X. Chen, P. Yan, and A. Serrani.
On ISS-based design for leader/follower formation control with
Accepted for publication on International Journal of Robust and
Nonlinear Control, March 2012.
This paper addresses the design of low-level controllers for leader-follower formations of non-holonomic vehicles in the presence of bounded measurement delays. The concept of input-to-state stability is extended to encompass the effect of bounded delays and restrictions on the input. A method is proposed to integrate a Smith predictor in a back-stepping design based on nested saturations and nonlinear small gain assignment, which allows for time delays in the feedback loop. Robustness analysis under uncertain bounded time delays is provided, and design tradeoffs resulting from the use of bounded controls are discussed. Illustrative simulations are shown to validate the design and robustness analysis in the context of a simple leader-follower trailing control problem.
An output regulation perspective on the model reference adaptive
Accepted for publication on the International Journal of
Adaptive Control and Signal Processing. Special Issue in honor of Prof.
Petros Ioannou, April 2012.
The paper resents a connection between the classic model reference adaptive control and recent development in the theory of adaptive output regulation. Specifically, it is shown how the certainty-equivalence model reference controller realizes an internal model of an extended exogenous system comprising the zero-dynamics of the plant driven by the steady-state trajectories of the reference model. Furthermore, the classic non-minimal realization of the certainty-equivalence controller required for adaptive redesign is equivalent to a canonical parameterization of the internal model in question, achieved via a non-observable (but detectable) system immersion.
L. Fiorentini and A. Serrani.
Adaptive restricted trajectory tracking for a non-minimum phase
hypersonic vehicle model.
Accepted for publication on Automatica, November 2011.
The design of a nonlinear robust controller for a non-minimum phase model of an air-breathing hypersonic vehicle is presented in this work. When flight-path angle is selected as a regulated output and the elevator is the only control surface available for the pitch dynamics, longitudinal models of the rigid-body dynamics of air-breathing hypersonic vehicles exhibit unstable zero-dynamics that prevent the applicability of standard inversion methods for control design. The approach proposed in this paper uses a combination of small-gain arguments and adaptive control techniques for the design of a state-feedback controller that achieves asymptotic tracking of a family of velocity and flight-path angle reference trajectories belonging to a given class of vehicle maneuvers, in spite of model uncertainties. The method reposes upon a suitable redefinition of the internal dynamics of a control-oriented model of the vehicle dynamics, and uses a time-scale separation between the controlled variables to manage the peaking phenomenon occurring in the system. Simulation results on a full nonlinear vehicle model, which includes structural flexibility, illustrate the effectiveness of the methodology.
A. Sinha, A. Serrani, and M. Samimy.
Development of empirical estimators for feedback control of
high-speed axisymmetric jets.
AIAA Journal, 49(9):1971-1987, September 2011.
Localized arc philament plasma actuators have demonstrated significant potential in controlling high-speed and high Reynolds number axisymmetric jets in open-loop. As a first step in incorporating feedback for this control system, the authors have developed an empirical reduced-order model of the essential flow dynamics in the region surrounding the end of the potential core of the unforced jet. An existing direct numerical simulation database, that is similar to the experimental configuration, formed the testbed for this modeling phase. Real-time ßow state estimation is a challenging problem in the implementation of feedback control for such complex flows of practical interest. Sensing the pressure in the irrotational near-field close to the nozzle exit offers a suitable non-intrusive measurement that is driven by the jet's shear layer dynamics. Owing to convection, such a configuration naturally results in the measured pressure having a time-lead compared to the state of the reduced-order model, which is very useful for feedback control. The proposed sensing configuration consists of an azimuthal ring array along with a linear array. Several estimation strategies are implemented and assessed using the numerical database. The time-invariant version of the linear Kalman filter is demonstrated to have similar or better accuracy compared to a quadratic stochastic estimator, which in turn significantly outperforms a linear stochastic estimator. The filter is only as computationally complex as the linear stochastic estimator, thereby making it the strategy of choice.
A. Sinha, K. Kim, J.-H. Kim, A. Serrani, and M. Samimy.
Extremizing feedback control of a high-speed and high Reynolds
AIAA Journal, 48(2):387-399, February 2010.
