Fixed point transformations in the adaptive control of fractional-order MIMO systems

Though the formal mathematical idea of introducing noninteger order derivatives can be traced from the 17th century in a letter by L’Hospital in which he asked Leibniz what the meaning of D n y if n = 1/2 would be in 1695 [1], it was better outlined only in the 19th century [2, 3, 4]. Due to the lack of clear physical interpretation their first applications in physics appeared only later, in the 20th century, in connection with visco-elastic phenomena [5, 6]. The topic later obtained quite general attention [7, 8, 9], and also found new applications in material science [10], analysis of earth-quake signals [11], control of robots [12], and in the description of diffusion [13], etc.

Improved Numerical Simulation for a Novel Adaptive Control Using Fractional Order Derivatives

A novel control technique is investigated in the adaptive control of a typical paradigm, an approximately and partially modeled cart plus double pendulum system. In contrast to the traditional approaches that try to build up ”complete” and ”permanent” system models it develops ”temporal” and ”partial” ones that are valid only in the actual dynamic environment of the system, that is only within some ”spatio-temporal vicinity” of the actual observations. This technique was investigated for various physical systems via ”preliminary” simulations integrating by the simplest 1st order finite element approach for the time domain. In 2004 INRIA issued its SCILAB 3.0 and its improved numerical simulation tool ”Scicos” making it possible to generate ”professional”, ”convenient”, and accurate simulations. The basic principles of the adaptive control, the typical tools available in Scicos, and others developed by the authors, as well as the improved simulation results and conclusions are presented in the contribution.

Hybrid adaptive control of a dragonfly model

Dragonflies show unique and superior flight performances than most of other insect species and birds. They are equipped with two pairs of independently controlled wings granting an unmatchable flying performance and robustness. In this paper, it is presented an adaptive scheme controlling a nonlinear model inspired in a dragonfly-like robot. It is proposed a hybrid adaptive (HA) law for adjusting the parameters analyzing the tracking error. At the current stage of the project it is considered essential the development of computational simulation models based in the dynamics to test whether strategies or algorithms of control, parts of the system (such as different wing configurations, tail) as well as the complete system. The performance analysis proves the superiority of the HA law over the direct adaptive (DA) method in terms of faster and improved tracking and parameter convergence.

Scalable and efficient data processing in networked control systems

Network control systems (NCSs) are spatially distributed systems in which the communication between sensors, actuators and controllers occurs through a shared band-limited digital communication network. However, the use of a shared communication network, in contrast to using several dedicated independent connections, introduces new challenges which are even more acute in large scale and dense networked control systems. In this paper we investigate a recently introduced technique of gathering information from a dense sensor network to be used in networked control applications. Obtaining efficiently an approximate interpolation of the sensed data is exploited as offering a good tradeoff between accuracy in the measurement of the input signals and the delay to the actuation. These are important aspects to take into account for the quality of control. We introduce a variation to the state-of-the-art algorithms which we prove to perform relatively better because it takes into account the changes over time of the input signal within the process of obtaining an approximate interpolation.

A scalable and efficient approach for obtaining measurements in CAN-Based control systems

The availability of small inexpensive sensor elements enables the employment of large wired or wireless sensor networks for feeding control systems. Unfortunately, the need to transmit a large number of sensor measurements over a network negatively affects the timing parameters of the control loop. This paper presents a solution to this problem by representing sensor measurements with an approximate representation-an interpolation of sensor measurements as a function of space coordinates. A priority-based medium access control (MAC) protocol is used to select the sensor messages with high information content. Thus, the information from a large number of sensor measurements is conveyed within a few messages. This approach greatly reduces the time for obtaining a snapshot of the environment state and therefore supports the real-time requirements of feedback control loops.

Visualizing control systems performance: A fractional perspective

This article presents a novel method for visualizing the control systems behavior. The proposed scheme uses the tools of fractional calculus and computes the signals propagating within the system structure as a time/frequency-space wave. Linear and nonlinear closed-loop control systems are analyzed, for both the time and frequency responses, under the action of a reference step input signal. Several nonlinearities, namely, Coulomb friction and backlash, are also tested. The numerical experiments demonstrate the feasibility of the proposed methodology as a visualization tool and motivate its extension for other systems and classes of nonlinearities.

On the robustness of the slotine-Li and the FPT/SVD-based adaptive controllers

A comparative study concerning the robustness of a novel, Fixed Point Transformations/Singular Value Decomposition (FPT/SVD)-based adaptive controller and the Slotine-Li (S&L) approach is given by numerical simulations using a three degree of freedom paradigm of typical Classical Mechanical systems, the cart + double pendulum. The effects of the imprecision of the available dynamical model, presence of dynamic friction at the axles of the drives, and the existence of external disturbance forces unknown and not modeled by the controller are considered. While the Slotine-Li approach tries to identify the parameters of the formally precise, available analytical model of the controlled system with the implicit assumption that the generalized forces are precisely known, the novel one makes do with a very rough, affine form and a formally more precise approximate model of that system, and uses temporal observations of its desired vs. realized responses. Furthermore, it does not assume the lack of unknown perturbations caused either by internal friction and/or external disturbances. Its another advantage is that it needs the execution of the SVD as a relatively time-consuming operation on a grid of a rough system-model only one time, before the commencement of the control cycle within which it works only with simple computations. The simulation examples exemplify the superiority of the FPT/SVD-based control that otherwise has the deficiency that it can get out of the region of its convergence. Therefore its design and use needs preliminary simulation investigations. However, the simulations also exemplify that its convergence can be guaranteed for various practical purposes.

