Journal Papers

In this paper, we consider a boundary control problem governed by the two-dimensional Burgers equation for a configuration describing convective flow over an obstacle. Flows over obstacles are important as they arise in many practical applications. Burgers equations are also significant as they represent a simpler form of the more general Navier-Stokes momentum equation describing fluid flow. The aim of the work is to develop a reduced-order boundary control-oriented model for the system with subsequent nonlinear control law design. The control objective is to drive the full order system to a desired 2D profile. Reduced-order modeling involves the application of an L2 optimization based actuation mode expansion technique for input separation, demonstrating how one can obtain a reduced-order Galerkin model in which the control inputs appear as explicit terms. Controller design is based on averaging and center manifold techniques and is validated with full order numerical simulation. Closed-loop results are compared to a standard LQR design based on a linearization of the reduced-order model. The averaging/center manifold based controller design provides smoother response with less control effort and smaller tracking error.

An adaptive control system using extremum-seeking optimization is developed to suppress subsonic cavity flow resonance. Firstly, a simple but effective linear feedback control law is employed. This control law uses pressure fluctuations measured at two different cavity side-wall locations as feedback signals. The influence of the control parameters (namely, a gain K and a phase shift φ) on the magnitude of the limit cycle in closed-loop is investigated analytically and experimentally. Secondly, an extremum-seeking algorithm is implemented to optimize in real time the selection of the most critical control parameter, φ, in such a way that the magnitude of the limit cycle is minimized in closed-loop. The performance of the resulting control system is compared with that of a linear-quadratic feedback controller of fixed structure, developed on the basis of a reduced-order model of cavity flow dynamics. Experimental results highlight the advantage of parameter adaptation provided by the extremum-seeking algorithm over the controller of fixed structure under varying flow conditions.

This paper considers the robust output regulation problem for parameterized families of periodic systems. To extend the solution of the output regulation problem to the periodic (or time-varying) setup, a classification of the immersion mappings based on various non-equivalent observability properties is derived. The connections between different canonical realizations of internal models that fully exploit such properties for robust and adaptive output regulation design in periodic systems are investigated. It is shown how non-minimal realizations of suitable periodic internal models are instrumental in achieving the possibility of performing adaptive redesign to deal with parameterized families of exosystem models. An important feature of the proposed solution is the fact that a persistence of excitation condition for the exogenous signals is not required for asymptotic regulation.

First-principle based models of the dynamics of flow systems are often of limited use for model-based control design, not only because of their nonlinear and infinite-dimensional nature, but also because the control input is generally specified as a boundary condition. Proper Orthogonal Decomposition and Galerkin Projection are among the most effective and commonly used methods to obtain reduced-order models of flow dynamics. However, the final form of these models may not account for the presence of a forcing or control input. From a control design perspective, it is desirable to obtain a reduced-order model in which the control input appears explicitly in the dynamical equations. In this paper, two methods for control input separation are introduced and comparatively evaluated in experimentally-based reduced-order modeling of cavity flow, both in their ability to reconstruct the forced flow field and to provide models suitable for feedback control design. The proposed methods, namely i) actuated POD expansion and ii) L2-optimization, extend the baseline flow model through the use of innovation vectors, which capture the deviation of the actuated flow from the baseline space. The new methods address some of the issues associated with the sub-domain separation technique employed in our previous works. Linear quadratic regulator controllers built using models obtained from the new methods have been tested on a cavity flow experiment. While the new models perform satisfactorily and comparably to our previous models in terms of suppression of cavity tones, they offer a substantial advantage in terms of the required input power to achieve a similar or better performance.

A control input separation method is proposed for reduced-order modeling in boundary control problems. The dynamics of flow systems are typically described by partial differential equations where the input affects the system through boundary conditions. From a control design perspective it is most desirable and natural to employ finite-dimensional representations in which the input enters the dynamics directly. The method proposed here to resolve the input from the boundary conditions is based on obtaining a proper orthogonal decomposition of the unforced flow of the system, and then augmenting this decomposition by optimally computed actuation modes, built using snapshots of the actuated flow. A reduced-order Galerkin model is then derived for this expansion, in which the input appears as an explicit term in the system dynamics. The model reduces exactly to the original baseline case under zero input conditions. The proposed method is then compared to an existing input separation technique, namely the sub-domain separation method. A boundary control example regarding the 2D incompressible Navier-Stokes equation is considered to illustrate the proposed method, where a controller is designed to achieve tracking of a desired 2D spatial profile for the flow velocity.