We present results of the development and application of extremizing feedback control to high-speed and high Reynolds number axisymmetric jets. In particular, we demonstrate control authority on the near-field pressure of a Mach 0.9 jet with a Reynolds number based on jet diameter of 6.4×105. Open-loop forcing experiments are presented wherein localized arc filament plasma actuators are shown to have two distinct effects on the near-field pressure, similar to their effect on the far-field acoustics reported earlier. At low forcing Strouhal numbers (StDF) near the jet column mode instability, a large amplification in the pressure fluctuations is observed. At higher StDF (close to the initial shear layer instability) an attenuation is observed in the near-field pressure fluctuations over a broad range of excitation frequency, especially in the axisymmetric mode. Previous experiments have shown that forcing the jet with these low and high frequencies result in jet mixing enhancement and far-field noise reduction, respectively. Two different gradient-free extremizing feedback control algorithms have been implemented, each of which can perform online minimum-seeking as well as maximum-seeking. Both methods demonstrate fast convergence to the optimum followed by steady operation. We also show that far-field acoustic spectrum in steady-state operation of the closed-loop control is quite similar to that observed with optimal open-loop forcing
A. Sinha, A. Serrani, and M. Samimy.
Initial development of reduced-order models for feedback control of
International Journal of Flow Control, 2(1):39-60, March 2010.
Active control of high-speed and high Reynolds number axisymmetric jets for noise attenuation and bulk mixing enhancement is a topic of great current interest. An essential initial step in the implementation of feedback control to achieve the above goals is the development of a reduced-order model of the unforced jet. A number of modeling strategies are formulated hereby, and they are evaluated using an existing direct numerical simulation database of an unforced jet similar to our experimental configuration. A combination of proper orthogonal decomposition, spectral stochastic estimation, and Galerkin projection is used to derive the model from empirical data. Simulations of the reduced-order model are demonstrated to be sufficiently faithful to the full-order original simulation results to warrant its use for future control design.
Z. Zhang and A. Serrani.
Global robust regulation with generalized immersion.
Dynamics of Continuous, Discrete and Impulsive Systems: Part A
- Mathematical Analysis, 17(6), 2010.
Special Issue in honor of Prof. H.K. Khalil.
The global robust output regulation problem is solved in this paper for classes of nonlinear systems that do not satisfy the standard conditions for the existence of a linear internal model, but admit a so-called “generalized immersion.” It is shown how the obstacle given by the presence of the exosystem dynamics in the generalized immersion mapping or the necessity to construct a nonlinear internal model can be overcome by resorting to a recently developed framework for time-varying adaptive internal model design.
L. Fiorentini, A. Serrani, M. Bolender, and D. Doman.
Nonlinear robust adaptive control of flexible air-breathing
AIAA Journal of Guidance, Control and Dynamics, 32(2),
This paper describes the design of a nonlinear robust adaptive controller for a flexible air-breathing hypersonic vehicle model. Due to the complexity of a first-principle model of the vehicle dynamics, a control-oriented model is adopted for design and stability analysis. This simplified model retains the dominant features of the higher fidelity model, including non-minimum phase behavior of the flight-path angle dynamics, flexibility effects and strong coupling between engine and flight dynamics. A combination of nonlinear sequential loop-closure and adaptive dynamic inversion is adopted for the design of a dynamic state-feedback controller that provides stable tracking of velocity and altitude reference trajectories and imposes a desired set-point for the angle of attack. A complete characterization of the internal dynamics of the model is derived for Lyapunov-based stability analysis of the closed-loop system, which includes the structural dynamics. The proposed methodology addresses the issue of stability robustness with respect to both parametric model uncertainty, which naturally arises in adopting reduced-complexity models for control design, and dynamic perturbations due to the flexible dynamics. Simulation results on the full nonlinear model show the effectiveness of the controller.
C. Kasnakoğlu, R.C. Camphouse, and A. Serrani.
Reduced-order model-based feedback control of flow over an obstacle
using center manifold methods.
ASME Journal of Dynamic Systems, Measurement, and Control,
131(1):011011-1-12, January 2009.
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.
K. Kim, C. Kasnakoglu, A. Serrani, and M. Samimy.
Extremum-seeking control of subsonic cavity flow.
AIAA Journal, 47(1):195-205, January 2009.
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.
S. Messineo and A. Serrani.
Adaptive feedforward disturbance rejection in nonlinear systems.
Systems & Control Letters, 58(7):576-583, July 2009.
