Reasoning Method between Polynomial Error Assertions

Error coefficients are ubiquitous in systems. In particular, errors in reasoning verification must be considered regarding safety-critical systems. We present a reasoning method that can be applied to systems described by the polynomial error assertion (PEA). The implication relationship between PEAs can be converted to an inclusion relationship between zero sets of PEAs; the PEAs are then transformed into first-order polynomial logic. Combined with the quantifier elimination method, based on cylindrical algebraic decomposition, the judgment of the inclusion relationship between zero sets of PEAs is transformed into judgment error parameters and specific error coefficient constraints, which can be obtained by the quantifier elimination method. The proposed reasoning method is validated by proving the related theorems. An example of intercepting target objects is provided, and the correctness of our method is tested through large-scale random cases. Compared with reasoning methods without error semantics, our reasoning method has the advantage of being able to deal with error parameters.

Phenomen by Fuller in the Problems of Analytical Design of Optimal Regulators

The problem of synthesis of an optimal controlled system with a quadratic quality criterion having an infinite number of switching points at a finite time inter val is discussed. In the theor y of optimal control, this phenomenon is called the "Fuller phenomenon". For more than 60 years, the Fuller problem has been very attractive, relevant, and still unsolved, especially for non-linear multidimensional dynamical systems of high order, and even more so, with obtaining a solution in an explicit analytical form for practical implementation in a control system.The purpose of this work is to demonstrate the theoretical aspects and practical features of the method of synthesis of optimal control systems by the fast acting criterion by the example of solving problems related to the Fuller phenomenon.When solving these problems, we use in the classical variations calculus and the Pontryagin maximum principle of the method of introducing a new additional phase variable into consideration, which is defined to the integral quality criterion and expands the original phase vector of the object. As a result, if the best optimal control in terms of fast acting for the control object is known then this technique makes it ver y easy to get a worse optimal control in terms of accuracy by including the Fuller accuracy criterion in the dynamics of the control object. It should be note that an important acquisition here is to increase the accuracy to the optimal value and reduce the established control error to zero, with all error coefficients (in position, speed, acceleration, jerk, etc.) equal to zeroin the presence of external and internal interference.Statements and solutions of the classical and modified Fuller problems are presented. As illustrative examples, we consider the traditional problems of the synthesis of optimal control in terms of speed, solved in well-known methods.

A DIAGONALLY IMPLICIT RUNGE-KUTTA-NYSTROM (RKN) METHOD FOR SOLVING SECOND ORDER ODES ON PARALLEL COMPUTERS

In this paper, diagonally implicit Runge-Kutta-Nystrom (RKN) method of high-order for the numerical solution of second order ordinary differential equations (ODE) possessing oscillatory solutions to be used on parallel computers is constructed. The method has the properties of minimized local truncation error coefficients as well as possessing non-empty interval of periodicity, thus suitable for oscillatory problems. The method was tested with standard test problems from the literature and numerical results compared with the analytical solution to show the advantage of the algorithm

An Integrated Geometric and Hysteretic Error Model of a Three Axis Machine Tool and Its Identification With a 3D Telescoping Ball-Bar

The ball-bar instrument is used to estimate a maximum number of hysteretic error sources. Machine error parameters include inter- and intra-axis errors as well as hysteresis effects. An error model containing cubic polynomial functions and modified qualitative variables, for hysteresis modeling, is proposed to identify such errors of the three nominally orthogonal linear axes machine. Such model has a total of 90 coefficients, not all of which being necessary. A numerical analysis is conducted to select a minimal but complete non-confounded set of error coefficients. Four different ball-bar test strategies to estimate the model coefficients are simulated and compared. The first one consists of circular trajectories on the primary planes XY, YZ, and XZ and the others use the XY plane, as an equator, and either four, five, or nine meridians. It is concluded that the five-meridian strategy can estimate the additional eight error coefficients: ECZ1, ECZ2, ECZ3, ECZb, EZY3, EZX3, ECX3, and ECXb. The Jacobian condition number is improved by increasing the number of meridians to 5. Further increasing the number of meridians from five to nine improves neither the number of estimable coefficients nor the conditioning, and so as it increases, the test time it was dismissed.

Research on Source Inversion for Nuclear Accidents Based on Variational Data Assimilation With the Dispersion Model Error

In a nuclear accident, radioactive release source term is the critical factor of nuclear emergency response and accident assessment. The modelling of source inversion based on variational data assimilation (VAR) is capable of balancing the environmental radioactive monitoring data to obtain the global optimal source term. But it could be influenced by the discrepancy between predictions of the atmospheric dispersion model and observations, which is defined as the dispersion model error in this study. In order to reduce this influence, the VAR with the dispersion model error (DME-VAR) is proposed. In the DME-VAR, the dispersion model error is quantified by the error coefficients at every monitoring station. These error coefficients and the release source term are estimated at the same time. For limiting the runtime, the DME-VAR program supports parallel processing. Two sets of wind tunnel experiment data for a typical Chinese nuclear power plant site are used to validate and evaluated the performance of the DME-VAR. The results demonstrate that the DME-VAR effectively estimates the error coefficients, and outperforms the VAR in both release rate estimation and radioactive contamination predicting. Moreover, the runtimes of these verification experiments are all reasonable, even for the application in the nuclear emergency response.

Offline Calibration for MEMS Gyroscope G-sensitivity Error Coefficients Based on the Newton Iteration and Least Square Methods

With the improvement of the bias instability of Micro-Electromechanical Systems (MEMS) gyroscopes, the g-sensitivity error is gradually becoming one of the more important factors that affects the dynamic accuracy of a MEMS gyroscope. Hence there is a need for correcting the g-sensitivity error. However, the traditional calibration of g-sensitivity error uses a centrifuge. The calibration conditions are harsh, the process is complex and the cost is relatively high. In this paper, a fast and simple method of g-sensitivity error calibration for MEMS gyroscopes is proposed. With respect to the bias and random noise of a MEMS gyroscope, the g-sensitivity error magnitude is relatively small and it is simultaneously coupled with the Earth's rotation rate. Therefore, in order to correct the g-sensitivity error, this work models the calibration for g-sensitivity error coefficients, designs an (8+N)-position calibration scheme, and then proposes a fitting method for g-sensitivity error coefficients based on the Newton iteration and least squares methods. Multi-group calibration experiments designed on a MEMS Inertial Measurement Unit (MEMS IMU) product demonstrate that the proposed method can calibrate g-sensitivity error coefficients and correct the g-sensitivity error effectively and simply.

Calibration for gimbaled platform inertial navigation system on centrifuge

In order to calibrate the error coefficients of the gimbaled platform inertial navigation system on precision centrifuge precisely and effectively, a six-position calibration scheme is provided. Firstly, the error models of the platform inertial navigation system are established and the applied acceleration equation is given. Then, the redundancy of the error coefficients is analyzed and a method of studying the observability based on the correlation coefficients is proposed. Finally, the optimal calibration scheme is obtained using the genetic algorithm. Simulation results show that the error coefficients can be effectively calibrated through the proposed scheme.