Tracking with Steady-State Optimization: an Application to Air-Breathing Hypersonic Vehicle Control

The development of an air-breathing hypersonic vehicle employing scramjet propulsion is an ongoing research endeavor. Because of high velocity (>Mach 5), length and positioning of the engine, and relative sleekness, the flexibility of the vehicle is significant and there are strong couplings between thrust and pitch . As a result, control design for such a vehicle is a challenge. In previous works, linear controllers have been designed for a model of the longitudinal dynamics of a specific air-breathing vehicle possessing the same number of inputs and outputs. In this paper we consider a control design for the same vehicle model, but we restrict our attention to controlling only two outputs, namely the altitude and velocity, while we employ as control inputs, the elevator deflection, total temperature change across the combustor and the diffuser area ratio of the combustor. The specific control problem addressed in the paper is the design of a controller that ensures asymptotic tracking of altitude and velocity reference trajectories, while using the redundancy in the inputs to optimize the performance in steady-state. As a matter of fact, since the system is not square, the steady state solutions that enforce perfect tracking are nonunique. The controller employs a parameterization of all possible steady state trajectories that is used for optimization of the steady state input while providing perfect tracking and fulfilment of constraint on the magnitude of the control input. Simulations results are provided to validate the proposed approach.

This paper presents a data-driven approach towards time-optimal trajectory generation for Unmanned Aerial Vehicles (UAV's) using a machine-learned trajectory generation mechanism for point-to-point time-optimal trajectories on-the-fly. To train this machine-learned black box trajectory generator off-line, a model-based optimization problem is first constructed for point-to-point time-optimal trajectory generation, with physical constraints on inputs, states, and rates. The formulated optimization problem is then solved off-line for a range of initial and terminal flight states to generate point-to-point data-sets that consist of the optimal state and input trajectories. This information is compressed by parameterizing the input and state trajectories using a set of basis functions. This data is then used to train the neural network-based trajectory planner. The output of the neural network is the basis function coefficient sets for the state and input trajectories (and the total flight time) which can then be used to reconstruct the flight trajectory. Once the neural network is trained, the data-driven on-board trajectory generator is ready to be deployed on the UAV for on-board planning. This approach is demonstrated for two scenarios: (1) the input to the neural network being the initial and terminal flight states and (2) the input to the neural network being initial and terminal flight states as well as physical constraints. To validate the performance of the machine-learned black-box trajectory generator, the root mean squared error between the neural network generated trajectories and the trajectories obtained from solving the optimization problem directly is statistically evaluated. These trajectories are also tested for violation of path constraints (which are not included explicitly in the training or input to the black box planner) by evaluating the mean constraint violation for each path-constrained variable.

This paper presents the development of an inverse simulation method for hypersonic vehicles and uses the method for design evaluation and trajectory analysis. Inverse simulation is a technique in which the control inputs, required to achieve a desired system output are computed through inversion of the system equations. Such analysis provides an insight into the capability of a vehicle to follow a given trajectory and allows the evaluation of vehicle controllability. In this work, the integration method of inverse simulation is used due to its increased exibility for vehicle models and trajectory inputs. Here the scramjet vehicle specific equations of motion, that incorporate look-up tables for vehicle aerodynamic properties are solved iteratively. In addtion the standard integration method is modified in order to mitigate non-convergence of the numerical method and to improve accuracy. The resulting inverse simulation routine was verified by evaluating a number of test trajectories described by sinusoidal fiight paths and a step increase in altitude. The results from these verification trajectories and the application of the inverse simulation algorithm to the linking trajectory used during the transition from the second stage (rocket powered) to third stage (scramjet powered) provide new insight into the controllability of the hypersonic Winged Cone Vehicle considered in this study.

Optimal grade transition of a HDPE plant by the modified two-step hierarchical dynamic optimization

This article proposes a phase-shifted model predictive control (PS-MPC) strategy to fully exploit the most relevant features of finite control set model predictive control (FCS-MPC) and phase-shifted pulse width modulation (PS-PWM) in a three-level active neutral point clamped (3L-ANPC) converter. Conventional PS-MPC strategies utilize a steady-state control input reference, typically a harmonic-free signal depending on the converter topology. However, this article demonstrates that the PS-MPC strategy applied to the 3L-ANPCconverter requires a control input containing a third-harmonic component with a specific magnitude and phase angle, which improves output current tracking and capacitor voltage balancing. By designing synchronized models for each carrier, the predictive controller optimizes duty cycles independently, ensuring the effective regulation of both control variables while addressing model nonlinearities. The proposed strategy is experimentally validated using a DSP F28379D microcontroller and a three-phase 3L-ANPCconverter using a total of 64 switching states in a grid-connected application. Compared to PS-PWM and FCS-MPC, the proposed approach maintains a fixed switching frequency, improves steady-state tracking, and enhances capacitor voltage balancing with a fast dynamic response. Additionally, it outperforms PS-MPC with control input change penalization (PS-MPC <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\boldsymbol\Delta} \boldsymbol{u}$</tex-math></inline-formula>) by reducing spectral dispersion while achieving lower execution time than both FCS-MPC and PS-MPC <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\boldsymbol\Delta} \boldsymbol{u}$</tex-math></inline-formula>, making it more suitable for real-time implementation. Such results are also discussed with a video demonstrating the real-time implementation.

