A neural gust alleviator for a non-linear combat aircraft model

This paper proposes a new method of designing a data-driven controller for aircraft maneuver. Assuming that we do not have knowledge of the controller and the controlled aircraft, we propose a controller design with explorations of the control inputs and their responses from the aircraft. Specifically, we utilize Bayesian optimization (BO) with Gaussian process (GP) regression for black-box modeling of the aircraft responses from the explored controls, which are selected as samples to experiment with BO. We tested the proposed controller with a rigid six degrees of freedom (6DoF) nonlinear aircraft model by varying the kernel structures of the GP regressions. Our proposed method shows shorter flight times and smaller deviations navigating fixed waypoints compared to the tuned Proportional Integral Derivatives (PID) controller. The proposed controller can be an alternative to PID control, particularly when both controller structure and controlled plant model information are unknown.

This paper describes a dual-loop control scheme for fault tolerant flight control system design. The dual-loop controller consists of an outer loop controller–so-called adaptive neural sliding mode control (ANSC) and an inner loop controller designed by using nonlinear dynamic inversion (NDI) technique. The merits of adaptive neural network and sliding mode control scheme are that 1) the ability of adaptive neural network control to deal with unstructured uncertainty and 2) the ability of sliding mode control to guarantee transient response. Using timescale separation principal, the aircraft dynamics can be decomposed into fast and slow dynamics and the decomposed dynamics are inversed for NDI controllers. For real-time pilot simulation, one-stage inverse dynamics is used and the pilot inputs are translated to roll, pitch and yaw rate commands. For cascade NDI, two-stage dynamic inversion is used. The stability analysis of the proposed controller is performed using Lyapunov theory. To verify the effectiveness of the proposed control scheme, numerical simulation is performed for six degree-of-freedom nonlinear aircraft model while a failure occurs in longitudinal control surface. Simulation results demonstrate that closedloop system has good performance while encountering lock-in-place, partial destruction and floating actuator failures. Nomenclature stick long δ , stick lat δ , stick dir δ = pilot inputs for longitudinal, lateral and directional command dir lon lat K K K , , = sticks and pedal gains ref p , ref q , ref r = reference model rate commands cmd z n , cmd y n = normal and lateral acceleration command

This note addresses disturbance suppression problem for uncertain plant systems using prior disturbance data which contain some measurement errors, and gives a further result which attains lower computational complexity than our previously proposed method. Under the conditions that the plant uncertainties are assumed to be expressed by bounded but time-invariant uncertain delays at the control input and the measurement errors are expressed as affine with respect to some bounded constant uncertain vector, we have already proposed a MPC-based controller which achieves disturbance suppression with robustness against the plant uncertainties and the measurement errors. In this paper, we tackle the same problem but under the condition that the implemented computing power is limited. For this problem, we propose a simple methodology, i.e. constant inputs are supposed for several steps. We apply our proposed method to flight controller design problem to suppress vertical acceleration driven by turbulence, i.e. Gust Alleviation (GA) flight controller design problem, and demonstrate the applicability with numerical simulations.

This paper addresses the design problem of flight controllers for suppressing aircraft motions due to turbulences, i.e. design problem of Gust Alleviation (GA) flight controllers. As LIght Detection And Ranging (LIDAR) system which can detect even Clear Air Turbulences (CAT) has recently been developed, flight controllers which exploit the prior turbulence data that are obtained using LIDAR system have been desired. In this note, we extend our previously proposed method to the even realistic situations in which there exist plant uncertainties and the measurement errors in current state variables for aircraft motions as well as in the prior turbulence data. We successfully propose a design method of GA flight controllers for our problem using Model Predictive Control (MPC). Numerical simulation results which demonstrate the applicability of our proposed method for GA feasibility study are included.

During ground manoeuvres, particularly at high velocity when exiting the runway, a loss of lateral stability due to the saturation of the main landing gear tyres can cause the aircraft to enter a skid or a spin. The lateral stability is governed not only by aspects of the gear design, such as its geometry and tyre characteristics but also by operational variables, for example, the weather and taxiway condition. In this paper we develop an improved understanding and a new presentation of the dynamics of an aircraft manoeuvring on the ground, ultimately aimed at optimisation and automation of ground operations. Using a modified version of a nonlinear computer model of an A320 passenger aircraft developed by the Landing Gear Group at Airbus in the UK, we apply numerical continuation to investigate turning manoeuvres. We present a bifurcation analysis to describe the underlying structure that governs the dynamics of turning manoeuvres across the steering angle-thrust parameter space. There is a detailed description of the behaviour when lateral stability is lost using a novel diagrammatic approach to explain the dynamic tyre ground interactions. The bifurcation diagrams identify parameter regions for which this undesirable behaviour is avoidable and, thus, they form a foundation for defining the safe operating limits during turning manoeuvres.