This paper addresses issues related to robust output feedback control for a model of an air-breathing hypersonic vehicle. The control objective is to provide robust velocity and altitude tracking in the presence of model uncertainties and varying flight conditions, using only limited state information. A baseline control design based on a robust full-order observer is shown to provide, in nonlinear simulations, insufficient robustness with respect to variations of the vehicle dynamics due to fuel consumption. An alternative approach to robust output-feedback design, which does not employ state estimation, is presented and shown to provide an increased level of performance. The proposed methodology reposes upon robust servomechanism theory and makes use of a novel internal model design. Robust compensation of the unstable zero-dynamics of the plant is achieved by using measurements of pitch rate. The selection of the plant's output map by sensor placement is an integral part of the control design procedures, accomplished by preserving certain system structures that are favorable for robust control design. The performance of each controller is comparatively evaluated by means of simulations on a nonlinear model of the vehicle dynamics, and tested on a given range of operating conditions.

Actuation devices are crucial components of closed-loop flow control schemes. Acoustic synthetic jet-like actuators, which are commonly employed in cavity flow control, exhibit a dynamic response that, if ignored, may significantly affect the overall characteristics of the closed-loop system. This paper presents the development and implementation of a dynamic compensator for a specific synthetic jet-like compression driver actuator which has been successfully implemented for feedback control of subsonic cavity flows. A time-delay model of the actuator dynamics is obtained from experimental data using subspace-based identification methods. The model is designed to match the frequency response of the physical system in a range of interest that covers the resonant frequencies of the cavity. The model is then used for the synthesis of a dynamic controller which employs a Smith predictor in conjunction with an H-infinity mixed-sensitivity design. Order reduction is applied to obtain a low-order digital controller amenable to real-time applications. The compensator is retrofitted to an existing cavity flow control architecture, and used to force the actuator output to closely follow the input commands, thereby compensating undesirable actuator dynamics. Experiments show that the integration of the actuator compensator within the cavity control system significantly improves closed-loop performance over existing results.

In this paper, nonlinear control systems whose dynamics are quadratic with respect to state and bilinear with respect to state and input, and which exhibit an oscillation caused by a stable limit cycle for zero input are studied. Galerkin systems which arise from reduced-order modeling of certain infinite-dimensional dynamical systems of interest in flow control belong to this category. For these models, it is customary to analyze the effect of linear control on the amplitude of the limit cycle using standard arguments involving Poincarè normal forms and center manifold theory. It is found that the oscillation amplitude depends both on terms linear in the control and nonlinear terms that depend on the center manifold. To exploit these latter, in this paper a nonlinear control law is proposed that aims at reducing the oscillation by shaping the center manifold. An oscillation preserving condition was defined and enforced on the system to ensure that the results are physically meaningful and practically implementable. The analysis of the closed loop system is simplified using a time varying periodic change of coordinates, time scaling, and averaging. Using center manifold theory, conditions governing the number and stability type of the limit cycles, and analytical expressions for the oscillation amplitude are derived. The results are verified using a finite dimensional cavity flow model as a case study.

The classical attitude control problem for a rigid body is revisited under the assumption that the measurements of the angular rates obtained by means of rate gyros are corrupted by harmonic disturbances, a setup of importance in several aerospace applications. The paper extends previous methods developed to compensate bias in the angular rate measurements by accounting for a more general class of disturbances, and by allowing uncertainty in the inertial parameters. By resorting to adaptive observers designed on the basis of the internal model principle, it is shown how converging estimates of the angular velocity can be obtained, and used effectively in a passivity-based certainty-equivalence controller yielding global convergence within the chosen parametrization of the group of rotations. Since a persistence of excitation condition is not required for the convergence of the state estimates, only an upper bound on the number of distinct harmonic components of the disturbance is needed for the applicability of the method.

