A new approach based on interval analysis is developed to find the global minimum-jerk (MJ) trajectory of a robot manipulator within a joint space scheme using cubic splines. MJ trajectories are desirable for their similarity to human joint movements and for their amenability to path tracking and to limit robot vibrations. This makes them attractive choices for robotic applications, in spite of the fact that the manipulator dynamics are not taken into account. Cubic splines are used in a framework that assures overall continuity of velocities and accelerations in the robot movement. The resulting MJ trajectory planning is shown to be a global constrained minimax optimization problem. This is solved by a newly devised algorithm based on interval analysis and proof of convergence with certainty to an arbitrarily good global solution is provided. The proposed planning method is applied to an example regarding a six-joint manipulator and comparisons with an alternative MJ planner are exposed.

The paper presents a comparison between different methods, based on fuzzy logic, for the tuning of PID controllers. Specifically considered are different control structures in which a fuzzy mechanism is adopted to improve the performances given by Ziegler–Nichols parameters. To verify the full capabilities of each controller, genetic algorithms are used to tune the parameters of the fuzzy inference systems (scaling coefficients, shape of the membership functions, etc.). Furthermore, a discussion about the practical implementation issue of the controllers is provided, and comparisons made with a typical PID-like fuzzy controller and a standard and a nonlinear PID controller. The results show the superiority of the fuzzy set-point weighting methodology over the other methods.

Tuning formulas for PID controllers applied to integral and unstable processes are presented. In particular, the controller parameters are determined, based on the process model, to minimise integral performance criteria such as ISE, ITSE and ISTE. Results have been obtained by means of genetic algorthms, in order to avoid local minima in the optimisation procedure. Both the set-point following and the load disturbance rejection design specifications are addressed. The achieved results can be adopted both for tuning purposes and for the evaluation of the performances of a pre-existing PID controller.

A methodology, based on fuzzy logic, for the tuning of proportional-integral-derivative (PID) controllers is presented. A fuzzy inference system is adopted to determine the value of the weight that multiplies the set-point for the proportional action, based on the current output error and its time derivative. In this way, both the overshoot and the rise time in set-point following can be reduced. The values of the proportional gain and the integral and derivative time constant are determined according to the well-known Ziegler-Nichols formula so that a good load disturbance attenuation is also assured. The methodology is shown to be effective for a large range of processes and is valuable for industrial settings since it is intuitive, it requires only a small extra computational effort, and it is robust with regard to parameter variations. The tuning of the parameters of the fuzzy module can be easily done by hand or by means of an autotuning procedure based on genetic algorithms

A set of tuning rules for standard (integer-order) proportional-integral-derivative (PID) and fractional-order PID controllers for integral and unstable processes is presented in this study. Based on a simple model of the process, the tuning rules have been devised in order to minimise the integrated absolute error. Both set-point tracking and load disturbance rejection tasks are considered. The achieved performance indexes can also be used for the assessment of the controller performance. A remarkable feature of the optimisation procedure employed for integral processes is highlighted. The provided results allow the user to quantify, for a given process, the performance improvement that can be obtained by using the fractional controller instead of the integer one.