ALGORITHM FOR SELF-TUNING THE PID CONTROLLER

An algorithm for self-tuning the PID controller to the second order systems is proposed in this paper. The proposed self-tuning procedure was developed according to the maximum stability degree criterion, the criterion that permits to achieve the high stability degree, good performance and robustness of the system. According to the proposed algorithm, the controller can be tuned according to the parameters that characterize the process and they can be determinate from the experimental response of the open loop system. To demonstrate the efficiency of proposed procedure of self-tuning the PID controller, the computer simulation was performed and the obtained results were compared with Haeri’s method, maximum stability degree method with iterations and parametrical optimization method. According to the developed algorithm, it was performed the control of the thermal regime in the oven.

Parametric Synthesis of a Robust Controller Based on the Method of Dominant Poles

In the paper a linear control system described by its characteristic polynomial with interval coefficients including parameters of controller linearly is considered. Problem of the research is finding parameters of a controller guaranteeing dynamic characteristics of a system despite interval parametric uncertainty of its object. It is proposed to base a controller synthesis on root quality indices: minimal stability degree and maximal oscillability degree. Desired values of these indices will be provided with the help of dominant poles method. Applying this method consists in placing a pair of complex-conjugate dominant poles; all other poles — unrestricted poles — will be placed by defining a right border of their allocation area on a complex plane. To apply dominant poles method, a feature of stability degree and oscillability degree to be determined by images of certain vertices of a parametric polytope was used. To synthesize a controller, it is proposed to divide its parameters in two groups: dependent ones and unrestricted ones. The first group of controller parameters is to provide desired allocation of dominant poles in one of vertices of parametric polytope (a dominant vertex). Unrestricted parameters of a controller are to provide desired distance between dominant poles and allocation area of unrestricted poles. To find coordinates of a dominant vertex and verifying vertices providing unrestricted poles allocation, an interval extension of basic phase equation of a root locus theory was developed. This resulted in interval phase inequalities, whose solution allows finding coordinates of desired vertices of characteristic polynomials coeffi cients polytope. Knowing a dominant vertex polynomial and dominant poles allows expressing dependent parameters of a controller from unrestricted ones. Obtained expressions allow placing unrestricted poles in a desired area of a complex plane. To do this, a D-partition by unrestricted parameters of a controller is performed in all verifying vertices of parametric polytope of a system. After choosing values of unrestricted parameters from intersection of all stability domains obtain during D-partition, dependent parameters of a controller can be calculated. An example of synthesizing a PID-controller guaranteeing desired values of dynamics characteristics for an interval control system of the fourth order is provided.

A Hierarchical Self-Adaptive Method for Post-Disturbance Transient Stability Assessment of Power Systems Using an Integrated CNN-Based Ensemble Classifier

Data-driven approaches using synchronous phasor measurements are playing an important role in transient stability assessment (TSA). For post-disturbance TSA, there is not a definite conclusion about how long the response time should be. Furthermore, previous studies seldom considered the confidence level of prediction results and specific stability degree. Since transient stability can develop very fast and cause tremendous economic losses, there is an urgent need for faster response speed, credible accurate prediction results, and specific stability degree. This paper proposed a hierarchical self-adaptive method using an integrated convolutional neural network (CNN)-based ensemble classifier to solve these problems. Firstly, a set of classifiers are sequentially organized at different response times to construct different layers of the proposed method. Secondly, the confidence integrated decision-making rules are defined. Those predicted as credible stable/unstable cases are sent into the stable/unstable regression model which is built at the corresponding decision time. The simulation results show that the proposed method can not only balance the accuracy and rapidity of the transient stability prediction, but also predict the stability degree with very low prediction errors, allowing more time and an instructive guide for emergency controls.

Analyzing Robust Stability of an Interval Control System on the Basis of Vertex Polynomials

In the paper, a characteristic polynomial of an interval control system, whose coefficients are unknown or may vary within certain ranges of values, is considered. Parametric variations cause migration of interval characteristic polynomial roots within their allocation areas, whose borders determine robust stability degree of the interval control system. To estimate a robust stability degree, a projection of a polytope of interval characteristic polynomial coefficients on a complex plane must be examined. However, in order to find a robust stability degree it is enough to examine some vertices of a coefficient polytope and not the whole polytope. To find these vertices, which fully determine a robust stability degree, it is proposed to use a basic phase equation of a root locus method. Considering the requirements to placing allocation areas of system poles an interval extension of expressions for angles included to the phase equation. The set of statements, allowing to find a sum of pole angles intervals in the case of degree of oscillating robust stability, were formulated and proved. From these statements, a set of double interval angular inequalities was derived. The inequalities determine ranges of angles of all root locus edge branches departure from every pole. Considered research resulted in a procedure of finding coordinates of verifying vertices of a coefficients polytope and vertex polynomials according to these vertices. Such polynomials were found for oscillating robust stability degree analysis of interval control systems of the second, the third and the forth order. Also, similar statements were derived for aperiodical robust stability degree analysis. Numerical examples of vertex analysis of oscillating and aperiodical robust stability degree were provided for interval control systems of the second, the third and the fourth order. Obtained results were proved by examining root allocation areas of interval characteristic polynomials examined in application examples of proposed methods.