This paper investigates the problem of adaptive feedforward compensation for a class of nonlinear systems, namely that of input-to-state (and locally exponentially) convergent systems. It is shown how, under suitable assumptions, the proposed scheme succeeds in achieving disturbance rejection of a harmonic disturbance at the input of a convergent nonlinear system, with a semi-global domain of convergence. The result is proved by combining averaging analysis and techniques for semi-global stabilization. An illustrative example shows the effectiveness of the scheme.
S. Messineo and A. Serrani.
Offshore crane control based on adaptive external model.
Automatica, 45(11):2546-2556, November 2009.
An adaptive controller for cranes employed in heavy-lift offshore marine operations is presented. The control objective is to reduce the hydrodynamic slamming load acting on a payload at water-entry of moonpool operations, while letting the payload track a given velocity profile. The adopted solution relies upon the use of an adaptive observer and two adaptive external models of the disturbance, employed to recover the unavailable information about the error to be regulated. As a result, the closed-loop system is rendered adaptive with respect to both the plant parameters and the frequencies of the harmonic disturbances affecting the system. A certainty-equivalence controller which makes use of the estimated parameters and the reconstructed tracking error is proposed, and the performance of the overall scheme is verified experimentally on a scale model. Results show a remarkable improvement over a previous approach based on an observer-based internal model control of fixed structure.
T Yang, E.R. Westervelt, A. Serrani, and J.P. Schmiedeler.
A framework for the control of stable aperiodic walking in
underactuated planar bipeds.
Autonomous Robots, 27(3):277-290, October 2009.
This paper presents a new definition of stable walking for point-footed planar bipedal robots that is not necessarily periodic. The inspiration for the definition is the commonly-held notion of stable walking: the biped does not fall. Somewhat more formally, biped walking is shown to be stable if the trajectory of each step places the robot in a state at the end of the step for which a controller is known to exist that generates a trajectory for the next step with this same property. To make the definition useful, an algorithm is given to verify if a given controller induces stable walking in the given sense. Also given is a framework to synthesize controllers that induce stable walking. The results are illustrated on a 5-link biped ERNIE in simulation and experiment.
X. Yuan, E. Caraballo, J. Little, M. Debiasi, A. Serrani, H. Özbay, J.H.
Myatt, and M. Samimy.
Feedback control design for subsonic cavity flows.
Applied and Computational Mathematics, 8(1):70-91, January
A benchmark problem in active aerodynamic flow control, suppression of strong pressure oscillations induced by flow over a shallow cavity, is addressed in this paper. Proper orthogonal decomposition and Galerkin projection techniques are used to obtain a reduced-order model of the flow dynamics from experimental data. The model is made amenable to control design by means of a control separation technique, which makes the control input appear explicitly in the equations. A prediction model based on quadratic stochastic estimation correlates flow field data with surface pressure measurements, so that the latter can be used to reconstruct the state of the model in real time. The focus of this paper is on the controller design and implementation. A linear-quadratic optimal controller is designed on the basis of the reduced-order model to suppress the cavity flow resonance. To account for the limitation on the magnitude of the control signal imposed by the actuator, the control action is modified by a scaling factor, which plays the role of a bifurcation parameter for the closed-loop system. Experimental results, in qualitative agreement with the theoretical analysis, show that the controller achieves a significant attenuation of the resonant tone with a redistribution of the energy into other frequencies, and exhibits a certain degree of robustness when operating in off-design conditions.
Z. Zhang and A. Serrani.
Adaptive robust output regulation of uncertain linear periodic
IEEE Transactions on Automatic Control, 54(2):266-278,
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.
E. Caraballo, C. Kasnakoğlu, A. Serrani, and M. Samimy.
Control input separation methods for reduced-order model-based
feedback flow control.
AIAA Journal, 46(9):2306-2322, September 2008.
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.
C. Kasnakoğlu, A. Serrani, and M.Ö. Efe.
Control input separation by actuation mode expansion for flow control
International Journal of Control, 81(9):1475-1492, September
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.
K. Kim, M. Debiasi, R. Schultz, A. Serrani, and M. Samimy.
Dynamic compensation of a synthetic jet-like actuator for closed-loop
cavity flow control.
AIAA Journal, 46(1):232-240, January 2008.
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.
