Development of Linear-Parameter-Varying Models for Aircraft
Skip to main content. Volume 27, Issue 2. No Access. Gary J. Tools Add to favorites Download citation Track citations. Previous article. Linear Fractional Transformation co-modeling of high-order aeroelastic systems for robust flutter analysis.
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Model reduction for linear parameter-varying systems through parameter projection. Consistent and computationally efficient estimation for stochastic LPV state-space models: realization based approach. Robust fault and icing diagnosis in unmanned aerial vehicles using LPV interval observers. Exponential stabilisation of nonlinear parameter-varying systems with applications to conversion flight control of a tilt rotor aircraft.
A unified approach to fixed-wing aircraft path following guidance and control. High-fidelity rotorcraft simulation model: analyzing and improving linear operating point models.
Robust LPV modeling and control of aircraft flying through wind disturbance.
State observer design for quadratic parameter varying QPV systems. Linear-parameter-varying-based adaptive sliding mode control with bounded L2 gain performance for a morphing aircraft. Analysis and design of quadratically bounded QPV control systems. Overview of control-centric integrated design for hypersonic vehicles. A robust analysis approach for a class of uncertain BPV systems. Observer-based tracking controller design for quasi-one-sided Lipschitz nonlinear systems.
A LPV modeling of turbocharged spark-ignition automotive engine oriented to fault detection and isolation purposes. Observer-based tracking controller design for a class of Lipschitz nonlinear systems. Smooth switching linear parameter-varying fault detection filter design for morphing aircraft with asynchronous switching.Thanks for helping us catch any problems with articles on DeepDyve. We'll do our best to fix them.
Check all that apply - Please note that only the first page is available if you have not selected a reading option after clicking "Read Article". Include any more information that will help us locate the issue and fix it faster for you. This procedure may complement existing nominal LPV identification algorithms, by adding the uncertainty and noise bounds which produces a set of models consistent with the experimental evidence.
Unlike standard invalidation results, the proposed method allows the computation of the necessary changes to the initial model in order to place it within the consistency set. Similar to previous LPV identification procedures, the initial parameter dependency is fixed in advance, but here a methodology to modify this dependency is presented. The application of the proposed method to the identification of nonlinear systems is also discussed.
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To improve the approximation capability of the LPV model, asymmetric Gaussian weighting functions are introduced and compared with commonly used symmetric Gaussian functions. By this mean, locations of operating points can be selected freely.
It has been demonstrated through simulations with a high purity distillation column that the identified models provide more satisfactory approximation. Moreover, an experiment is performed on real HVAC heating, ventilation, and air-conditioning to further validate the effectiveness of the proposed approach. In nonlinear system identification, numerous black box modeling structures have been developed in pieces of literature.
Among them, nonlinear AR MA X and neural-network models are often used by researchers, due to their mature theoretical results. However, the complexity in those structures and calculation cost limit their applicability especially in process control applications. Meanwhile, block-oriented nonlinear models such as Hammerstein models and Wiener models consisting of linear time invariant LTI dynamics and static memoryless nonlinearities have been studied widely.
Although they are comparatively simpler, only the model nonlinearity in static gains is integrated, which cannot ensure the accuracy and efficiency of the model, particularly for nonlinear plants operating over a large number of different operating points. Recently, linear parameter varying LPV model identification has attracted great attention from both academia and practitioners [ 1 ].
Many significant breakthroughs have taken place in the intervening years to mature the underlying theory. According to [ 2 ], the existing LPV identification approaches can be categorized in terms of their LPV model structures. Subspace approaches are studied by Verdult and Verhaegen [ 34 ] and Felici et al. On the other hand, the practicality of the LPV approaches has caught the attention of practitioners outside of academia, and interests in the LPV approach are evidenced by the applications of such methods to aerospace systems including high performance aircraft, missiles, and turbofan engines [ 11 ].
In studying input-output LPV methods, most available references are parameter interpolation based, which consider the parameters of the transfer function as nonlinear functions of the scheduling variable. Because complex nonlinear functions appear in the denominator of the transfer function, model stability cannot be guaranteed, which may result in numerical problems during model identification [ 12 ].
Besides, the input excitation signal for this representation results in too much upset, which can be costly or even unrealistic in practice [ 13 ]. To circumvent these difficulties, Zhu and Xu [ 12 ] proposed a multimodel LPV model based on blended linear models. The identification method is relatively simple and the stability of this kind of LPV models has been proved in Huang et al. Proper weighting functions are required to combine all the local linear models into a global LPV model in the multimodel LPV structure.