Robot Manipulator Systems: Analysis and Control

Manipulator systems are rather complex and highly nonlinear which makes difficult their analysis and control. Classic system theory is veil known, however it is inadequate in the presence of strong nonlinear dynamics. Nonlinear controllers produce good results [1] and work has been done e. g. relating the manipulator nonlinear dynamics with frequency response [2–5]. Nevertheless, given the complexity of the problem, systematic methods which permit to draw conclusions about stability, imperfect modelling effects, compensation requirements, etc. are still lacking. In section 2 we start by analysing the variation of the poles and zeros of the descriptive transfer functions of a robot manipulator in order to motivate the development of more robust (and computationally efficient) control algorithms. Based on this analysis a new multirate controller which is an improvement of the well known “computed torque controller” [6] is announced in section 3. Some research in this area was done by Neuman [7,8] showing tbat better robustness is possible if the basic controller structure is modified. The present study stems from those ideas, and attempts to give a systematic treatment, which results in easy to use standard engineering tools. Finally, in section 4 conclusions are presented.

Optimal intelligent supervisory control system in cyber-physical intelligence

This paper studies Optimal Intelligent Supervisory Control System (OISCS) model for the design of control systems which can work in the presence of cyber-physical elements with privacy protection. The development of such architecture has the possibility of providing new ways of integrated control into systems where large amounts of fast computation are not easily available, either due to limitations on power, physical size or choice of computing elements.

PCMAT, an adaptive learning platform

This paper is about PCMAT, an adaptive learning platform for Mathematics in Basic Education schools. Based on a constructivist approach, PCMAT aims at verifying how techniques from adaptive hypermedia systems can improve e-learning based systems. To achieve this goal, PCMAT includes a Pedagogical Model that contains a set of adaptation rules that influence the student-platform interaction. PCMAT was subject to a preliminary testing with students aged between 12 and 14 years old on the subject of direct proportionality. The results from this preliminary test are quite promising as they seem to demonstrate the validity of our proposal.

Parallel real-time support for distributed adaptive embedded applications

Real-time embedded applications require to process large amounts of data within small time windows. Parallelize and distribute workloads adaptively is suitable solution for computational demanding applications. The purpose of the Parallel Real-Time Framework for distributed adaptive embedded systems is to guarantee local and distributed processing of real-time applications. This work identifies some promising research directions for parallel/distributed real-time embedded applications.

Fractional calculus: application in modelling and control

This contribution introduces the fractional calculus (FC) fundamental mathematical aspects and discuses some of their consequences. Based on the FC concepts, the chapter reviews the main approaches for implementing fractional operators and discusses the adoption of FC in control systems. Finally are presented some applications in the areas of modeling and control, namely fractional PID, heat diffusion systems, electromagnetism, fractional electrical impedances, evolutionary algorithms, robotics, and nonlinear system control.

Adaptive tackling of the swinging problem for a 2 DOF crane – payload system

The control of a crane carrying its payload by an elastic string corresponds to a task in which precise, indirect control of a subsystem dynamically coupled to a directly controllable subsystem is needed. This task is interesting since the coupled degree of freedom has little damping and it is apt to keep swinging accordingly. The traditional approaches apply the input shaping technology to assist the human operator responsible for the manipulation task. In the present paper a novel adaptive approach applying fixed point transformations based iterations having local basin of attraction is proposed to simultaneously tackle the problems originating from the imprecise dynamic model available for the system to be controlled and the swinging problem, too. The most important phenomenological properties of this approach are also discussed. The control considers the 4th time-derivative of the trajectory of the payload. The operation of the proposed control is illustrated via simulation results.

Fractional Calculus: Application in modeling and control

This contribution introduces the fractional calculus (FC) fundamental mathematical aspects and discuses some of their consequences. Based on the FC concepts, the chapter reviews the main approaches for implementing fractional operators and discusses the adoption of FC in control systems. Finally are presented some applications in the areas of modeling and control, namely fractional PID, heat diffusion systems, electromagnetism, fractional electrical impedances, evolutionary algorithms, robotics, and nonlinear system control.

Simple Kinematic Design for Evading the Forced Oscillation of a Car-Wheel Suspension System

An adaptive control damping the forced vibration of a car while passing along a bumpy road is investigated. It is based on a simple kinematic description of the desired behavior of the damped system. A modified PID controller containing an approximation of Caputo’s fractional derivative suppresses the high-frequency components related to the bumps and dips, while the low frequency part of passing hills/valleys are strictly traced. Neither a complete dynamic model of the car nor ’a priori’ information on the surface of the road is needed. The adaptive control realizes this kinematic design in spite of the existence of dynamically coupled, excitable internal degrees of freedom. The method is investigated via Scicos-based simulation in the case of a paradigm. It was found that both adaptivity and fractional order derivatives are essential parts of the control that can keep the vibration of the load at bay without directly controlling its motion.