Local Linear Time-invariant Models Research Articles

Experimental linear parameter-varying model identification of an elastic kinetic roof structure

Elastic kinetic structures are a recent approach to design transformable lightweight structures. Their transformation is based on elastic bending, exploiting the compliant material behavior of the structural members. This enables transformable structures with a stable transformation process. However, due to their lightweight and flexible design, elastic kinetic structures are highly sensitive to static and dynamic disturbances. Moreover, such transformable structures exhibit a transformation state dependent dynamic behavior, due to geometric nonlinearities. Nevertheless, most of current research focuses on the principles of elastic kinetic transformation than on effective disturbance mitigation. The latter is usually designed based on low-order control-oriented models. This paper describes a system identification methodology, suitable to identify low-order models for the transformation state dependent dynamics of elastic kinetic structures. The system identification is carried out using a local approach in the linear parameter-varying (LPV) framework. For the identification of local linear time-invariant (LTI) models, the system realization using the information matrix (SRIM) method is applied. The collection of local LTI models is internally balanced using a balancing transformation, in order to represent the locally estimated models with respect to a common state–space basis. Via linear interpolation, an LPV system in grid-based representation is derived. This methodology is experimentally validated with data from an active hybrid roof structure prototype.

Interpolation-Based Modeling Methodology for Efficient Aeroelastic Control of a Folding Wing

The aeroelastic model of a folding wing varies with different configurations, so it actually represents a parameter-varying system. Firstly, a new approach based on interpolation of local models is proposed to generate the linear parameter-varying model of a folding wing. This model is capable of predicting the aeroelastic responses during the slow morphing process and is suitable for subsequent control synthesis. The underlying inconsistencies among local linear time-invariant (LTI) models are solved through the modal matching of structural modes and the special treatment of the rational functions in aerodynamic models. Once the local LTI models are represented in a coherent state-space form, the aeroservoelastic (ASE) model at any operating point can be immediately generated by the matrix interpolation technique. Next, based on the present ASE model, the design of a parameterized controller for suppressing the gust-induced vibration is studied. The receptance method is applied to derive fixed point controllers, and the effective independence method is adopted and modified for optimal sensor placement in variable configurations, which can avoid solving ill-conditioned feedback gains. Numerical simulation demonstrates the effectiveness of the proposed interpolation-based modeling approach, and the parameterized controller exhibits a good gust mitigation effect within a wide parameter-varying range. This paper provides an effective and practical solution for modeling and control of the parameterized aeroelastic system.

Active Vibration Control of a Convertible Structure based on a Linear Parameter-Varying Model

This paper investigates modelling and active vibration control (AVC) of ultra-lightweight convertible structures based on the elastic kinetic motion mechanism with a focus on civil and structural engineering applications. Model building is carried out in the linear parameter-varying (LPV) framework for the example of a convertible Fin Ray structure. In a first step local linear time-invariant (LTI) models are derived from a finite element model of the structure for different transformation states. On the basis of this collection of local LTI models, a grid-based LPV model is established. An AVC of multiple modes is implemented by means of a modal velocity feedback control. Single-input single-output (SISO) control design is carried out with the root locus method for the first and second mode using the same control input under the assumption of well separated eigenfrequencies. The implemented AVC is validated in simulation.

Linear Parameter-Varying Models for Convertible Structures in Civil and Structural Engineering

This paper investigates the feasibility of the linear parameter-varying (LPV) framework for modelling the dynamic behaviour of ultra-lightweight convertible structures based on the elastic kinetic motion mechanism with a focus on civil and structural engineering applications. Model building is carried out for the example of a Fin Ray structure. In a first step local linear time-invariant (LTI) models are derived from a finite element model of the structure for different transformation states. On the basis of this collection of local LTI models, a grid-based LPV model is established. The derived LPV model is validated in simulation by comparison with data from a finite element model.

LPV System Local Model Interpolation Based on Combined Model Reduction

The local approach to linear parameter varying (LPV) system identification consists in interpolating a collection of linear time invariant (LTI) models, which have been estimated from data acquired at different working points of a nonlinear system. Interpolation is essential in this approach. When the local LTI models are in state-space form, as each local model can be estimated with an arbitrary state basis, it is widely acknowledged that the local models should be made coherent before their interpolation. In order to avoid the delicate task of making local state-space models coherent, a new interpolation method of local state-space models is proposed in this paper, which does not require coherent local models. This method is based on the reduction of the large state-space model built by combining the local models. Numerical examples are presented to illustrate the effectiveness of this method.

From structurally independent local LTI models to LPV model

The local approach to linear parameter varying (LPV) system identification consists in interpolating individually estimated local linear time invariant (LTI) models corresponding to fixed values of the scheduling variable. It is shown in this paper that, without any global structural assumption of the considered LPV system, individually estimated local state-space LTI models do not contain sufficient information for determining similarity transformations making them coherent. It is possible to estimate these similarity transformations from input–output data under appropriate excitation conditions.

