Open-loop Control Law Research Articles

Feedback control of thermoacoustic instabilities in sequential combustor with nanosecond repetitively pulsed discharges

Controlling thermoacoustic instabilities is a necessary task for the development and operation of gas turbines. With the increasing proportion of renewable energy sources, gas turbines must have flexibility in terms of both fuel and load. This implies that thermoacoustic instabilities must be controlled under different operating conditions. Active control strategies are indeed very suitable in this case, as they can adapt to the changes in operating conditions. Nanosecond repetitively pulsed discharges (NRPD) has shown to be promising active control actuators because they require no moving parts. In this study, the effectiveness of feedback and open-loop control law with NRPD actuation to suppress thermoacoustic instabilities in a lab-scale sequential combustor is evaluated. The effect of the controller parameters on the NO emissions of the combustor is also quantified. The results indicate that there is a trade-off between acoustic pulsation reduction and NO emission.

Stable nullspace adaptive parameter identification of 6 degree-of-freedom plant and actuator models for underactuated vehicles: Theory and experimental evaluation

Model-based approaches to navigation, control, and fault detection that utilize precise nonlinear models of vehicle plant dynamics will enable more accurate control and navigation, assured autonomy, and more complex missions for such vehicles. This paper reports novel theoretical and experimental results addressing the problem of parameter estimation of plant and actuator models for underactuated underwater vehicles operating in 6 degrees-of-freedom (DOF) whose dynamics are modeled by finite-dimensional Newton-Euler equations. This paper reports the first theoretical approach and experimental validation to identify simultaneously plant-model parameters (parameters such as mass, added mass, hydrodynamic drag, and buoyancy) and control-actuator parameters (control-surface models and thruster models) in 6-DOF. Most previously reported studies on parameter identification assume that the control-actuator parameters are known a priori. Moreover, this paper reports the first proof of convergence of the parameter estimates to the true set of parameters for this class of vehicles under a persistence of excitation condition. The reported adaptive identification (AID) algorithm does not require instrumentation of 6-DOF vehicle acceleration, which is required by conventional approaches to parameter estimation such as least squares. Additionally, the reported AID algorithm is applicable under any arbitrary open-loop or closed-loop control law. We report simulation and experimental results for identifying the plant-model and control-actuator parameters for an L3 OceanServer Iver3 autonomous underwater vehicle. We believe this general approach to AID could be extended to apply to other classes of machines and other classes of marine, land, aerial, and space vehicles.

Aerodynamic Identification and Control Law Design of a Missile Using Machine Learning

The new generation of air vehicle is confronted with a more intricate environment and challenging missions, which puts forward higher requirements for the flight control system. In this study, the aerodynamic identification and control law design based on machine learning for a missile configuration is investigated through numerical simulations. The missile pitch and elevator deflection are realized via the combination of a rigid dynamic grid method and an overlapping grid technology, while the computational fluid dynamics/rigid body dynamics (CFD/RBD) strong coupling method is implemented to simulate the unsteady flows associated with the motion of the missile. Firstly, the aerodynamic data of the missile are gathered through forced pitching motion involving elevator deflection, and an aerodynamic model is constructed using a deep neural network to identify the aerodynamic moment with only a small number of unsteady aerodynamic data. Then, the accuracy and fidelity of the model are checked with the open-loop control law. Afterward, a missile pitch control law is generated through deep reinforcement learning based on the aerodynamic model, which enables the realization of a robust and exact angle-of-attack control process. Finally, the control law is transferred to a numerical environment and numerical virtual flight based on CFD is conducted, which demonstrates that stable control can be maintained even in continuous maneuvering. This study verifies the possibility of applying a deep neural network to air vehicle aerodynamic identification and deep reinforcement learning to a complicated flight control law design with excellent generalization ability. Machine learning is expected to play a significant role in the design and research for the novel generation of air vehicle.

