Based on the new interval polynomial stability criterion and Lyapunov theorem, a robust optimal proportional -integral -derivative (PID) controller is proposed here to design for different plants that contain the perturbations of multiple parameters. A new stability criterion of the interval polynomial is presented to determine whether the interval polynomial belongs to Hurwitz polynomial. The robust optimal PID controller is acquired through minimising an augmented integral squared error (AISE) performance index. The robust optimal control problem is transformed into a non-linear constraint optimisation (NLCO) problem by applying new polynomial stability criterion and Lyapunov approach. The robust optimal PID parameters are obtained from solving the NLCO problem. The robustness and performances of the proposed method and other different tuning methods are compared. The ability of the proposed PID tuning method and other tuning methods to reject disturbances is discussed as well. The simulation results are presented to demonstrate the effectiveness of the proposed method and show better robustness of the robust optimal PID controller.
This paper addresses on the robust stability problem of interval polynomials and matrices of the continuous-time linear system (C-TLS) and discrete-time linear system (D-TLS) that contain the real uncertain parameters. The robust stability of the interval polynomials and matrices can be determined by three different robust stability criterions that check the global minimum of each order Hurwitz determinant or check the global minimum of each element in first column of Routh array. The linear matrix inequality (LMI) methods and parameters dependent Lyapunov functions (PDLF) methods are often used to effectively determine the robust stability of the interval matrices and polynomials, and in this paper, these robust criterions are also effective to determine the stability of the interval matrices and polynomials. The robust stability of the interval matrices can be transformed into the stability of an interval polynomial too. The third robust criterion can reduce the number of the optimization objectives, and as well as the computational complexity when determining the robust stability of the interval polynomials and matrices. Through applying the bilinear transformation, the three robust criterions can be extended into the interval polynomials and matrices of discrete-time linear system. Different examples of interval polynomials and matrices are studied to show the effectiveness and accurateness of the robust stability checking methods.
There are many reasons for the poor accuracy of steam measurement data. The most important reasons can be concluded as follows:1. The working conditions of the instrument deviating from the designed conditions Data Processing Approaches for the Measurements of Steam Pipe Networks in Iron and Steel Enterprises 245At present, the mass flow rates are mostly deduced by the volume flow rates and the density. However, the changes of temperature and pressure in the transmission process would lead to the density of steam deviate from the original designed value [3]. The measurement errors would be very large [1]. Any more, some superheated steam would change into a vapor-liquid two-phase medium, which making precision worse. The Complexity of Steam CharacteristicsWith the ambient temperature changing, the total amount of the condensate water in the transmission process will be different. That makes difference between the amount of the production and the consumption of steam. In addition, the steam pipe leakage will add to the difference. Therefore, the accumulated readings are always doubtful.3. The Occurrence of wearing or damage to the Key Components As the orifice differential pressure flow rate meter being in use for long time, the size of aperture would differ from the original size because of the adhered foreign bodies, or erosion by the durative high temperature steam flow. As the parameters can not be adjusted on time, and it is hard to calibrate the instrument, the measurement errors will accumulate.
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