A new technique is presented for generating linear fractional transformation-based uncertainty models for use in the robustness analysis of flight control systems using the structured singular value p. The proposed approach can be almost fully automated and does not require closed-form linear expressions for how the aircraft dynamics vary as a function of the uncertain aircraft parameters. Only a nonlinear software model of the closed-loop aircraft, which can be efficiently trimmed and linearized numerically, is required. In the proposed technique, linear dependencies of the aircraft dynamics on the uncertain parameters are modeled by a multidimensional regression plane. Additional nonlinear dependencies are modeled using a band structure defined by nonlinearity compensation parameters. The capability of the proposed approach to identify worst-case uncertain parameter combinations is demonstrated through the robustness analysis of a lateral-axis control law for a generic civil transport aircraft. The approach is compared with classical analysis methods via the robustness analysis of a multivariable glide-slope coupler control law for a Boeing 747 transport aircraft.

This paper presents a method of pole placement in the linear quadratic regulator and its application to the flight control system design. There are three features in the proposed method. First, a weighting matrix that gives desired closed-loop pole locations is obtained by solving a set of differential equations. They are derived from the characteristic equation of the Hamilton matrix. Second, poles can be placed exactly at the desired positions and arbitrarily except the symmetry of complex conjugate poles with respect to the real axis. Third, it is a diagonal weighting matrix that is obtained by the proposed method. The third feature makes output regulation with desired pole locations possible. After demonstrating the effectiveness of the method through a simple literature example, it is then applied to the F-4 aircraft's lateral dynamic model. HE optimal regulator, or linear quadratic regulator (LQR), is a typical state-space design method. It has several features. For example, by imposing penalty on state variables and control inputs in a quadratic performance index, one can investigate tradeoff between system performance and control efforts. Besides, it is well known that the LQR has infinite gain margin and 60-deg phase margin for single-input systems. However, by this technique one cannot assign closed-loop pole locations. Since pole locations have a large effect on time-response characteristics, such as overshoot, rise time, etc., it is desirable to assign pole positions in the LQR design. Pole placement in the LQR is a problem associated with the selection of appropriate weighting matrices, when a set of desired closed-loop eigenvalues (CLEs) are known. This problem has been studied by many researchers since early 1970s, and many papers113 have been published in this research area. Among them, the study of Hayase 1 provides a relation between the weighting matrix and the feedback gains for a single-input system in controllable canonical form. Recently, Ohta et al. 2 showed a simple derivation of the relation. Meanwhile, for multi-input systems, Saif3 established a simple method using aggregation to compute a weighting matrix by which arbitrary and exact pole placement can be attained in a general form. He integrated the previously proposed three approaches.46 All of the aforementioned methods for multi-input systems follow Solheim's approach for placing imaginary parts as well as for placing real parts using the mirror image property.7 Another approach, which is completely different from the preceding approaches, is that of Graupe. In his method, first, differential equations of a weighting matrix with respect to the CLEs are derived, and then a weighting matrix is found as a solution of an optimization problem, wherein the difference between CLEs and assigned eigenvalues is made as small as possible.8 However, it is complicated and does not seem practical. Besides the preceding approaches, there are many approaches such as assigning eigenvalues with prescribed degree of stability, 9 placing eigenvalues into a specified region,10'11 and achieving pole placement asymptotically.12'13 In this paper, we propose a method of pole placement that is very different from the previously proposed methods. Whereas Graupe's differential equations are derived from the Riccati equation, we

This paper presents a new numerical method to compute control solutions achieving minimum-time state transfer for a linear dynamical system with bounded control input. The method can be used to generate bang-bang control input solutions in cases that would pose difficulties for methods based on solving directly for input switch-times. For the considered problem, the optimum control input is uniquely determined by the initial value of the co-state vector. The proposed method is based on an iterative computation of the initial co-state vector, as embedded in the geometry of the reachable set. True optimality of the solution is implicit from Pontryagin's minimum principle, while the convexity property of the reachable set ensures that the solution converges to match the required boundary conditions. Example simulation results involving motion control of flexible structures are given to demonstrate the usefulness of the algorithm in solving practical control problems.

