A polynomial matrix method for computing stable rational doubly coprime factorizations

The primary purpose of this paper is to present a frequency domain compensation scheme which is completely analogous to the time domain (state-space) employment of a Luenberger state estimator for approximating a linear state variable feedback (l.s.v.f.) design. To accomplish this objective we (i) employ a ‘ factorization ’ of the rational transfer matrix, T(s), of a given system as the product R(s)P(s)−1, where R(s) and R(s) are ‘ relatively right prime ’ polynomial matrices, (ii) present a frequency domain characterization of l.s.v.f. in terms of its effect on T(s) (actually on R(s) and P(s)), and (iii) extend the notion of the classical ‘ eliminant matrix ’ of two polynomials and its determinant, the ‘ resultant ’, to the matrix case. An example is employed to illustrate the various steps involved and some comparisons are then made to other related investigations.

Time-series analysis of pressure fluctuations in gas–solid fluidized beds – A review

The subject of study is the process of forming algorithms for controlling the angular and translational movements of a two-wheeled experimental sample (TWES). The aim is to develop approaches to the formation of control algorithms for the translational and angular movements of a non-stationary automatic control object. Tasks: to concretize the process of synthesis of a control algorithm by state according to the criterion of the minimum integral of the weighted error modulus for a linear mathematical description of an automatic control object in the state space. Form a block diagram of an automatic control system by the state. Improve the approach to the synthesis of output control algorithms for mathematical description in the frequency domain of short-period and long-period motions of TWES. Illustrate the peculiarity of the approach using a specific example of a TWES under control and disturbing influences. Develop a simulation scheme in the Simulink environment and investigate responses to external step influences. Develop an approach to the formation of control algorithms by the diagnosis of TWES as an object of automatic control. Describe the procedure and means of deep diagnostics of emergencies of TWES. Develop algorithms for restoring the operability of the automatic rational control system. Used methods are a method of state space, the method of relative functions, the method of transfer functions, the method of optimization by integral criterion, the method of synthesis by logarithmic asymptotic frequency characteristics, methods of diagnosing and restoring operability. The following Results: three approaches were formed to the formation of control algorithms of the angular and translational movements of the TWES using linear mathematical descriptions in the time and frequency domains. Conclusions. The scientific novelty lies in the formation of approaches to the combined control of angular and translational movements, considering the structural and parametric features of the mathematical descriptions of TWES.

On the Standard H2 Problem

Deep reinforcement learning based planning method in state space for lunar rovers

Embedding, i.e expanding a nonsquare matrix to a square one, plays a significant role in systems and control theory. For instance, embedding a polynomial matrix P(î) unimodularlyallowed us to solve the pole placement problem in chapter 3 and stable embedding(a less restrictive version) yielded a solution for the stabilization problem.In this chapter we will discuss existing and new algorithms1 to solve the embedding problem. The scope of the chapter is as follows. In section 5.1 we define the problem and give some motivating examples, in section 5.2 we give an overview of existing algorithms to solve the embedding problem, and we give a couple of examples to show that the method based on the Smith form does not give acceptable answers. After that we turn to the algorithm of Beelen [4],[5] based on matrix pencils. In section 5.3 we introduce matrix pencils, in section 5.4 we relate the embedding problem for an arbitrary polynomial matrix to one for a pencil by using a state space representation. In section 5.5 we give the solution for the embedding problem for a pencil, section 5.6 describes the way to calculate that solution, in section 5.7 we describe the algorithm that gives a unimodular or stable embedding starting from a polynomial matrix.

In this paper an in-flight tracking control system minimizing vibratory loads at the frequencies 1/rev and 2/rev using steady deflections of active trailing-edge flaps is examined. The control system is based on the relaxed HHC algorithm and uses the Moore-Penrose pseudoinverse of a symmetrized transfer matrix to calculate the control commands for vibration reduction. The focus of the current investigation is on symmetrization effects of the transfer matrices used for controller design on the performance of the control system. In a theoretical pre-flight analysis bounds for the stationary solution of the state-space representation of the closed loop control system are derived on the basis of the Kalman decomposition controller in the frequency domain is calculated. This analysis shows the vibration reduction by the controller using the symmetrized transfer matrices to be close to the optimally achievable reduction. Subsequent, flight tests on a full-scale experimental helicopter in open and closed loop configuration not only verify the functionality of the in-flight tracking control system, but also validate the insignificance of the degradation in control performance due to transfer matrix symmetrization predicted by the theoretical analysis.

The polynomial matrix using the block coefficient matrix representation auto-regressive moving average (referred to as the PM-ARMA) model is constructed in this paper for actively controlled multi-degree-of-freedom (MDOF) structures with time-delay through equivalently transforming the preliminary state space realization into the new state space realization. The PM-ARMA model is a more general formulation with respect to the polynomial using the coefficient representation auto-regressive moving average (ARMA) model due to its capability to cope with actively controlled structures with any given structural degrees of freedom and any chosen number of sensors and actuators. (The sensors and actuators are required to maintain the identical number.) under any dimensional stationary stochastic excitation.

