Design of proportional-integral-derivative (PID) controller with proportional, integral, and derivative gains given by ,  and  respectively, for time-delay systems is presented in this study. The centroid of the convex stability region (CCSR) method in the -  plane for fixed  is used. PID controller design for time-delay systems in the -  plane for a fixed  and -  plane for a fixed  have been extensively researched. Despite the amenability of CCSR method to design of PID controller in the -  plane for fixed , its application in this regard has not been given serious attention. The stability region in -  plane for fixed  was determined and the required controller gains in the region were determined using the CCSR method. Using the determined controller gains, the system closed loop unit step response for all the considered regions was plotted on same axes. Based on the obtained results, different combinations of controller gains can be implemented depending on the system time domain performance measures (TDPMs) requirements. However, selection of an appropriate controller gains combinations, requires compromise among any of the conflicting TDPMs.

The development of structured methods for proportional-integral (PI) controller design for systems with time delay are proposed in this article. Several PI controller design methods for time-delay systems have been reported. However, combining two or more methods to form new ones have not been given serious attention. The system stability region in the controller parameters space was determined by plotting the stability boundaries. In this study, the controller gains were first obtained using genetic algorithm (GA), weighted geometric center (WGC), and centroid of convex stability region (CCSR). Thereafter, these gains were combined by finding the centroids of lines joining any of the two gain locations, and triangle whose vertices are the location of the three gains in the convex stability region, thus yielding four additional methods, M1, M2, M3, and M4. Compared to a particular existing method, some of the proposed methods yield faster response speed at the expense of reference input tracking, while the reverse is the case for others. Any of the proposed methods (M1, M2, M3, and M4) can be selected depending on the system performance specifications.

Tool development and prime mover selection for optimum tillage operation require both the knowledge of soil and tillage tool interaction dynamics which is a function of some system parameters. The actual value of these parameters can only be determined either from field or soil bin experiment via appropriate instrumentation systems. Several published works have been reported on development of soil bin instrumentation system. However, development of a system that can measure and log all the required parameters simultaneously in real time remains an active area of research. The distance moved and the forces acting on the tool were sensed using potentiometer and load cells, respectively. The sensed parameters and the calculated tool linear velocity were processed in parallel using microcontroller with optimised code to ensure real-time and simultaneous logging. The developed system was used for measuring and logging the distance moved by the tool, its velocity as well as the x-, y-, and z- components of force acting on the tool. The values of the distance, velocity and force were determined any time from the start of tillage operation are available on the chats of distance/velocity/force against time obtained from this work. 10 seconds from the start of tillage operation, the distance moved by the tool, tool velocity, , , and  are 2.56 m, 0.27 m/s, 147.00 N, 5.00 N, and 15.00 N, respectively.

In Internet stream monitoring, computing the expected parameters and distributions for the stream process under self-similarity and long-range dependency requires appropriate and exact methods queueing analyses to obtain performance of the Internet. Our method avoids fitting a non-heavy tailed distribution to Internet stream data by specifically fitting Gamma distribution to its service time process, which enhances the features of correlated events that explain self-similarity and long-range dependency compared to the classical memoryless assumptions of standard Poisson arrival and Exponential service. We propose the specific expectations of the parameters for a class of M/Ga/1/k queueing system (‘M’ represents a Markovian arrival process that follows Poisson distribution, ‘Ga’ represents a Gamma distribution service process, ‘1’ represents a single server, ‘k’ represents the buffer size) in an exact closed-form derivations using the Pollaczek Khintchine formulae alongside the Laplace transform to obtain the performance of   queue. The adequacy of the proposed model was confirmed using simulated data of Internet traffic. Keywords- Gamma distribution, Internet stream, M/Ga/1/K model, Self-similarity, heavy-tail distribution

High-intensity concurrent arrivals of request packets in Internet traffic can cause dependence of event-to-event-times of the requests being served, which causes non-memoryless, modelled with heavy-tail distributions unlike common known traffics. The performance of Internet traffic can be examined using analytical models for the purpose of optimizing the system to reduce its operating costs. Therefore, our study examined a Ga/M/1/K Internet queue class (Gamma arrival processes, Ga; with memoryless-Poisson service process, M; a single server, 1, and K waiting room) and proposed specific derivations of its performance indicators. Real-life data of a corporate organisation Internet server was monitored at both peak and off-peak periods of its usage for Internet traffic data analysis. The minimum ‘0’ in the arrival process indicates self-similarity and was assessed using Hurst parameter, H, and their (standard deviation). ‘H’ > 0.5 arrival process in the peak period only, indicates self-similarity. Performance of Ga/M/1/K was compared with various queuing Internet traffic models used in existing literatures. Results showed that the value of the waiting room size for Ga/M/1/K has closest ties with true self-similar model at peak-periods usage of the Internet, which indicates possible concurrent arrival of clients' requests leading to more usage of the waiting room, but with light-tailed queue model at the off-peak periods. Therefore, the proposed Ga/M/1/K model can assist in evaluating the performance of high-intensity self-similar Internet traffic.      Keywords: Internet traffic; self-similarity; Ga/M/1/K model; gamma distribution