Impact of the Sampling Period on the Design of Digital PID Controllers

The impact of the sampling period on the parameterization of a digital PID controller in the frequency domain is attempted using three different digital approximations of the integral action. The controller is implemented in the industrial process of regulation of the cement sulphates in the cement mill outlet. The maximum sensitivity, Ms, has been utilized as a main robustness criterion. For the same Ms, proportional and differential gain, a rise of the sampling period leads to a decrease of the integral gain ki for all the three approximations. For the same sampling period, the function between proportional and integral gain differs for the three approximations studied. If the design satisfies two criteria simultaneously, maximum sensitivity and phase margin in the current study, then the permissible PID gains zone becomes narrower.

Sampling Rate and Performance of DC/AC Inverters with Digital PID Control—A Case Study

The huge influence of the sampling rate on the performance of the digital PID control of a voltage source inverter (VSI) is revealed. It is shown that an appropriately chosen continuous-time model of a digital controller with the PWM power converter behaves like the actual discrete-time system, which allows for a simple controller analysis and design. The variable structure nature of the inverter with both the RC rectifier and an abruptly changing resistive load with two modes of operation within the sampling period is directly taken into account. Two simulation models, a discrete-time PWM and a continuous-time, of an inverter are presented, which are used to tune the PID controller and to evaluate the control performance. The behavior of the system in both modes is explained on the basis of the root loci and frequency characteristics. The results obtained for three sampling rates: 12.8, 25.6, and 51.2 kHz, are presented and compared with an actual VSI experiment. A comparison with other results obtained for this VSI shows that properly tuned PID control outperforms the more sophisticated solutions based on the coefficient diagram method (CDM) and the passivity based control (PBC).

Simulation model of autonomous module of digital PID controller

Three-channel PID controllers are widely used in industrial control systems. It is noted that the popularity of PID controllers in the control of industrial processes is explained by their ability to ensure high quality of processes in a wide range of modes, as well as functional simplicity that allows engineers to operate them without any problems.

Sintesis Kendali PID Digital dengan Diskritisasi Langsung dan Backward Difference

ABSTRAKKendali PID analog, yang realisasinya menggunakan komponen elektronika, memiliki keterbatasan yaitu nilai toleransi yang terbatas. Saat ini spesifikasi kontroler dituntut untuk dapat berkomunikasi dengan sistem yang lebih besar seperti SCADA dan DCS sehingga lebih cocok menggunakan pengendali digital. Penelitian ini menganalisis metode konversi PID analog ke digital agar dihasilkan difference equation yang dapat direalisasikan ke dalam pemrograman komputer. Metode yang dipakai adalah diskritisasi langsung dan Backward Difference. Perbandingan kedua metode dilakukan dengan menganalisis respons berdasarkan initial paramater yang dihasilkan oleh metode Ziegler Nichols. Hasil pengujian menunjukkan kendali PID diskrit menggunakan Backward Difference menghasilkan respons sistem yang lebih baik dibandingkan metode diskritisasi langsung dengan nilai Kp, Ti, dan Td adalah 50, 80 dan 0,001 menghasilkan respons dengan nilai rise time, settling time dan overshoot berturut-turut sebesar 33,66s, 90,39s dan 0,9%.Kata kunci: PID diskrit, diskritisasi langsung, Backward Difference, Ziegler Nichols ABSTRACTThe analog PID control, where its parameters are realised using the electronic component, has disadvantages due to the limitation of its tolerance value. Currently, the specifications of controller are required to be able to communicate with larger systems such as SCADA and DCS, therefore digital controller is more appropriate to use. This study analyzes the analog to digital PID conversion method to generate a difference equation that can be realized in computer programming. The direct discretization and Backward Difference method are used. Comparison of both methods is by analyzing response based on initial parameters obtained of Ziegler Nichols method. The results show that discrete PID control using the Backward Difference indicates a better response than using the direct discretization method with Kp, Ti, and Td values are 50, 80, and 0,001, respectively. Those parameters generate response with rise time, settling time, and overshoot values of 33,66s, 90,39s, and 0,9%, respectively.Keywords: discrete PID, direct discretization, Backward Difference, ZieglerNichols

Optimization of transient processes of the pneumatic servo drive taking into account the friction model with the Stribeck effect

The aim of the work is to select the optimal values of the parameters of the digital PID controller to eliminate self-oscillations in systems, as well as to optimize the type of transient processes of the servo pneumatic drive. The reason for the study was the problem of the occurrence of self-oscillations in pneumatic systems when using friction models that are closest to reality. The scientific novelty of the article consists in the creation of a computer model and the application of opti-mization methods to improve the quality of transient processes of the pneumatic servo drive, taking into account the Striebeck friction model. The authors of the article optimized the transient processes of the pneumatic servo drive taking into account the selected friction model. The optimal parameters of the PID controller were selected using computer simulation. And the instability of the system was eliminated as well. To optimize the system performance, the gradient descent method was chosen. An assessment of the quality in-dicators of transient processes before and after optimization was made. Based on the simulation re-sults of the pneumatic servo drive system, it can be concluded that the gradient descent method can be used to determine the parameters of the PID controller. The transition from an analog (continuous) system to a digital (discrete) system has been made It is necessary to determine the sampling period for its implementation. The article indicates the main methods for determining the sampling period and shows the disadvantages of these methods. Anal-ysis of the results shows that the methods described in the article should be used only for the first approximation, and the value of the indicated quantity should be selected from the calculation of the minimum error between an analog (continuous) and digital (discrete) system. An error of less than 1% allows the selection of a programmable logic controller. The topic of the article is relevant for scientific research and includes the provision of practical recommendations for determining the parameters of a digital PID controller and selecting a controller for specialists who are inloved in the design of systems that include a pneumatic servo drive.

Multivariable Unconstrained Pattern Search Method for Optimizing Digital PID Controllers Applied to Isolated Forward Converter

Most of the traditional PID tuning methods are heuristic in nature. The heuristic approach-based tuned PID controllers show only nominal performance. In addition, in the case of a digital redesign approach, mapping of the heuristically-designed continuous-time PID controllers into discrete-time PID controllers and in case of the direct digital design approach, mapping of the continuous-time plant (forward converter) into the discrete-time plant, results in frequency distortion (or warping). Besides this, nonlinear elements such as ADC and DAC, and delay in the digital control loop deteriorate the control performance. There is a need to tune conventionally-designed digital controllers to enhance performance. This paper proposes optimized discrete-time PID controllers for a forward DC–DC converter operating in continuous conduction mode (CCM). The considered conventional digital PID controllers designed on the basis of the digital redesign and direct digital approaches are tuned by one of the multivariable unconstrained pattern search methods named Hooke–Jeeves (H–J) search method to ensure excellent output voltage regulation performance against the changes in input voltage and load current. Numerical results show that the H–J-based optimized PID compensated forward converter system shows tremendous improvement in performance compared to its unoptimized counterpart and simulated annealing (SA)-based compensated system, thus justifying the applicability of the H–J method for enhancing the performance.