Trajectory planning and control of convection reaction models with storage effects

Distributed parameter systems consisting of several convection-reaction equations, which are distributed coupled with a reaction equation are considered. An alternative model description for this class of systems is obtained using the method of characteristics. The alternative description is constituted by a single partial differential equation of first order with respect to time. The proposed reformulation of the model allows for the efficient simulation of the system and for the straightforward calculation of inversion-based open-loop control laws. The stability of the original and the inverse models are discussed. The proposed method is illustrated by means of an example.

Stochastic Primer Vector for Robust Low-Thrust Trajectory Design Under Uncertainty

Any space trajectories are subject to state uncertainty due to imperfect state knowledge, random disturbances, and partially known dynamical environments. Ideally, such uncertainty and associated risks must be properly quantified and taken into account in the process of trajectory design, ensuring a sufficiently low risk of causing hazardous events. To bridge the gap between the ideal goal and current practice in mission design, this paper extends Lawden’s primer vector theory and develops a solution method to solve the problem of low-thrust trajectory optimization under state uncertainty. The new primer vector, termed stochastic primer vector, provides an analytical open-loop optimal control law that respects a probabilistic path constraint with a user-specified confidence level (chance constraint). A numerical aspect of the indirect method is also extended by introducing a smoothing approach across constraint corner discontinuities, enabling efficient solution methods for constrained optimal control problems. The validity and effectiveness of the theoretical development are demonstrated with two numerical examples, which clarify the behavior of chance-constrained optimal low-thrust trajectories and confirm through Monte Carlo simulations that the designed trajectories indeed satisfy the imposed constraints under uncertainty with the prescribed confidence level.

Introduction to the Pontryagin Maximum Principle for Quantum Optimal Control

Optimal control theory is a powerful mathematical tool, which has known a rapid development since the 1950s, mainly for engineering applications. More recently, it has become a widely used method to improve process performance in quantum technologies by means of highly efficient control of quantum dynamics. This tutorial aims at providing an introduction to key concepts of optimal control theory that is accessible to physicists and engineers working in quantum control or in related fields. The different mathematical results are introduced intuitively, before being rigorously stated. This tutorial describes modern aspects of optimal control theory, with a particular focus on the Pontryagin maximum principle, which is the main tool for determining open-loop control laws without experimental feedback. The different steps to solve an optimal control problem are discussed, before moving on to more advanced topics such as the existence of optimal solutions or the definition of the different types of extremals, namely normal, abnormal, and singular. The tutorial covers various quantum control issues and describes their mathematical formulation suitable for optimal control. The connection between the Pontryagin maximum principle and gradient-based optimization algorithms used for high-dimensional quantum systems is described. The optimal solution of different low-dimensional quantum systems is presented in detail, illustrating how the mathematical tools are applied in a practical way.2 MoreReceived 10 December 2020Revised 21 May 2021DOI:https://doi.org/10.1103/PRXQuantum.2.030203Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCoherent controlOptimization problemsQuantum controlQuantum Information

Segment Drift Control with a Supervision Mechanism for Autonomous Vehicles

Stable maneuverability is extremely important for the overall safety and robustness of autonomous vehicles under extreme conditions, and automated drift is able to ensure the widest possible range of maneuverability. However, due to the strong nonlinearity and fast vehicle dynamics occurring during the drift process, drift control is challenging. In view of the drift parking scenario, this paper proposes a segmented drift parking method to improve the handling ability of vehicles under extreme conditions. The whole process is divided into two parts: the location approach part and the drift part. The model predictive control (MPC) method was used in the approach to achieve consistency between the actual state and the expected state. For drift, the open-loop control law was designed on the basis of drift trajectories obtained by professional drivers. The drift monitoring strategy aims to monitor the whole drift process and improve the success rate of the drift. A simulation and an actual vehicle test platform were built, and the test results show that the proposed algorithm can be used to achieve accurate vehicle drift to the parking position.

