Linear Parameter-Varying Embedding of Nonlinear Models with Reduced Conservativeness

In this paper, a systematic approach is developed to embed the dynamical description of a nonlinear system into a linear parameter-varying (LPV) system representation. Initially, the nonlinear functions in the model representation are approximated using multivariate polynomial regression. Taking into account the residuals of the approximation as the potential scheduling parameters, a principle component analysis (PCA) is conducted to introduce a limited set of auxiliary scheduling parameters in coping with the trade-o? between model accuracy and complexity. In this way, LPV embedding of the nonlinear systems and scheduling variable selection are jointly performed such that a good trade-o? between complexity and conservativeness can be found. The developed LPV model depends polynomially on some of the state variables and affinely on the introduced auxiliary scheduling variables, which all together comprise the overall scheduling vector. The methodology is applied to a two-degree of freedom (2-DOf) robotic manipulator in addition to an academic example to reveal the effectiveness of the proposed method and to show the merits of the presented approach compared with some available results in the literature.Comment: 7 pages, 2 figures, IFAC World Congress, Berlin, 202

Actuator fault diagnosis of singular delayed LPV systems with inexact measured parameters via PI unknown input observer

© 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksIn this study, actuator fault diagnosis of singular delayed linear parameter varying (SDLPV) systems is considered. The considered system has a time-varying state delay and its matrices are dependent on some parameters that are measurable online. It is assumed that the measured parameters are inexact due to the existence of noise in real situations. The system with inexact measured parameters is converted to an uncertain system. Actuator fault diagnosis is carried out based on fault size estimation. For this purpose, the system is transformed to a polytopic representation and then a polytopic proportional integral unknown input observer (PI-UIO) is designed. The proposed observer provides simultaneous state and actuator fault estimation while attenuating, in the H8H8 sense, the effects of input disturbance, output noise and the uncertainty caused by inexact measured parameters. The design procedure of PI-UIO is formulated as a convex optimisation problem with a set of Linear Matrix Inequality (LMI) constraints in the vertices of the parameter domain, guaranteeing robust exponential convergence of the PI-UIO. The efficiency of the proposed method is illustrated with an electrical circuit example modelled as an SDLPV system.Peer ReviewedPostprint (author's final draft

Fault detection in uncertain LPV systems with imperfect scheduling parameter using sliding mode observers

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.This paper presents a sliding mode fault detection scheme for linear parameter varying (LPV) systems with uncertain or imperfectly measured scheduling parameters. In the majority of LPV systems, it is assumed that the scheduling parameters are exactly known. In reality due to noise or possibly faulty sensors, it is sometimes impossible to have accurate knowledge of the scheduling parameters and a design based on the assumption of perfect knowledge of the scheduling parameters cannot be guaranteed to work well in this situation. This paper proposes a sliding mode observer scheme to reconstruct actuator and sensor faults in a situation where the scheduling parameters are imperfectly known. The efficacy of the approach is demonstrated on simulation data taken from the nonlinear RECONFIGURE benchmark model.This work is supported by the EU-FP7 Grant (FP7-AAT-2012-314544

Observer-based controllers with data dropout rate adaptation

In this work, we address the observer-based control problem for networked control systems with an unknown time-varying packet arrival rate (PAR) and under root mean square-norm bounded disturbances. We assume packetized transmissions of both measurement and control input through a communication network with successful delivery acknowledgement. Using the measurement reception state and the control transmission acknowledgement, we derive a filter to estimate the PAR. We consider that the PAR changes sporadically from a constant value to another one; that is, it has two different behaviours: transient and steady state. While the observer only updates the state estimation using the current received measurements, the controller computes the control action employing the current state estimation and the previous applied control input. We propose to schedule both the observer and controller with rational functions of the PAR estimation. We show that the separation principle applies, and then, seeking higher performance accuracy, we develop an optimization math formula observer and controller design procedure that considers the two possible behaviours of the PAR. This optimization procedure attempts to maximize the estimation and control performances for each of the possible constant values of the PAR while offering robustness against PAR estimation errors and variations of the PAR. By exploiting sum-of-squares decomposition techniques, the design procedure involves an optimization problem over polynomials. A numerical example illustrates the effectiveness of the proposed approach.This work has been supported by MICINN project number TEC2015-69155-R from the Spanish government, project number P1·1B2015-42 and grant PI15734 from Universitat Jaume I

Robust Guaranteed Cost Output-Feedback Gain-Scheduled Controller Design

In the paper a new robust guaranteed cost output-feedback gain-scheduled PID controller design technique is presented for affine linear parameter-varying systems under polytopic model uncertainty, with the assumption that the scheduled parameters are affected with absolute uncertainty. The proposed centralized or decentralized method is based on the Bellman-Lyapunov equation, guaranteed cost, and parameter-dependent quadratic stability. The robust stability and performance conditions are translated to an optimization problem subject to bilinear matrix inequalities, which can be solved or further linearized. As the main result, the suggested stability and performance conditions without any restrictions on the controller structure are convex functions of the scheduling and uncertainty parameters. Hence, there is no need for applying multi-convexity or other relaxation techniques and consequently the proposed solution delivers a less conservative design method. The viability of the novel design technique is demonstrated and evaluated through numerical examples

