Vol. 8, No. 1 (2019): Regular Issue

Fractional order differentiation is a generalization of classical integer differentiation to real or complex orders. In the last couple of decades, a more profound understating of fractional calculus, as well as the developments in computing technologies combined with the unique advantages of fractional order differ-integrals in capturing closely complex phenomena, lead to ongoing research regarding fractional calculus and to an increasing interest towards using fractional calculus as an optimal tool to describe the dynamics of complex systems and to enhance the performance and robustness of control systems. The research community has managed to bring forward ideas and concepts that justify the importance of fractional calculus for future engineering and science discoveries. Since the emergence of the CRONE controllers and the generalization of the classical PID controller, many researchers have focused on the design problem of fractional order controllers, the optimal tuning, the possible extensions of fractional calculus in advanced control strategies, the problems regarding their implementation, and so on. There are still many issues and open problems left unattended in this area. This special issue aims at presenting some recent developments in the field of fractional order controllers, in order to further raise the interest regarding the increasing tendency of adopting fractional calculus in applications related to modeling and design of control systems.

In this paper, a PI-PD controller tuning method is proposed for fractional order systems based on standard forms. SBL fitting integer order approximation method is directly used to obtain appropriate integer order transfer function required in standard forms for the controller design. The controller tuning parameters for approximate transfer function are calculated by using optimization of ISTE integral performance criterion. The obtained tuning parameters are performed for fractional order transfer function. Results give good performance. The results show that the performance of the proposed method is practicable and that the controller parameters for the fractional order models can be tuned by using its integer order approximation transfer function. Also, the results shows that the other methods such as Oustaloup’s and Matsuda’s methods which enable one to obtain integer order approximate transfer functions, cannot be used directly because they do not conform to the standard form.

The existence of active wave control has been known in the field of the vibration control of large-size space structures (LSS) since the 1960s. Recently, with the goal of energy and resource conservation, active wave control has come into the spotlight again in the field of the vibration suppression of light and thin members widely used in mechanical structures, including automobiles. Therefore, achieving active wave control is both an old and a new problem. A vibration suppression problem for a thin cantilevered beam is presented as an example for discussion. Results clarified √ that the active wave controller includes s and s3/2 terms. Those terms are realized as a 1/2-order derivative and a 3/2-order derivative using fractional calculus. The active wave controller is realized through fractional calculus, which is shown to be an important step in the analysis of this problem. Specifically, the active wave controller can be implemented using fractional derivative feedback. The controller involving the fractional derivatives is realized with a digital signal processor based on definitions of fractional calculus. The vibration suppression effect of active wave control is demonstrated both numerically and experimentally.

This work deals with the design of model predictive control (MPC) strategy for linear fractional-order (FO) systems. Two FO systems with different characteristics, highly oscillatory response and nonminimum phase type, are considered to test the performance of the MPC design. Conventionally, a system with FO dynamics is represented using a finite memory integer-ordermodel. In order to evaluate the performance of MPC for such a situation, the integer-order rational approximation (Oustaloup’s recursive approximation) of the FO system is considered as the model, whereas the output of FO plant is calculated analytically by solving the linear FO differential equation at each sampling instant. The MPC methodology is applied in a constrained environment with limitations on the control input magnitude and its rate. The results confirm that designed MPC strategy works satisfactorily for the FO systems.

This paper presents the application of fractional-order control strategy for the velocity control of a manipulator robot joint. A wellknown approach for robot joint control is to use an independent controller for each joint axis with a nested structure: an outer loop which computes the desired joint velocity in order to minimize the position error; and an inner loop which ensures the required velocity of the joint. A fractional-order controller was designed, tested and implemented on a manipulator robot. The communication between the robot and the controller was established via the Robotics System Toolbox fromMatlab® and the ROS (Robot Operating System) platform. The experimental results indicate that the flexibilities of the fractional-order PI controller allows it to outperform the conventional integer-order PI controller.

Continuous casting technology implies an exotherm process from liquid steel to solid slab. During this process, the temperature at the surface of the slab is one of the most important parameters for evaluating the cooling process and inherent material properties. To ensure a specific temperature gradient, several control elements need to be evaluated; e.g. to optimize casting speed, to determine intensity of the second cold and determine liquid depth. In this paper a fractional order control strategy is proposed to control the steel slab temperature, governed by delay dominant dynamics. The reference tracking for deisred temperature at end of casting line is evaluated by means of performance metrics. The results obtained indicate that the proposed methodology outperforms other strategies used for comparison.

This paper deals with vehicle body control under driver inputs through a pneumatic system using the CRONE approach and follows the objective of vehicle level control through the same system. A comparison between this active system and a passive metallic suspension equipping a Citroën C4 Picasso is presented after modeling the pneumatic (leveling) system of a quarter vehicle model with two degrees-of-freedom. Results show an excellent body control as well as, by using the CRONE approach, a robustness of the stability-degree.

In the paper presented is a method allowing for determination of a set of (A,B,C,D) realizations for fractional-order dynamic systems. Proposed method is an extension of previously proposed algorithm that was used to determine realizations of fractional-order 1D single-input single-output (SISO) dynamic systems for both single-input multipleoutput (SIMO) and multiple-input single-output (MISO) fractional dynamic systems. The main advantage of the method over canonical forms is that the algorithm finds a set of realizations, not just a single realization. Also, the solutions found tend to be minimal in terms of size of state matrix A. Additionally, the method allows for the possibility of obtaining a set of state matrices directly from digraph form of the system and can be efficiently used as GPGPU computer algorithm. Proposed method is presented in pseudo-code and illustrated with example.