Full simulation models for flexible air-breathing hypersonic vehicles include intricate couplings between the engine and flight dynamics, along with complex interplay between flexible and rigid modes, resulting in intractable systems for nonlinear control design. In this paper, starting from a high-fidelity model, a control-oriented model in closed form is obtained by replacing complex force and moment functions with curve fitted approximations, neglecting certain weak couplings, and neglecting slower portions of the system dynamics. The process itself allows a thorough understanding of the system-theoretic properties of the model, and enables the applicability of model-based nonlinear control techniques. While the focus of this paper is on the development of the control-oriented model, an example of control design based on approximate feedback linearization is provided. Simulation results demonstrate that this technique achieves excellent tracking performance, even in the presence of moderate parameter variations. The fidelity of the truth model is then increased by including additional flexible effects which render the original control design ineffective. A more elaborate model with an additional actuator is then employed to enhance the control authority of the vehicle, required to compensate for the new flexible effects, and a new design is provided.

Development, experimental implementation, and the results of reduced-order model based feedback control of subsonic cavity flows are presented and discussed in this paper. Particle image velocimetry (PIV) data and the proper orthogonal decomposition (POD) technique were used to extract the most energetic flow features or POD eigenmodes. The Galerkin projection of the Navier-Stokes equations onto these modes was used to derive a set of non-linear ordinary differential equations, which govern the time evolution of the modes, for the controller design. Stochastic estimation was used to correlate surface pressure data with flow field data and dynamic surface pressure measurements were used to estimate the state of the flow in real-time. Five sets of PIV snapshots of a Mach 0.3 cavity flow with a Reynolds number of 10⁵ based on the cavity depth were used to derive five different reduced-order models for the controller design. One model used only the snapshots from the baseline (unforced) flow while the other four models each used snapshots from the baseline flow combined with those from an open-loop sinusoidal forcing case. Linear-quadratic optimal controllers based on these models were designed to reduce cavity flow resonance and evaluated experimentally. The results obtained with feedback control show a significant attenuation of the resonant tone and a redistribution of the energy into lower frequency modes with smaller energy levels. This constitutes a significant improvement in comparison with the results obtained using open-loop forcing. These results affirm that reduced-order model based feedback control represents a formidable alternative to open-loop strategies in cavity flow control problems even in its current state of infancy.

Allocation of control authority among redundant control effectors, under hard constraints, is an important component of the inner loop of a re-entry vehicle guidance and control system. Whereas existing control allocation schemes generally neglect actuator dynamics, thereby assuming a static relationship between control surface deflections and moments about a three-body axis, in this work a dynamic control allocation scheme is developed which implements a form of model predictive control. In the approach proposed here, control allocation is posed as a sequential quadratic programming problem with constraints, which can also be cast into a linear complementarity problem and therefore solved in a finite number of iterations. Accounting directly for non-negligible dynamics of the actuators with hard constraints, the scheme extends existing algorithms by providing asymptotic tracking of time-varying input commands for this class of applications. To illustrate the effectiveness of the proposed scheme, a high-fidelity simulation for an experimental reusable launch vehicle is utilized, where results are compared to those of static control allocation schemes in situations of actuator failures.

We consider the systematic design of tracking controllers for Euler-Lagrange systems which are affected by unmeasurable harmonic disturbances. The problem addressed in the paper departs from the classic setup of the regulator problem and its solution based on the internal model principle in two aspects. First, the presence of an exogenous disturbance affecting the output channel as well as the input channel of the plant is taken into account. Second, we aim at designing a nominal tracking controller using standard techniques, independently of the device that is used to provide asymptotic rejection of the disturbance. This latter is then placed outside the stabilizing loop, in such a way that stability is preserved, and asymptotic cancellation of the disturbance is guaranteed under mild conditions. The device in question is referred to as an external model of the exogenous system, to emphasize the departure from the classic internal model-based design. The external model is endowed with an adaptation mechanism that allows to deal with uncertainties on the frequencies of the exogenous signals as well. To validate our approach, we provide experimental results for a 2-DOF helicopter model.