Stochastic recruitment control of shape memory alloy cellular actuators based on multi-state Markov chain model

A new broadcast stochastic recruitment approach to the control of shape memory alloy (SMA) cellular actuators is proposed. The control design is based on a Markov chain model of multi-state cells, which is able to better characterize the inherent hysteresis of SMA in phase transition. The closed-loop and open-loop control laws are derived from random Lyapunov stability analysis and the stability conditions are analyzed. Simulation experiments demonstrate the effectiveness of the proposed method.

Machine learning open-loop control of a mixing layer

We develop an open-loop control system using machine learning to destabilize and stabilize the mixing layer. The open-loop control law comprising harmonic functions is explored using the linear genetic programming in a purely data-driven and model-free manner. The best destabilization control law exhibits a square wave with two alternating duty cycles. The forced flow presents a 2.5 times increase in the fluctuation energy undergoing early multiple vortex-pairing. The best stabilization control law tames the mixing layer into pure Kelvin–Helmholtz vortices without following vortex-pairing. The 23% reduction of fluctuation energy is achieved under the dual high-frequency actuations.

Numerical Virtual Flight Simulation of Quasi-Cobra Maneuver of a Fighter Aircraft

By using a computational-fluid-dynamics-based numerical virtual flight (NVF) simulator, a simplified quasi-Cobra maneuver of a typical third-generation fighter is simulated and the unsteady aerodynamics, such as the dynamic forces and moments and the flow separation, are analyzed preliminarily. The NVF simulator integrates an unsteady Reynolds-averaged Navier–Stokes (RANS) solver on dynamic unstructured/hybrid grids, a rigid-body dynamics solver, and user-defined flight control system. To analyze the complex multiphysics coupling problem, four cases with increasing complexity are studied, including 1) static state simulation; 2) one-degree-of-freedom (1-DOF) forced pitchup; 3) 1-DOF pitchup by open-loop control of the elevators; and 4) three-degree-of-freedom (3-DOF) quasi-Cobra maneuvering. By applying a cosine function open-loop flight control law to the elevators and introducing a simplified vector thrust model, the fighter can pitch up to a high angle of attack from the cruising state, and then it can pitch down quickly, the whole process is similar to a Cobra maneuver. Even though the RANS simulations are not necessarily highly accurate for the large angle of attack, the multidisciplinary application in this work demonstrates the potential of the NVF simulator for the simulations of realistic poststall maneuvers.

Virtual Model Reduction-based Control Strategy of Planar Three-link Underactuated Manipulator with Middle Passive Joint

This paper presents a position control strategy for a planar active-passive-active (APA) underactuated manipulator with second-order nonholonomic characteristics. According to the structural characteristics of the planar APA system, we divide the system into two parts: a planar virtual Pendubot (PVP) and a planar virtual Acrobot (PVA). For the PVP, we mainly fulfill the target angle of the first link, which is calculated through the geometry method, and make the system stable. In this stage, via keeping the states of the third link being zero, the system is reduced to the PVP. Meanwhile, we design an open-loop control law based on the nilpotent approximation (NA) model of the PVP to make the second link stable and the first link stabilize at its target angle. Then, the planar APA system is reduced to a PVA with all links’ angular velocities being zero. For the PVA, we mainly realize the other two links’ target angles obtained via the particle swarm optimization (PSO) algorithm. Thus, the control objective of the planar APA system is achieved. Finally, above control strategy is verified by simulation results.

Prescribed-time tracking for triangular systems of reaction-diffusion PDEs

Approximate controllability of systems of coupled parabolic partial differential equations has been of interest for a few decades, where the existence of open-loop control laws performing approximate state transitions within a finite time is studied. In this work, we specialize to systems of reaction-diffusion equations where the connectivity structure is triangular in the reaction parameters and the controls appear at the boundary. We first generate controllers by combining a decoupling backstepping approach with differential flatness that allow us to generate admissible trajectories for system outputs from a given initial condition. As a byproduct of our approach, we achieve approximate state transitioning for the system within a finite terminal time. We enhance our control law by introducing time-varying error feedback controllers which reject variations in initial conditions within the terminal time. The resulting control law not only performs the approximate control task but also output trajectory tracking, all within the terminal time which can be prescribed independently of initial conditions.