We consider field-oriented speed control of induction motors without mechanical sensors. We augment the traditional approach with a flux observer and derive a sixth-order nonlinear model that takes into consideration the error in flux estimation. A high-gain speed observer is included to estimate the speed from field-oriented currents and voltages. The observer design is independent of the feedback controller design. By high-gain-observer theory, we define a virtual speed output for the sixth-order nonlinear model, which can now be used to design a feedback controller whose performance is recovered by the speed observer when the observer gain is chosen high enough. We then focus on the traditional field oriented control (FOC) approach where the flux is regulated to a constant reference and high-gain current controllers are used. By designing a flux regulator to maintain the flux at a constant reference, and a current regulator to regulate the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -axis current to its command, we derive a third-order nonlinear model that captures the essence of the speed regulation problem. The model has the speed and two flux estimation errors as the state variables, the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -axis current as the control input, and the virtual speed as the measured output. It enables us to perform rigorous analysis of the closed-loop system under different controllers, and under uncertainties in the rotor and stator resistances and the load torque. In this paper, we emphasize the design of feedback controllers that include integral action. The analysis reveals an important role played by the steady-state product of the flux frequency and the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -axis current in determining the control properties of the system. The conclusions arrived at by using the reduced-order model are collaborated by simulation and experimental results.

Based on the working principle of a ship with a controllable pitch propeller (CPP), a mathematical model of the ship-propeller subsystem, the engine-propeller subsystem, and the ship main engine subsystem was established. The model was represented by a set of differential equations, in which the ship speed, the rotational speed of the propeller, and the rotational speed of the main engine were used as the state variables, and the angle of pitch and the fuel injection quantity were used as the control input. The equation set was a multi-input nonlinear speed control system with the characteristics of coupling and nonlinearity. In order to design a sliding mode variable structure (SMVS) controller, appropriate coordinates were selected for the nonlinear state transformation, and the multi-input nonlinear system was decomposed into two single-input systems to solve the equivalent control through the manifold calculation. MATLAB simulation results showed that under the control of the angle of pitch and the fuel injection quantity, the ship speed, the rotational speed of the propeller, and the rotational speed of the main engine could quickly approach the given values, verifying the advantages of the SMVS control for complex multi-input nonlinear systems.

A Nonlinear State-Space Model of Diesel Propulsion Plant Operation Using Neural Nets

The objective of the paper is to develop a boundary control method for the Black–Scholes PDE which describes option dynamics. It is shown that the procedure for numerical solution of Black–Scholes PDE results into a set of nonlinear ordinary differential equations (ODEs) and an associated state equations model. For the local subsystems, into which a Black–Scholes PDE is decomposed, it becomes possible to apply boundary-based feedback control. The controller design proceeds by showing that the state-space model of the Black–Scholes PDE stands for a differentially flat system. Next, for each subsystem which is related to a nonlinear ODE, a virtual control input is computed, that can invert the subsystem’s dynamics and can eliminate the subsystem’s tracking error. From the last row of the state-space description, the control input (boundary condition) that is actually applied to the Black–Scholes PDE system is found. This control input contains recursively all virtual control inputs which were computed for the individual ODE subsystems associated with the previous rows of the state-space equation. Thus, by tracing the rows of the state-space model backwards, at each iteration of the control algorithm, one can finally obtain the control input that should be applied to the Black–Scholes PDE system so as to assure that all its state variables will converge to the desirable setpoints.

ABSTRACTThe problem of feedback control of bandwidth allocation for Internet links is analysed in this article. It is shown that the procedure for numerical solution of a fluid flow partial differential equation (PDE) which describes the bandwidth allocation on a link results into a set of ordinary differential equations (ODEs) and into an associated state-space equations model. For the local subsystems, into which the flow PDE is decomposed, it becomes possible to apply boundary-based feedback control. The solution of the control problem proceeds by showing that the state-space model of the flow PDE stands for a differentially flat system. Next, for each subsystem which is related to an ODE, a virtual control input is computed, which can invert the subsystem’s dynamics and can eliminate the subsystem’s tracking error. From the last row of the state-space description, the control input (boundary condition) that is actually applied to the data-flow PDE is found. This control input contains recursively all virtual control inputs which were computed for the individual ODE subsystems associated with the previous rows of the state-space equation. Thus, by tracing the rows of the state-space model backwards, at each iteration of the control algorithm, one can finally obtain the control input that should be applied to the data flow PDE of the communication network so as to assure that all its state variables will converge to the desirable set points.

The paper proposes derivative-free nonlinear Kalman Filtering for MIMO nonlinear dynamical systems. The considered nonlinear filtering scheme which is based on differential flatness theory extends the class of systems to which Kalman Filtering can be applied without the need for calculation of Jacobian matrices. To deduce if a dynamical system is differentially flat, the following should be examined: (i) the existence of the flat output, which is a variable that can be written as a function of the system's state variables (ii) the system's state variables and the input can be written as functions of the flat output and its derivatives. Nonlinear systems satisfying the differential flatness property can be written in the Brunovsky form via a transformation of their state variables and control inputs. After transforming the nonlinear system to the canonical form it is straightforward to apply the standard Kalman Filter recursion. The performance of the proposed derivative-free nonlinear filtering scheme is tested through simulation experiments on benchmark nonlinear multi-input multi-output dynamical systems, such as robotic manipulators.

Stabilized MPC formulations for robust reconfigurable flight control