We address the problem of rejecting harmonic disturbances occurring at the input of a linear controller in a stable loop. The task is to recover regulation of the plant output, using only information corrupted by harmonic noise of unknown frequency. The problem departs from the standard output regulation framework, as the assumption of the explicit availability of an error signal to be regulated to zero is not met. We take a novel approach of observing and rejecting the disturbance by means of reconstructing asymptotically the steady state behavior of the closed-loop system that would occur if the disturbance was not compensated. The solution is provided by an adaptive external model (a device placed outside the stabilizing loop), which possesses a hybrid system structure due to the specific form of the associated certainty-equivalence solution. The geometric characterization of the solution is emphasized throughout the paper, and its relation with the classic internal model principle discussed. The important issue of convergence in absence of persistence of excitation is addressed in full.

The focus of this paper is on the design of a control architecture of decentralized type for controlling a leader/follower formation of autonomous non-holonomic vehicles. A fundamental constraint in formation control requires that each agent employs local sensor information to process data on the relative position and velocity between its neighboring vehicles, without relying on global communication with mission control. This poses a challenge in the design of the control system, as the reference trajectory to be tracked, which in the case considered in this paper is related to the unknown trajectory of the leader of the formation, It is shown in the paper that this specific formation control problem can be approached from the point of view of the internal model paradigm. In particular, once a model of the autonomous dynamics of the leader of the formation is embedded in a decentralized dynamic controller, the design of the controller can be completed with a robust stabilizer, obtained using ISS-gain assignment techniques. It is shown that asymptotic convergence of the formation to an arbitrarily small neighborhood of the desired steady-state configuration is achieved, despite the presence of possibly large parameter uncertainties, while the motion of each agent remains confined into specified sectors, to avoid possible collision between neighboring vehicles during transients. Simulations results are presented to illustrate the design methodology.

The problem of asymptotic output regulation for linear systems driven by time-varying, T-periodic exosystems is considered in this paper. Necessary and sufficient condition for its solvability based on the existence of periodic solutions of differential Sylvester equations are derived. These conditions constitute a generalization to the periodic case of the celebrated algebraic regulator equations of Francis. A general algorithm for the synthesis of an error-feedback regulator is given. For the case of minimum-phase systems, it is shown that the regulator design can be carried out without the knowledge of the Floquet decomposition of the exosystem, thus extending significantly the applicability of the general result. The more challenging issue of robust regulation by error feedback is also addressed, and solved under a stronger observability condition.

In the process of implementing modular fault diagnostics for X-by-Wire systems, it was discovered that distinguishing between the model uncertainties and occurrence of faults is a real challenge. It is imperative to solve the problems that exist in using fixed observer and threshold, including the observer model mismatch, generated threshold misfit, diagnostic parameter uncertainties, and incorrect diagnostic output during high stress but normal vehicle operation. Compared to the fixed observer and threshold strategy, the improved adaptive threshold-based diagnostics described in this report are more robust and applicable because of the addition of adaptation into the diagnostic observer and threshold generator. The report also describes an approach to fault detection and isolation in the presence of model and parameter uncertainties. This approach has been successfully implemented in the NAVDyn (Non-Linear Analysis of Vehicle Dynamics) simulation model using Matlab Simulink, and simulation results are provided to verify that the strategy and implementation are viable.

This paper deals with the design of an internal model-based semiglobal output feedback regulator for possibly nonminimum phase nonlinear systems. Taking advantage of the design tool proposed in a recent paper by Isidori,we show how the problem of output regulation can be reformulated into an output feedback stabilization problem of a suitably-defined extended auxiliary system. The output feedback stabilization of the extended auxiliary system is addressed in the second part of the paper, where an observer-based stabilizer is proposed. The existence of the latter is characterized in terms of necessary and sufficient conditions which can be interpreted as nonlinear non-resonance conditions between the modes of the exosystem and the zero dynamics of the controlled plant.

