designs in the sense that they do not require complete aircraft model knowledge. The main research question for the research presented here was: How can an advanced fault-tolerant flight control system be designed to increase the survivability of an aircraft? This led to two subsidiary questions: (1). How can the candidate function approximation methods, i.e. multivariate simplex B-splines and kernel methods, be improved in terms of approximation accuracy and computational efficiency, to meet the need of model-based adaptive control and online flight envelope protection? (2). What are the benefits of using an acceleration measurements-based control approach, i.e., the sensor based backstepping, as an alternative to a model-based adaptive control approach, when designing a reconfigurable flight controller to deal with aircraft failures in a generic fault-tolerant flight control (FTFC) system? With regard to reconfigurable control, the identified model should enable the controller to achieve active reconfiguration and restore the control performance. To answer these questions, four different global model identification methods and two nonlinear incremental adaptive controllers were developed. Two model identification methods use a parametric model structure namely standard multivariate simplex B-splines. The focus was placed on how to achieve fast parameter estimation during the research process for these two methods. In the third identification method, a new model structure called tensor-product simplex B-splines was extended from a single dimension case to a multidimensional case, with a focus on demonstrating the advantage of this new compound model structure in terms of the flexibility in model structure selection, computational efficiency and approximation power. The fourth method uses a kernel type model structure which is also parametric. The new recursive kernel approach was developed by combining a classical recursive kernel method with a novel support vector regression approach. A model identification method using standard multivariate simplex B-splines has many advantages, it can avoid the over-fitting problem which occurs with an ordinary polynomial method using a triangulation technique. The approximation power of a simplex B-spline based method is determined by the per-simplex polynomial order and smoothness order, and can be increased by increasing the density of the subdomains in a triangulation. This simplex B-spline based function approximation method guarantees that its output is bounded by the maximum and minimum B-coefficients, this facilitates its certification for future real life applications. The linear regression formulation of the simplex B-spline based method allows for applying most of the constrained recursive parameter estimation methods. Furthermore, the simplex B-spline based method has a sparse property, which can lead to high computational efficiency by adopting distributed computation or other modern computing techniques. However, a simplex B-spline method can easily yield a large amount of unknown parameters if the function dimension exceeds 4, which results in a high computational load considering the smoothness maintaining and covariance matrix updating. To enhance the computational efficiency of the model identification methods using simplex B-splines, two recursive linear-regression model identification methods were developed in this thesis: a substitution-based multivariate simplex B-spline (SB-MVSB) method and a recursive sequential multivariate simplex B-spline (RS-MVSB) method. In the SB-MVSB method, an efficient recursive solver is developed for a constrained linear regression problem when using simplex B-splines. The constrained linear regression problem is converted into a constraint-free linear regression problem using a general solution for the equality constraints. This transformation was shown to reduce the scale of the identification problem in terms of the number of unknown parameters, and thus the computational load required for the model identification method can be reduced. The RS-MVSB method consists of two consecutive procedures at one model evolution step. The first procedure achieves updating of a local model covering the current data point instead of a global model. The requirement of updating a complete covariance matrix is avoided by only updating one local model, and therefore the computational efficiency of this method is greatly enhanced. The second procedure guarantees a smooth transition between this local model and its neighboring local models. The computational complexity of SB-MVSB and RS-MVSB was given from a mathematician point of view, then, they were validated using simulated flight test data generated using a high-fidelity nonlinear model of an F-16 aircraft. Simulation results showed that both methods can achieve higher approximation accuracy than ordinary polynomial based methods, and both can be many, e.g. 10, times faster than an equality constraint recursive least squares based MVSB (ECRLS-MVSB) method. The second feature of these two methods facilitates their future onboard applications. Tensor-product simplex (TPS) B-splines provide a compound structure, which