Generalized robust gain-scheduled PID controller design for affine LPV systems with polytopic uncertainty

In the paper a generalized guaranteed cost output-feedback robust gain-scheduled PID controller synthesis is presented for affine linear parameter-varying systems under polytopic model uncertainty. The controller synthesis is generalized in a sense that it covers robust, robust gain-scheduled, and robust switched (with arbitrary switching algorithm) PID controller design. The proposed centralized/decentralized controller method is based on Bellman–Lyapunov equation, guaranteed cost, and parameter-dependent quadratic stability. The proposed sufficient robust stability and performance conditions are derived in the form of bilinear matrix inequalities (BMI) which can efficiently be solved or further linearized. As the main result, the suggested performance and stability conditions without any restriction on the controller structure are convex functions of the scheduling and uncertainty parameters. Hence, there is no need for applying multi-convexity or other relaxation techniques and consequently the proposed solution delivers a less conservative design method. The viability of the novel design technique is demonstrated and evaluated through numerical examples

Efficient LMI-based quadratic stabilization of interval LPV systems with noisy parameter measures

none2openL. IETTO; Valentina OrsiniIetto, Leopoldo; Orsini, Valentin

Affine linear parameter-varying embedding of non-linear models with improved accuracy and minimal overbounding

In this paper, automated generation of linear parameter-varying (LPV) state-space models to embed the dynamical behavior of nonlinear systems is considered, focusing on the trade-off between scheduling complexity and model accuracy and on the minimization of the conservativeness of the resulting embedding. The LPV state-space model is synthesized with affine scheduling dependency, while the scheduling variables themselves are nonlinear functions of the state and input variables of the original system. The method allows to generate complete or approximative embedding of the nonlinear system model and also it can be used to minimize complexity of existing LPV embeddings. The capabilities of the method are demonstrated on simulation examples and also in an empirical case study where the first-principle motion model of a 3-DOF control moment gyroscope is converted by the proposed method to LPV model with low scheduling complexity. Using the resulting model, a gain-scheduled controller is designed and applied on the gyroscope, demonstrating the efficiency of the developed approach

Low Complexity Model Predictive Control of a Diesel Engine Airpath.

The diesel air path (DAP) system has been traditionally challenging to control due to its highly coupled nonlinear behavior and the need for constraints to be considered for driveability and emissions. An advanced control technology, model predictive control (MPC), has been viewed as a way to handle these challenges, however, current MPC strategies for the DAP are still limited due to the very limited computational resources in engine control units (ECU). A low complexity MPC controller for the DAP system is developed in this dissertation where, by "low complexity," it is meant that the MPC controller achieves tracking and constraint enforcement objectives and can be executed on a modern ECU within 200 microseconds, a computation budget set by Toyota Motor Corporation. First, an explicit MPC design is developed for the DAP. Compared to previous explicit MPC examples for the DAP, a significant reduction in computational complexity is achieved. This complexity reduction is accomplished through, first, a novel strategy of intermittent constraint enforcement. Then, through a novel strategy of gain scheduling explicit MPC, the memory usage of the controller is further reduced and closed-loop tracking performance is improved. Finally, a robust version of the MPC design is developed which is able to enforce constraints in the presence of disturbances without a significant increase in computational complexity compared to non-robust MPC. The ability of the controller to track set-points and enforce constraints is demonstrated in both simulations and experiments. A number of theoretical results pertaining to the gain scheduling strategy is also developed. Second, a nonlinear MPC (NMPC) strategy for the DAP is developed. Through various innovations, a NMPC controller for the DAP is constructed that is not necessarily any more computationally complex than linear explicit MPC and is characterized by a very streamlined process for implementation and calibration. A significant reduction in computational complexity is achieved through the novel combination of Kantorovich's method and constrained NMPC. Zero-offset steady state tracking is achieved through a novel NMPC problem formulation, rate-based NMPC. A comparison of various NMPC strategies and developments is presented illustrating how a low complexity NMPC strategy can be achieved.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120832/1/huxuli_1.pd

Feedback Control for Systems with Uncertain Parameters Using Online-Adaptive Reduced Models

We consider control and stabilization for large-scale dynamical systems with uncertain, time-varying parameters. The time-critical task of controlling a dynamical system poses major challenges: using large-scale models is prohibitive, and accurately inferring parameters can be expensive, too. We address both problems by proposing an offine-online strategy for controlling systems with time- varying parameters. During the offine phase, we use a high-fidelity model to compute a library of optimal feedback controller gains over a sampled set of parameter values. Then, during the online phase, in which the uncertain parameter changes over time, we learn a reduced-order model from system data. The learned reduced-order model is employed within an optimization routine to update the feedback control throughout the online phase. Since the system data naturally reects the uncertain parameter, the data-driven updating of the controller gains is achieved without an explicit parameter estimation step. We consider two numerical test problems in the form of partial differential equations: a convection-diffusion system, and a model for ow through a porous medium. We demonstrate on those models that the proposed method successfully stabilizes the system model in the presence of process noise.DARPA EQUiPS program (award number UTA15-001067)United States. Department of Energy. Office of Advanced Scientific Computing Research (grant DE-FG02-08ER2585)United States. Department of Energy. Office of Advanced Scientific Computing Research (grant DE-SC000929