A matrix Euclidean algorithm induced by state space realization

Three existing numerical procedures for solution of a linear matrix polynomial equation AX+BY=C have been tested, evaluated and compared in experimental manner. Thousands of examples have been computed thus far covering both generic (randomly created) data and ill-conditioned cases (with 'almost common factors'). The most successful method in the triple appears to be the one based on interpolation (PIM). It has been able to handle generic examples with the polynomial matrices A, B up to sizes 20/spl times/20 of degree 5 as well as ill-conditioned cases with 5/spl times/5 matrices of degree 5 suffering with almost common factors different from the precise ones (for which the equation becomes unsolvable) relatively only by 2/sup -30/. The other two methods considered based on elementary operations and state space realization were found to exhibit some drawbacks in their present form. >

During the past decades some very interesting results have been obtained in controller synthesis using Linear Parameter-Varying (LPV) systems. However, the LPV models are commonly required to be transformed into State Space (SS) form. We tackle the LPV SS identification problem directly in the frequency domain. To the best of our knowledge, this is a novel approach. When the input and scheduling are chosen to be periodic and synchronized, the state space equations are structured and sparse in the frequency domain. The parameters of these state space equations are estimated by minimizing a weighted non-linear least squares criterion. Starting values are generated via the Best Linear Time-Invariant (BLTI) approximation. The resulting model is also valid for non-periodic scheduling and input signals.

: This paper is concerned with the development of a complete set of invariants and canonical forms under feedback for linear systems characterized by proper rational transfer matrices. The invariants are determined in the frequency domain and consist of the Kronecker set of controllability indices together with a canonical form for the numerator of the transfer matrix under the action of a stabilizer subgroup of the unidoular group of polynomial matrices. Techniques used are algebro-geometric in nature. (Author)

Various analytical techniques are available for modeling multivariate time series data. One such approach is the State Space Model, which can be employed to model this type of data. In this study, the data to be analyzed are data on the Indonesia Rupiah (IDR) exchange rate (ExR) against the US Dollar (USD), oil and gas exports (OGE), money supply (MS) and non-oil and gas exports (non-OGE) from January 2008 to December 2019. The aim of this study is to identify the most suitable state space model for the given data. In this research, the state space method will be applied to multivariate time series data, with the state space represented in the Vector Autoregressive (VAR) model to explore the interrelationships among groups of observed variables. The VAR model is a statistical technique used to analyze the relationships between variables in the dataset, employing the Granger Causality Test. The state space model is utilized to model and forecast multiple interconnected time series, where the variables exhibit dynamic interactions and to examine additional unobserved variables in the time series data. Based on the analysis results and the minimum value of the Akaike Information Criterion (AIC), the optimal VAR model identified is the VAR (6) model. The results of forecasting values using the state space model show that the predicted values and the real values for the state space model are very closed to each other.

There exist two fundamental tools for modeling and simulating wave action of internal combustion engines. The first is a nonlinear time domain solution of the Euler equations using a space–time meshing. The second is a frequency domain solution of the linear wave equations. These two methods exist with a wide range of complexity and sophistication. Hybrid coupled methods also exist; they attempt to bridge the gap between the two techniques while maintaining the overall goal of engine simulation in mind. This work deals with the frequency characterization of a complex intake element, the charge air cooler. First, a transfer matrix for a simple tube is defined and measured. Two identical versions of the previous tube serve for identifying the transfer matrix of the charge air cooler directly on an operating four-cylinder turbocharged engine. Once the transfer matrix is measured, it is coupled to GT-Power as four transfer functions coded into Simulink. The final validation comprises two tubes in GT-Power with measured boundary conditions of pressure and mass flow with the Simulink model in between. Results are presented in the time and frequency domains with future objectives and perspectives as well.

In order to study dynamics response of a launch vehicle under ground wind loads, the dynamics model of a launch vehicle erected on the pad is developed based on transfer matrix method for multibody systems and the theory of structural wind engineering. The overall transfer equation, overall transfer matrix, and characteristics equation of the system are deduced based on the automatic deduction theorem of overall transfer equation of multibody system. The equation governing the motion of the launch vehicle is obtained by using the orthogonality of augmented eigenvector. The vibration characteristics, and frequency domain and time domain dynamics response under ground wind loads of the launch vehicle are simulated. The simulation results show that the eigenfrequencies obtained by the proposed method and ordinary dynamics method have good agreements. The paper provides an effective approach to compute the dynamics response of the launch vehicle under ground wind loads.