Development of a CAD of control systems which realizes coordination of modeling of plant and design of controller is introduced. It enables us to do not only analysis of control systems and design of controllers but also online modeling of plants in the same environment. By utilizing this software, the control engineer is able to repeat the procedure of design of control systems efficiently to archive the best performance, which depends on the controller as well as the model of the plant. It is also shown how to improve the speed of computation by introducing the technique of memory management for real time control and how to change the parameters of the controller without stopping real time control.

This paper presents the development of direct adaptive control laws to enable an autonomous unmanned aerial vehicle (UAV) to track reference trajectories in the presence of external disturbances. A maneuver database of reference trajectories is computed offline from a linear UAV dynamic model using an optimization routine. Each maneuver in the database is therefore represented as a state trajectory, as well as the control input sequence that generates that trajectory. The trajectory tracking control laws are designed to enable a UAV to follow reference trajectories from this maneuver database. A disturbance accommodating control law is first developed and applied for the tracking of reference trajectories while the UAV is subjected to a persistent external disturbance. This control design requires a state-space disturbance generator model and the derivation of ideal trajectories from a reference model, which requires the solution of a set of matching conditions. A direct adaptive controller is then developed to enable the UAV to track reference trajectories while subject to modeling error and external disturbances. The adaptive controller also requires a disturbance model and the existence of ideal trajectories, but it does not require the explicit solution of the matching conditions. Simulation results for the disturbance accommodating controller and the adaptive controller are presented using a linear six-degree-of-freedom dynamic model that is representative of typical UAV dynamics. The results show that, although both controllers track reference trajectories and provide disturbance rejection, the adaptive controller is better suited for handling modeling errors or uncertainties.

Minimum phase systems are the only systems that allow (in disturbance-free unconstrained case) the achievement of perfect tracking in presence of arbitrary reference signals. The question is whether this still holds when the control input is subject to input saturation constraint. Surprisingly, most works on global output tracking in presence of input saturation focused on nonminimum phase systems. Then, perfect tracking is only achievable for constant references. In this paper, it is shown that more powerful tracking results are achievable for minimum phase systems. Specifically, perfect tracking is guaranteed for arbitrary type reference signals that satisfy a well defined strict compatibility condition. When, the reference signal is just compatible in the mean then the tracking quality depends on the reference variation rate. For periodic reference signals (not necessarily compatible with constraint), all the closed-loop system signals are shown to be periodic with the same period.

This chapter covers two issues (along many others) relating to complex systems control. The main theme is connected with control of Multi-Input Multi-Output (MIMO) systems. If the controlled system has more inputs than outputs (further labelled as MI+MO) there exist many combinations of the inputs for one combination of the outputs. We are able to reach desired system outputs (the main control aim) with many input combinations. This situation is very interesting from practical point of view. Usually optimal inputs combination exists – from some point of view. This combination leads for example to minimum energy consumption, maximum production efficiency or minimum machinery load etc. In practice the set of possible inputs combination is reduced because of constrains and the best feasible combination lies very often on constrain. It would be suitable to extend the controller design to include supplementary demand simultaneously with the fulfilment of the main control aim – to ensure best feasible input combination, too. The common advanced controller like LQ controller has no problem with MIMO system which has different number of inputs and outputs in contrary to standard controllers designed as decentralized control. However the constrains respecting within the standard LQ controller design is not possible. Another advanced controller – Model Predictive Controller (MPC) allows constrains handling (Camacho & Bordons, 1999), (Maciejowski, 2002), (Rossiter, 2003) but the standard controller design doesn’t solve which combination of inputs will occur in the steady-state in case of system with more inputs than outputs. One possibility how to achieve optimal inputs combination is to formulate one term of the cost function connected with inputs penalization as a deviation from ideal inputs combination. This approach is used e.g. in (Novak, 2009) but according to the opinion of authors this approach isn’t as universal as following proposal. We have suggested adding another term into the cost function of predictive controller – terminal state in a form of the deviation from desired terminal state. The desired terminal state is chosen that it corresponds to feasible optimal inputs combination and a value of the set-point at the end of the control horizon. Authors call this technique Steady-state optimization because the influence of the terminal state deviation comes to light namely in steady-state when the main control aim (desired output combination) is or has been already fulfilled see also (Dusek & Honc, 2009). The controller ensures both main and supplementary control aims – achievement of desired outputs and inputs moving to an optimal combination. An incorporation of the terminal state into the cost function has also another advantage. The