provide more flexibility than a standard simplex B-spline model during model structure selection. Using TPS B-splines, different dimension of inputs can be treated differently depending on their characteristics determined from a priori knowledge. In the work presented in this thesis, the TPS B-spline concept was extended from a single dimension case into a more general multidimensional case. Compared to standard simplex B-splines, TPS B-splines can make better use of a priori model knowledge. By reducing many unnecessary basis polynomials from the regression vector, TPS B-splines have the potential to lead to a lower computational load than standard simplex B-splines. The TPS B-spline method was validated using a data set generated from a high-fidelity nonlinear F-16 model. Simulation results showed that TPS B-splines can yield higher approximation power than standard simplex B-splines with less B-coefficients. Two similar recursive parametric kernel methods namely weight varying least squares support vector regression (WV-LSSVR) and Gaussian process kernel based LSSVR (GPK-LSSVR) were developed for aerodynamic model identification in this thesis. The focus of this work was enhancing the approximation power of a recursive parametric kernel method by choosing an optimal set of kernels for the kernel scheme. An offline method called improved recursive reduced LSSVR (IRR-LSSVR) was used to determine optimal kernels for a classical recursive kernel method. The new kernel method was validated using a series of public available benchmark data sets well known to researchers from the field of pattern recognition. GPK-LSSVR showed a higher approximation power than WV-LSSVR, and both of them showed a higher approximation power than a classical recursive kernel method based on k-means clustering. A novel type of acceleration measurements-based incremental flight control laws was investigated with the aim of providing a reconfigurable control unit with a powerful non-conventional flight control approach which could accommodate sudden structural or actuator failures occurring in an aircraft. The preferred model-free, incremental control approach used in this thesis was the SBB approach, which was initially developed for control designs of nonlinear nonaffine-in-control systems. The SBB approach achieves an accurate reference command tracking performance by approximate dynamic inversion. The SBB approach was extended to deal with sudden model changes in an aircraft caused by structural or actuator failures. A hybrid two-loop angular controller and a joint two-loop angular controller were designed for the RECOVER model. In the hybrid two-loop angular controller, the angular control loop was designed using a nonlinear dynamic inversion (NDI) control law, and the angular rate loop controller using the SBB approach. In the joint two-loop angular controller, the overall controller was designed using a backstepping technique with each loop stabilized recursively. Both angular controllers were validated using the RECOVER model with a focus on dealing with perturbed aircraft flight performance caused by failures. Two benchmark fault scenarios were selected: a rudder runaway case and a flight 1862 engine separation scenario. Simulation results showed that both control setups can guarantee the safety of the post-failure aircraft and achieve a proper reference tracking performance. In comparison with the hybrid NDI/SBB angular controller, the joint SBB angular controller resulted in a better reference tracking performance for the sideslip angle, especially in the engine separation case. An SBB controller contains a time scale parameter, other incremental control laws such as incremental NDI (INDI) and incremental backstepping (IBKS) involve a control effectiveness matrix. Before we can investigate how the time scale parameter or a control effectiveness matrix affect the control performance of an incremental flight controller, the parameter variations of a control effectiveness matrix need to be estimated and analyzed. The TPS B-spline method and an immersion and invariance (I&I) method were chosen to estimate a control effectiveness matrix for an F-16 aircraft. Although the I&I approach initially was not aimed at high modeling accuracy, it was assumed in this thesis that it is able to estimate the changing trend of the control derivatives. Simulation results showed that TPS B-splines capture the changes in the control derivatives better than the I&I approach in terms of consistency. For F-16, the control effectiveness matrix does not evidently affect the control performance of an incremental flight controller when a flight maneuver is moderate in terms of the variation of angle of attack and airspeed. Further research on modular adaptive reconfigurable control is required, for example incorporating the SB-MVSB method or the WV-LSSVR method into control designs to further check how well they are suited for modular adaptive control in terms of approximation power and onboard computational efficiency. Further research on acceleration measurements based reconfigurable control should include tests on the SIMONA simulator, realistic test-flight with UAV and research aircraft.