D.O. Sigthorsson, P. Jankovsky, A. Serrani, S. Yurkovich, M. Bolender, and
Robust linear output feedback control of an air-breathing hypersonic
AIAA Journal of Guidance, Control, and Dynamics,
31(4):1052-1066, July-August 2008.
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.
C. Kasnakoğlu and A. Serrani.
Attenuation of oscillations in Galerkin systems using
European Journal of Control, 13(5):529-542, December 2007.
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.
Y. Luo, A. Serrani, S. Yurkovich, M.W. Oppenheimer, and D.B. Doman.
A model-predictive dynamic control allocation scheme for re-entry
AIAA Journal of Guidance, Control, and Dynamics,
30(1):100-113, January 2007.
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.
J.T. Parker, A. Serrani, S. Yurkovich, M.A. Bolender, and D.B. Doman.
Control-oriented modeling of an air-breathing hypersonic vehicle.
AIAA Journal of Guidance, Control, and Dynamics,
30(3):856-869, May 2007.
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.
P. Pisu and A. Serrani.
Attitude tracking with adaptive rejection of rate gyro disturbances.
IEEE Transactions on Automatic Control, 52(12):2374-2379,
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.
M. Samimy, M. Debiasi, E. Caraballo, A. Serrani, X. Yuan, J. Little, and J.H.
Feedback control of subsonic cavity flows using reduced-order models.
Journal of Fluid Mechanics, 579:315-346, May 2007.
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.
G. Zarikian and A. Serrani.
Harmonic disturbance rejection in tracking control of
Euler-Lagrange systems: an external model approach.
IEEE Transactions on Control Systems Technology,
15(1):118-129, January 2007.
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.
X. Chen and A. Serrani.
An internal model approach to autonomous leader/follower trailing for
International Journal of Robust and Nonlinear Control, 16(14),
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.
P. Pisu, A. Serrani, S. You, and L. Jalics.
Adaptive threshold based diagnostics for steer-by-wire systems.
Transactions of ASME. Journal of Dynamic Systems, Measurement
and Control, 128(2), June 2006.
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.
Rejection of harmonic disturbances at the controller input via hybrid
adaptive external models.
Automatica, 42(11):1977-1985, November 2006.
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.
Z. Zhang and A. Serrani.
The linear periodic output regulation problem.
Systems and Control Letters, 55(7):518-529, July 2006.
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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.
L. Marconi, A. Isidori, and A. Serrani.
Non-resonance conditions for uniform observability in the problem of
nonlinear output regulation.
Systems and Control Letters, 53(3-4):281-298, November 2004.
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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.
A. Isidori, L. Marconi, and A. Serrani.
Robust nonlinear motion control of a helicopter.
IEEE Transactions on Automatic Control, 48(3):413-426, March
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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.
T-J. Tarn, M. Zhang, and A. Serrani.
New integrability conditions for differential constraints.
Systems and Control Letters, 49(5):335-345, August 2003.
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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.
L. Marconi, A. Isidori, and A. Serrani.
Autonomous vertical landing on an oscillating platform: an
internal-model based approach.
Automatica, 38(1):21-32, January 2002.
[ http ]
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.
L. Marconi, A. Isidori, and A. Serrani.
Input disturbance suppression for a class of feedforward uncertain
Systems and Control Letters, 45:227-236, March 2002.
[ http ]
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.
A. Serrani, A. Isidori, and L. Marconi.
Semiglobal nonlinear output regulation with adaptive internal model.
IEEE Transactions on Automatic Control, 46(8):1178-1194,
[ .pdf ]
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.
A. Serrani and A. Isidori.
Global robust output regulation for a class of nonlinear systems.
Systems and Control Letters, 39:133-139, February 2000.
[ http ]
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.
A. Serrani, A. Isidori, and L. Marconi.
Semiglobal robust output regulation of minimum-phase nonlinear
International Journal of Robust and Nonlinear Control,
10(5):379-396, April 2000.
Special Issue on Output Regulation of Nonlinear Systems.
[ http ]
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.
G. Conte and A. Serrani.
Robust nonlinear motion control for AUVs.
IEEE Robotics and Automation Magazine, 6(2), June 1999.
Special Issue on Design and Navigation of Autonomous Underwater
[ .pdf ]
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.
G. Conte and A. Serrani.
Robust control of a remotely operated underwater vehicle.
Automatica, 34(2), February 1998.
[ http ]
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.
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