Experimental Study on an Electric Variable Valve Timing Actuator: Linear Parameter Varying Modeling and Control

This paper presents experimental investigation results of an electric variable valve timing (EVVT) actuator using linear parameter varying (LPV) system identification and control. For the LPV system identification, a number of local system identification tests were carried out to obtain a family of linear time-invariant (LTI) models at fixed engine speed and battery voltage. Using engine speed and battery voltage as time-varying scheduling parameters, the family of local LTI models is translated into a single LPV model. Then, a robust gain-scheduling (RGS) dynamic output-feedback (DOF) controller with guaranteed H∞ performance was synthesized and validated experimentally. In contrast to the vast majority of gain-scheduling literature, scheduling parameters are assumed to be polluted by measurement noises and the engine speed and battery voltage are modeled as noisy scheduling parameters. Experimental and simulation results show the effectiveness of the developed approach.

A local identification method for linear parameter-varying systems based on interpolation of state-space matrices and least-squares approximation

This paper proposes a novel state-space matrix interpolation technique to generate linear parameter-varying (LPV) models starting from a set of local linear time-invariant (LTI) models estimated at fixed operating conditions. Since the state-space representation of LTI models is unique up to a similarity transformation, the state-space matrices need to be represented in a common state-space form. This is needed to avoid potentially large variations as a function of the scheduling parameters of the state-space matrices to be interpolated due to underlying similarity transformations, which might degrade the accuracy of the interpolation significantly. Underlying linear state coordinate transformations for a set of local LTI models are extracted by the computation of similarity transformation matrices by means of linear least-squares approximations. These matrices are then used to transform the local LTI state-space matrices into a form suitable to achieve accurate interpolation results. The proposed LPV modeling technique is validated by pertinent numerical results.

LPV System Common State Basis Estimation from Independent Local LTI Models

For the identification of a linear parameter varying (LPV) system steered by a scheduling variable evolving within a finite set, the local approach consists in separately estimating local linear time invariant (LTI) models corresponding to fixed values of the scheduling variable. It is shown in this paper that, without any global structural assumption of the considered LPV system, the local state-space LTI models do not contain the necessary information about the similarity transformations making them coherent. Nevertheless, it is possible to estimate these similarity transformations from input-output data under appropriate input excitation conditions. These estimations result in a common state basis of the transformed local LTI models, so that they form a coherent global LPV model, suitable for numerical simulations in the case of fast scheduling variable evolutions.

Fuzzy modeling and control of rotary inverted pendulum system using LQR technique

Rotary inverted pendulum (RIP) system is a nonlinear, non-minimum phase, unstable and underactuated system. Controlling such system can be a challenge and is considered a benchmark in control theory problem. Prior to designing a controller, equations that represent the behaviour of the RIP system must be developed as accurately as possible without compromising the complexity of the equations. Through Takagi-Sugeno (T-S) fuzzy modeling technique, the nonlinear system model is then transformed into several local linear time-invariant models which are then blended together to reproduce, or approximate, the nonlinear system model within local region. A parallel distributed compensation (PDC) based fuzzy controller using linear quadratic regulator (LQR) technique is designed to control the RIP system. The results show that the designed controller able to balance the RIP system.

Interpolated Modeling of LPV Systems Based on Observability and Controllability

This paper presents a State-space Model Interpolation of Local Estimates (SMILE) technique to compute linear parameter-varying (LPV) models for parameter-dependent systems through the interpolation of a set of linear time-invariant (LTI) state-space models obtained for fixed operating conditions. Since the state-space representation of LTI models is not unique, a suitable coherent representation needs to be computed for the local LTI models such that they can be interpolated. In this work, this coherent representation is computed based on observability and controllability properties. It is shown that compared with the state of the art in the literature, this new method has three strong appeals: it is general, fully automatic and results in numerically well-conditioned LPV models. An example demonstrates the potential of the new SMILE technique.

Identification of Interpolating Affine LPV Models for Mechatronic Systems with one Varying Parameter

This paper presents a technique to identify an affine parameter-dependent model based on a set of Linear- Time-Invariant (LTI) models that are identified in local operating points of the varying system. The systems under investigation are mechatronic systems in which the dynamic behaviour is depending on a single varying parameter. By fitting specific pole and zero loci on the poles and zeros of the local LTI models, an affine state-space model can be constructed. Since the resulting affine model is well conditioned and has a low complexity, it is suitable to be used for Linear- Parameter-Varying (LPV) control. The applicability of the presented technique is shown on an industrial pick-and-place machine with position-dependent dynamics.