Model-based Strategies of Drug Dosing for Pharmacokinetic Systems

The aim of this paper is to report analytical and individual-based methods for antibiotic dose selection, that are based on tools from system and control theory. A brief system analysis of standard population pharmacokinetic models proves that such models are nonnegative and stable. Then, an input-output analysis leads to an open-loop control law which yields a dosing for the “average” patient, based on the equilibrium trajectory of the system. This approach is then incorporated into a “worst-case” analysis based on the monotony of the state trajectories with respect to the clearance (model parameter). Finally, an heuristic method of an estimated state feedback is presented. Thanks to numerical simulations, these methods were successively illustrated on a model describing the pharmacokinetic of meropenem, an intravenous antibiotic for treatment of severe sepsis.

Electric sail trajectory correction in presence of environmental uncertainties

An Electric Solar Wind Sail (E-sail) is an innovative propellantless propulsion system that generates a propulsive acceleration by exchanging momentum with the solar wind charged particles. Optimal E-sail trajectories are usually investigated by assuming an average value of the solar wind characteristics, thus obtaining a deterministic reference trajectory. However, recent analyses have shown that the solar wind dynamic pressure should be modeled as a random variable and an E-sail-based spacecraft may hardly be steered toward a target celestial body in an uncertain environment with just an open-loop control law. Therefore, this paper proposes to solve such a problem with a combined control strategy that suitably adjusts the grid electric voltage in response to the measured value of the dynamic pressure, and counteracts the effects of the solar wind uncertainties by rectifying the nominal trajectory at suitably chosen points. The effectiveness of such an approach is verified by simulation using two-dimensional transfer scenarios.

Variational Calculus Approach to Optimal Interception Task of a Ballistic Missile in 1D and 2D Cases

The paper presents the application of variational calculus to achieve the optimal design of the open-loop control law in the process of anti-ballistic missile interception task. It presents the analytical results in the form of appropriate Euler–Lagrange equations for three different performance indices, with a simple model of the rocket and the missile, based on the conservation of momentum principle. It also presents the software program enabling rapid simulation of the interception process with selected parameters, parametric analysis, as well as easy potential modification by other researchers, as it is written in open code as m-function of Matlab.

Reactive Power Compensation in Distribution Systems Through the DSTATCOM Integration Based on the Bond Graph Domain

In this paper, the distribution static compensator model based on the bond graph (BG) domain is presented. The methodology is applied to reactive power compensation in distribution systems where a traditional phase lock loop for sensing the AC grid frequency is not needed. The control law is developed using the inverse BG model, which is extracted using the bi-causality concept. In this way, it is possible to perform the distribution system analysis completely in the BG domain. This means that the graphical model is inverted by obtaining the open-loop control law structure, and then the close loop is formulated. The balanced and unbalance conditions are analyzed, generating a control structure that is robust and efficient. The efficacy of the proposed methodology is shown through: partial and complete system simulations in MATLAB/Simulink® (MATLAB r2015b, Natick, Massachusetts, 01760, USA), as well as experimental laboratory tests. Such tests use: the rapid control prototyping concept and the real-time simulator Opal-RT Technologies® (Montreal, QC, Canada).

Stochastic control of wave energy converters with constrained displacements for optimal power absorption

An semi-analytical solution is derived for the optimal control of the power take-off of a single-degree of freedom heave point absorber with constraints on the displacement. At first the control force is derived during states, where the displacement constraint is active. This results in an open-loop control law dependent on the external wave load on the absorber. Next, the analytical solution for the optimal control in the unconstrained state is indicated, which turns out to be of the closed loop type with feedback from the present displacement and acceleration and from future velocities. The derived control law contains an undetermined constant, which is calibrated at the interface to the previous constrained state. The approach requires the estimation of the wave load during the constrained states, and the prediction of the future velocity response during unconstrained states. An algorithm has been devised in the paper for handling these problems. The theory has been validated against numerical solutions obtained by nonlinear programming.