This paper discusses differential-form-based integrability conditions for dynamic constraints using the Frobenius theorem. The conditions can be used for the classification of holonomic and nonholonomic constraints. Some of the previous conditions used for this purpose are only sufficient. The conditions presented here are both necessary and sufficient. The paper's main interest is on differential constraints for under-actuated mechanical systems. Different from many discussions in classical mechanics that deal with mostly on kinematics constraints, the constraints discussed here are from the Lagrange equations, which correspond to unactuated part of the system dynamics.

We consider the problem of controlling the vertical motion of a nonlinear model of a helicopter, while stabilizing the lateral and horizontal position and maintaining a constant attitude. The reference to be tracked is given by a sum of a constant and a fixed number of sinusoidal signals, and it is assumed not to be available to the controller. This represents a possible situation in which the controller is required to synchronize the vehicle motion with that of an oscillating platform, such as the deck of a ship in high seas. We design a nonlinear controller which combines recent results on nonlinear adaptive output regulations and robust stabilization of systems in feedforward form by means of saturated controls. Simulation results show the effectiveness of the method and its ability to cope with uncertainties on the plant and actuator model.

This paper deals with the problem of asymptotically rejecting bounded unknown disturbances affecting the input channel of a feedforward uncertain nonlinear system. The problem is solved assuming that the matched disturbance belongs to the class of signals generated by an autonomous neutrally stable exosystem whose state is not accessible. We design an internal model-based regulator capable on one hand to reject the matched disturbance for any initial state of the exosystem and, on the other hand, to robustly globally asymptotically stabilize the system using state feedback.

We address the design of an autopilot for the autonomous landing of a vertical take off and landing vehicle on a ship whose deck oscillates in the vertical direction due to high sea states. The deck motion is modeled as the superposition of a fixed number of sinusoidal functions of time, of unknown frequency, amplitude and phase. We design an internal-model-based error-feedback dynamic regulator that is robust with respect to uncertainties on the mechanical parameters that characterize the model and secures global convergence.

We address the problem of output regulation for nonlinear systems driven by a linear, neutrally stable exosystem whose frequencies are not known a priori. We present a classical solution in terms of the parallel connection of a robust stabilizer and an internal model, where the latter is adaptively tuned to the device that reproduces the steady-state control necessary to maintain the output-zeroing condition. We obtain robust regulation (i.e. in presence of parameter uncertainties) with a semi- global domain of convergence for a significant class of nonlinear minimum-phase system.

We address the problem of semiglobal robust output regulation for a general class of single-input, single-output nonlinear systems. The proposed solution does not require the assumption of input-to- state stability of the zero-dynamics of the plant. The design method is based on a classical decomposition of the control law into a stabilizing feedback and a feedforward control, where the latter is asymptotically reconstructed by an internal model. The scheme exploits the passivity properties of the internal model, and combines small-gain and high-gain feedback. Simulation results for an illustrative example are included.

The problem of global robust output regulation is solved for a class of nonlinear systems driven by a linear neutrally stable exosystem. The proposed scheme makes use of a dynamic controller which processes information from the regulated error only. Robust regulation is achieved for every initial condition in the state space, and for all possible values of the uncertain parameter vector and the exogenous signal ranging over arbitrary compact sets. The regulator synthesis is based upon a recursive procedure, and takes advantage of both the speciall normal form of the plant equations and the passivity property of the internal model.

We show how an efficient nonlinear controller for a general model of autonomous underwater vehicles (AUVs) dynamics, with uncertainties and external disturbances, can be designed by means of Lyapunov techniques. The control task we consider consists of tracking a given reference trajectory. As part of the design strategy, both model uncertainties and external disturbances physically corresponding to the effect of an underwater current are represented as a bounded perturbation of a nominal model of the vehicle dynamics.

A control strategy for an underwater vehicle based on a scheduling of linear H infinity controllers has been proposed, and the overall performance of the closed-loop system have been evaluated by means of nonlinear simulation in a broad range of working conditions, with particular attention to the effects of the underwater current that acts on the vehicle.