This paper presents an application of the Virtual Reference Feedback Tuning (VRFT) to control of the single-phase inverters. The VRFT is a data-driven method able to tuning controllers from data, this method only requires one data batch (input/output) to estimate parameters of a controller, and does not require the plant model. Under the VRFT framework, this work explores different controller structures and input designs, in order to find that controllers are able to deal with disturbances and nonlinear loads for a single phase inverter. Simulated results show that is possible controller design for a single phase inverter from data, avoiding the plant modeling. The main purpose of this research is to comparate VRFT with a standard controller model-driven.

SUMMARYThe problem of tracking control for a longitudinal air‐breathing hypersonic vehicle model with flexible effects and intricate couplings between the engine dynamics and flight dynamics is investigated in this paper. In order to overcome the analytical intractability of this model, a simplified model is constructed during the feedback controller design. High‐order dynamic sliding mode control is proposed to force the velocity and altitude of the flexible air‐breathing hypersonic vehicle (FAHV) to the desired reference commands in finite time. In addition, the adaptive control method is employed to identify bounded uncertainties for eliminating the requirement of boundaries needed in the robust controller design and to guarantee the property of finite time stability without information of upper bound of uncertainties. Finally, simulations are presented to illustrate the effectiveness of the control strategies.Copyright © 2013 John Wiley &amp; Sons, Ltd.

This paper aims at introducing H2 and H∞ robustness into the well-known characteristic model-based golden-section adaptive control law, and applying the robust adaptive control scheme to the attitude control of hypersonic cruise vehicles that are subject to external disturbances and aerodynamic coefficients uncertainties. When maneuvering at ultra high speeds, the attitude system of the hypersonic cruise vehicle is extremely sensitive to external disturbances and aerodynamic coefficients variations, and therefore the adaptiveness and the robustness of the attitude system are crucial during the controller design. To enhance the robustness of the existing golden-section adaptive control law, a golden-section robust adaptive control law is proposed. Compared to the existing control law where the design of the parameter λ depends on experience and is carried out offline, linear matrix inequality-based synthesis of λ is proposed such that the closed-loop system is stable with guaranteed H2 and H∞ performance. It is suitable for online computing and provides a time-varying λ(k) that is adjusted towards the optimal H2 and H∞ performance. When being applied to the attitude control of hypersonic vehicles during re-entry, the adaptive nature of the proposed control law provides the attitude system the capability to accommodate large flight conditions, and its H2 and H∞ robustness brought by λ(k) guarantees satisfying tracking performance in the presence of disturbances including both external disturbance and absolute aerodynamic coefficients errors.

Design of dynamic plant model and model-based controller for a heat recovery system with a swirling flow incinerator

In this article, we propose a two stage control design scheme for simultaneous flux regulation and angular position reference trajectory tracking in induction motors. The first outer loop design stage uses a linear GPI observer based robust control, aimed at on-line load torque estimation, thus making possible its cancellation from the controller. The stator currents act as auxiliary control input variables, within a field oriented control scheme, which uses a nonlinear asymptotic flux reconstructor. The designed current signals are used then as reference trajectories for the second, inner loop, design stage, corresponding to a switched stator input voltage strategy based on an average generalized proportional integral control design. This average design defines a discontinuous control input by means of a properly set sign function on the input tracking error. The second controller design stage, largely overcomes the effects of nonlinearities, including unknown motor parameters, present in the rotor voltages-to-rotor currents multi-variable dynamics.

The identification and compensation methods of torque ripple based on steady state error analysis are presented in order to reduce the fluctuation of steady-state error of servo system and create environment for the accurate identification of the friction model.The relationship between steady state errors and input and interference of signals in servo system is determined.On this basis,the composition of steady state error for the uniform motion is researched.The steady state error induced by system disturbance including torque ripple,friction moment and others is obtained.The function form of torque ripple is obtained by using methods such as spectrum analysis and least squares criterion.The compensation of ripple can be achieved by programmable multi-axis controller(PMAC).The experimental results show that the fluctuation of steady state error decreases to different degrees.It has obvious effect at low speed;the peak-to-peak value reduces from 10 μm to 3.3 μm after compensation.At high speed,the peak-to-peak value also decreases to 3.2 μm after compensation.Besides,the Stribeck curve can be apparently acquired.Therefore,the method proposed can effective compensate the torque ripple and lay the foundation for precise compensation of friction disturbance and improvement of dynamic performance of servo system.