Several options are available in the literature, namely, linear weight function [ 14 ], polynomial function [ 12 ], cubic spline function [ 15 ], and Gaussian weight function [ 13 ]. However, due to large number of parameters to be estimated and unconstrained shapes for polynomial or cubic spline function, they will easily lead to an ill-conditioned and may not be suitable for identification of complex nonlinear processes [ 2 ].
Meanwhile, the linear weight function is not accurate enough to capture the full dynamic behaviors of a nonlinear process.
In the realm of multimodel structures [ 16 ] and fuzzy sets [ 17 ], Gaussian weighting functions have been widely adopted, which have relative small number of parameters and naturally better functions than linear functions.
However, a disadvantage of Gaussian weighting functions is that the operating points should have an equal distance with respect to a scheduling variable, while other functions do not have this restriction, which brings large inconveniences and limits their capabilities for usage in actual applications. Therefore, this paper aims at improving the performance in identifying multimodel LPV models by adopting the asymmetric Gaussian weighing function, such that multilocal models can be smoothly interpolated to approximate the global dynamical behaviors of the process.
This means that the locations of the operating points can be freely selected. The LPV model with two scheduling variables using asymmetric Gaussian weighing is also discussed.
Simulation study is employed to demonstrate the efficiency of the proposed LPV model identification scheme. Further, the experiment is conducted on an HVAC system in our lab. It should be noted that there are some references available in the literature [ 18 ] about the modeling of the HVAC system.
However, the identification with multimodel LPV structure is very rare.Benefits: Economical: low initial cost, plus cost savings by eliminating the pounding, poking, and hammering of hoppers, ensures material flow with cost savings. Minimal maintenance: limited maintenace required for life of the vibrator when used with a filtered and lubricated air supply. Versatility: variable control of force and frequency to meet a variety of material conditions.
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Air cushioned units are available by designating a Q at the end of the model number. This reduces noise by eliminating metal to metal impact. All air cushioned units are equipped with a starter spring. All Deca LPV series vibrators must be operated by filtered and lubricated air. Request Information Print Page. Product Table Item. Controlled Through Air Pressure Regulation. Products Industry Application.We've introduced Autoregressive models and Moving Average models in the two previous articles.
Now it is time to combine them to produce a more sophisticated model. These models will form the basis for trading signals and risk management techniques. If you've read Part 1 and Part 2 you will have seen that we tend to follow a pattern for our analysis of a time series model. I'll repeat it briefly here:. In order to follow this article it is advisable to take a look at the prior articles on time series analysis. They can all be found here.
In Part 1 of this article series we looked at the Akaike Information Criterion AIC as a means of helping us choose between separate "best" time series models.
Essentially it has similar behaviour to the AIC in that it penalises models for having too many parameters. This may lead to overfitting. The Ljung-Box test is a classical hypothesis test that is designed to test whether a set of autocorrelations of a fitted time series model differ significantly from zero.
The test does not test each individual lag for randomness, but rather tests the randomness over a group of lags. While the details of the test may seem slightly complex, we can in fact use R to calculate the test for us, simplifying the procedure somewhat. The former model considers its own past behaviour as inputs for the model and as such attempts to capture market participant effects, such as momentum and mean-reversion in stock trading. The latter model is used to characterise "shock" information to a series, such as a surprise earnings announcement or unexpected event such as the BP Deepwater Horizon oil spill.
Hence, an ARMA model attempts to capture both of these aspects when modelling financial time series. Note that an ARMA model does not take into account volatility clustering, a key empirical phenomena of many financial time series.
It is not a conditionally heteroscedastic model. The ARMA p,q model is a linear combination of two linear models and thus is itself still linear:. One of the key features of the ARMA model is that it is parsimonious and redundant in its parameters. As with the autoregressive and moving average models we will now simulate various ARMA series and then attempt to fit ARMA models to these realisations. We carry this out because we want to ensure that we understand the fitting procedure, including how to calculate confidence intervals for the models, as well as ensure that the procedure does actually recover reasonable estimates for the original ARMA parameters.
That is, an autoregressive model of order one combined with a moving average model of order one. Such a model is given by:. We need to specify the coefficients prior to simulation. We can see that there is no significant autocorrelation, which is to be expected from an ARMA 1,1 model. Finally, let's try and determine the coefficients and their standard errors using the arima function:.
