The results of experimental and theoretical investigation of dynamic and static characteristics of a thermal object (electric oven) as a controlled plant are presented in the paper. The up-to-date microprocessor instruments were applied during the investigation. The experimental study of the plant was made by obtaining the step response curves for the controlling action channel and for the disturbance channel. Fifteen step response curves were recorded during the study. These curves were applied for development of the mathematical model of the plant in the form of static characteristics equations, transfer functions and differential equations. The structure of the model was chosen. The numerical values of the model parameters were calculated. The adequacy of the model was verified. The relative errors of the calculated values of the static characteristics points do not exceed 5 %. The maximum reduced error of the simulated step response curve in comparison to the experimental curve is 7% for the proposed combined method of defining the time constants. The developed model was implemented in a programmable logic controller in order to provide the possibility of studying the automatic control loop with various control laws.

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Various vehicle and tire dynamics models with different levels of complexity have been developed and used for predicting and studying vehicle traction and handling. This paper offers an overview of research work that was done on the tire relaxation length and time constant in the longitudinal and lateral directions with regard to tire/vehicle traction and handling characteristics. Several analytical and empirical models of the tire relaxation length and time constant from technical literature are compared by applying these models to a tire and, thus, analyzing and comparing computational results that come out from the models. Based on the overview and analysis of the longitudinal/lateral relaxation length and time constant data, the paper also provides an analysis of the impact of the tire normal reaction, tire inflation pressure, tire slippage and wheel actual velocity on the relaxation constants. The paper concludes with recommendations on the analytical methods and experimental data of the tire relaxation length and time constant computing that are more suitable for real-time modeling of agile traction and handling characteristics and, thus, can be profound for agile control synthesis. Therefore, the core contribution of the paper is to provide a fundamental analysis of the relaxation length effect for its further incorporation in agile tire slippage control.

The results of the pulse-width modulation algorithms analysis are presented in the paper. The following two algorithms are analyzed: pulse-width modulator (PWM) based on the sawtooth waveform generator and PWM based on an integrator and a switch element. Mathematical formulae for designing the tuning parameters of PWM algorithms are presented. An improved PWM algorithm is suggested for a programmable logic controller (PLC) operating with integer variables without a filter of the input signal. The improved algorithm provides elimination of the influence of the input signal's noise on the PLC output signal. PLC output relay contact bouncing is eliminated by means of the improved algorithm. The reliability of PLC is improved and the operation time of PLC output relay contact is prolonged thanks to the improved PWM algorithm. The example of PWM application in an automatic controller for controlling a thermal plant is presented. The advantages of the improved PWM algorithm application are demonstrated. The technique for PWM pulses period defining with taking into account the dynamical properties of the controlled plant is presented.

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