Analysis of the frequency characteristics of the control system for the processes of fuel supply to the cylinders of the power unit

The idea of monitoring the identity of the cylinder capacities of an internal combustion engine under conditions of incomplete information is proposed and a computer system is built on its basis. The signal of the instantaneous rotation speed of the crankshaft of the power unit was used as input information. In the development of the hardware architecture, injectors with piezoelectric actuators, the principle of direct digital control, and the principle of control with feedback on the state of fluctuations of the crankshaft rotation speed were used. The Laplace transform was used as a mathematical apparatus for analyzing the structural diagram of a computer system for programmed control of the processes of supplying fuel and air to the cylinders of the power unit. Mathematical models of the components of the hardware for controlling the processes of supplying the fuel-air mixture were constructed, and as a result of the analysis of the structural diagram of the computer system, the transfer function was obtained. Using the capabilities of the Matlab software environment, the transient and impulse transient characteristics of the system are obtained, the Nyquist hodograph is constructed, and the logarithmic amplitude-frequency characteristics of the hardware are established. It was found that the frequency characteristics of the mathematical model of a computer system have the necessary dynamic characteristics. Using the method of expansion into simple fractions, an expression is obtained for a discrete transfer function, the coefficients of the power polynomials of which are established using the method of determinants and computational capabilities of the Mathcad software environment. On the basis of a discrete transfer function, a scheme for computer modeling of the process of processing the signal of the instantaneous speed of rotation of the crankshaft by hardware is constructed. The output signal was obtained by computer simulation, as a result of the analysis of which the speed of the hardware for processing the input information was established.

A new algorithm for a CFE-approximated solution of a discrete-time noninteger-order state equation

In the paper, a new method for solution of linear discrete-time fractional-order state equation is presented. The proposed method is simpler than other methods using directly discrete-time version of the Grünwald-Letnikov operator. The method is dedicated to use with any approximator to the operator expressed by a discrete transfer function, e.g. CFE-based Al-Alaoui approximation. A simulation example confirms the usefulness of the method.

Time Integration Method Based on Discrete Transfer Function

Complex structural dynamic problems are normally analyzed by finite element and numerical integration techniques. An explicit time integration algorithm with second-order accuracy and unconditional stability is presented for dynamic analysis. Utilizing weighted factors, the current displacement and velocity relations are defined in terms of the accelerations of two previous time steps. The concept of discrete transfer function and the pole mapping rule from the control theory are exploited to develop the new algorithm. Several linear and nonlinear dynamic analyses are performed to verify the efficiency of the method compared with the well-known Newmark method.

Realization and Comparison of System Identification Based on Different Least Squares Methods

System identification, which includes parameter identification and non-parameter identification, is to estimate its mathematical model based on the input and output observation in system. This paper discusses the system identification theory and establishes a transfer function of 1/4 vehicle’s second-order vibration system model. Through the discrete transfer function, the system’s difference equation can be obtained to identify the system in two ways, RLS (recursive least squares) and RELS (extended recursive least squares). Finally, the paper makes a comparative analysis about RLS and RELS in connection with the vehicle model. The results show that RELS method is more accurate and has stronger convergence than RLS method, which provides the basis for the researching of control system’s algorithm, simulation and making control strategy.

Compact Method to Calibrate Frequency Response of Ultrasonic Transducer

Frequency response character of ultrasonic transducer often influences on the test signal partly, and then test errors arise. To the problem, a compact method is proposed to calibrate the frequency response in this paper. The experiment data was obtained in water- immerging test of the transducers, and a discrete transfer function is established based on system identification algorithms and then used for transducer calibration. The method is validated effective by experiment. Not only can the characteristic of transducers be indicated, but also a referenced method is presented for calibrating frequency response of LTI system.

AN ALTERNATIVE APPROACH FOR OBTAINING 2D DISCRETE FILTERS BY CASCADING SECTIONS EACH HAVING UNITY DEGREE IN EACH VARIABLE

The properties of a 2D discrete transfer function with degree of each variable being unity are discussed. The coefficients of the denominator polynomial contain a parameter k (having real values) whose bounds are determined by stability considerations. These bounds are obtained by testing the overall polynomial at only four points z1=±1 and z2=±1. Suitable numerator polynomial can be associated to get the overall transfer function. Such structures can be cascaded so that the overall magnitude response can be changed by altering the response of one or more sections.