Let's now try an ARMA 2,2 model. That is, an AR 2 model combined with a MA 2 model. This outlines the danger of attempting to fit models to data, even when we know the true parameter values! However, for trading purposes we just need to have a predictive power that exceeds chance and produces enough profit above transaction costs, in order to be profitable in the long run.
To show this method we are going to firstly simulate a particular ARMA p,q process. We will select the model with the lowest AIC and then run a Ljung-Box test on the residuals to determine if we have achieved a good fit.
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Minimal LPV state-space realization driven set-membership identification. Cerone, V. Abstract Set-membership identification algorithms have been recently proposed to derive linear parameter-varying LPV models in input-output form, under the assumption that both measurements of the output and the scheduling signals are affected by bounded noise.
In order to use the identified models for controller synthesis, linear time-invariant LTI realization theory is usually applied to derive a statespace model whose matrices depend statically on the scheduling signals, as required by most of the LPV control synthesis techniques. Unfortunately, application of the LTI realization theory leads to an approximate state-space description of the original LPV input-output model.
A suitable nonconvex optimization problem is formulated to select the model in the feasible set which minimizes a suitable measure of the state-space realization error. The solution of the identification problem is then derived by means of convex relaxation techniques. Authors Close. Assign yourself or invite other person as author. It allow to create list of users contirbution. Assignment does not change access privileges to resource content.Canal systems are complex nonlinear, distributed parameter systems with changing parameters according to the operating point.
In this paper, a linear parameter-varying LPV state-space canal control model is obtained by identification in a local way using a multimodel approach.
This LPV identification procedure is based on subspace methods for different operating points of an irrigation canal covering the full operation range. Different subspace algorithms have been used and compared.
The model that best represents the canal behavior in a precise manner has been chosen, and it has been validated by error functions and analysis correlation of residuals in a laboratory multireach pilot canal providing satisfactory results.
Water is one of the most used resources by industrial and agricultural sectors, and obviously by population. One fundamental use of water is the irrigation activity, and one the main challenges in this area is to prevent water losses and to permit an efficient use of this scarce and vital resource. These aspects have led to the usage of automatic control systems and the implementation of different advanced control algorithms for the regulation of open-flow irrigation canals.
Hence, those control techniques will allow fulfilling the desired performance and the ecological flow in irrigation as well as saving water at the same time. To design an effective controller, a good control model is needed.
Therefore, advanced process modeling techniques are required to make an accurate control model. Modeling and control of nonlinear complex systems is a challenging task. Unfortunately, the higher the complexity, the lower our ability to deal with it and to understand it. Open-flow canals are complex systems, that is, they are large distributed parameter systems that have the following main characteristics: nonlinear behavior and dependence of the parameters with the operating point and coupling among pools [ 1 ].
This representation is the most used model to describe the physical dynamics of a real irrigation canal. However, this complex model is based on a nonlinear hyperbolic partial differential equations system that has analytical solution only in very special cases, requiring the use of numerical methods to solve it properly [ 3 ]. This complex representation of the system is suitable for simulation models, but it is not suitable to design controllers that fulfill the control design needs.
Development of Linear-Parameter-Varying Models for Aircraft
Distributed parameter systems with a very large number of states, that is, systems with coupling, have been approximated by decoupled low-order linear time invariant LTI models in order to use classical linear control design tools, as a usual practice in control engineering. LTI control models widely used are Hayami model [ 10 ], Muskingum model [ 3 ], IDZ model [ 411 ], or black-box models identified using parameter estimation by classical identification methods [ 11213 ].
However, these systems are not completely amenable using conventional linear modeling approaches due to the lack of precise, formal knowledge about the system; strongly nonlinear behavior; high degree of uncertainty; time varying characteristics; dynamic parameters changing over the operating point and coupling between pools. Then, simplified control model structures are needed preserving their information.
Taking into account these previous properties, a linear parameter varying LPV model is required, which consists in a model that regards both the parameter and delay variations with respect to the operating points. In this way, the system information is preserved while it would be lost with a linear control model. These LPV control models permit the design and computation of LPV controllers that rigorously guarantee the system stability and performance [ 14 ] for smooth variations of system parameters as well as abrupt ones [ 15 ]; this is the case of irrigation canals.
The preferred representation scheme for complex plants multivariable systems involving large system orders is a state-space model.