A lagrangian flight simulator for airborne wind energy systems

• A constraint-free simulator for airborne wind energy systems is presented. • Fly- and ground-generation systems are considered. • Trade-off analysis of parallelization and lagrangian versus Hamiltonian formulations. • Self-consistent figure-of-eight trajectories are presented. • Open- and close-loop control strategies are considered. A parallelized flight simulator for the dynamic analysis of airborne wind energy (AWE) systems for ground- and fly-generation configurations is presented. The mechanical system comprises a kite or fixed-wing drone equipped with rotors and linked to the ground by a flexible tether. The time-dependent control vector of the simulator mimics real AWE systems and it includes the length of the main tether, the geometry of the bridle, the torque of the motor controllers of the rotors, and the deflections of ailerons , rudder and elevator. The use of a lagrangian formulation with a minimal coordinate approach and discretizing the main tether as a chain of inelastic straight rods linked by ideal (dissipative-less) rotational joints, yielded a non-stiff set of ordinary differential equations free of algebraic constraints. Several verification tests, including a reel-in maneuver that admits an analytical solution, are presented. The efficiency of the parallelization with the number of tether segments, and trade-off analysis of the lagrangian and hamiltonian formulations are also considered. The versatility of the simulator is highlighted by analyzing two maneuvers that are relevant for AWE scenarios. First, the simulator is used to compute periodic figure-of-eight trajectories with an open-loop control law that varies the geometry of the kite’s bridle, as frequently done in ground-generation AWE systems. Second, an unstable equilibrium state of a tethered drone equipped with two rotors for energy harvesting is stabilized by implementing a closed-loop control strategy for the deflection of the control aerodynamic surfaces .

Particle swarm algorithm-based damage-mitigating control law analysis and synthesis for liquid-propellant rocket engine

The damage-mitigating control is a novel technique to ameliorate the reliability and safety of liquid-propellant rocket engines by achieving an optimized trade-off level between overall dynamic performance of the liquid-propellant rocket engine and structural durability of some selected critical damageable components under the condition of no impact on the achievement of the launch and flight mission. Thus, it is needed to be solved for the damage-mitigating control that the global optimization of the best trade-off between the damage of the critical damageable components and the performance of rocket engine. The major challenge should focus on: (i) to construct model of a certain rocket engine system dynamics, critical components structural dynamics, and damage dynamics; (ii) to optimize open loop feed-forward control law based on liquid-propellant rocket engine system dynamic model, structural and damage dynamics model, by using particle swarm optimization algorithm; (iii) to synthesize an intelligent damage-mitigating control system using the optimized open loop control law. In this paper, synthesis procedure of damage mitigation is introduced; structure and damage dynamic model of damageable components are formulated. The results of the simulation computation show that the synthesized control laws are implemented and achieve the effect of damage mitigating for the liquid-propellant rocket engine. It can provide important theoretical and practical value not only for improving the safety and reliability of the liquid-propellant rocket engine, but also for the complex thermo-flow-mechanical systems such as airplane engines, automobile engines, and fossil-fueled power plant because their service life is very critical too.

New Marx Generator Architecture With a Controllable Output Based on IGBTs

In this paper, a new architecture of a high-voltage Marx pulse generator based on isolated gate bipolar transistors (IGBTs) is proposed. It allows continuous control of the output voltage by acting on the IGBTs activation time: “on-time.” The final after-charging capacitors’ voltage can be higher than the double of the input voltage. A simplified mathematical description of the system was developed in order to find a relation between the output voltage and the “On-time” (an open-loop control law). A SPICE simulation was implemented to check the expected performances and to verify the developed model. A three-stage generator was built according to the proposed structure using commercial IGBTs with a maximum output voltage of 3.6 kV. All results were compared to check and confirm the validity of the proposed architecture.