PID Control of Planar Nonlinear Uncertain Systems in the Presence of Actuator Saturation

This paper investigates PID control design for a class of planar nonlinear uncertain systems in the presence of actuator saturation. Based on the bounds on the growth rates of the nonlinear uncertain function in the system model, the system is placed in a linear differential inclusion. Each vertex system of the linear differential inclusion is a linear system subject to actuator saturation. By placing the saturated PID control into a convex hull formed by the PID controller and an auxiliary linear feedback law, we establish conditions under which an ellipsoid is contractively invariant and hence is an estimate of the domain of attraction of the equilibrium point of the closed-loop system. The equilibrium point corresponds to the desired set point for the system output. Thus, the location of the equilibrium point and the size of the domain of attraction determine, respectively, the set point that the output can achieve and the range of initial conditions from which this set point can be reached. Based on these conditions, the feasible set points can be determined and the design of the PID control law that stabilizes the nonlinear uncertain system at a feasible set point with a large domain of attraction can then be formulated and solved as a constrained optimization problem with constraints in the form of linear matrix inequalities (LMIs). Application of the proposed design to a magnetic suspension system illustrates the design process and the performance of the resulting PID control law.      

Digital twin-based analysis of volumetric error mapping procedures

The evaluation of the volumetric accuracy of a machine tool is an open challenge in the industry, and a wide variety of technical solutions are available in the market and at research level. All solutions have advantages and disadvantages concerning which errors can be measured, the achievable uncertainty, the ease of implementation, possibility of machine integration and automation, the equipment cost and the machine occupation time, and it is not always straightforward which option to choose for each application. The need to ensure accuracy during the whole lifetime of the machine and the availability of monitoring systems developed following the Industry 4.0 trend are pushing the development of measurement systems that can be integrated in the machine to perform semi-automatic verification procedures that can be performed frequently by the machine user to monitor the condition of the machine. Calibrated artefact based calibration and verification solutions have an advantage in this field over laser based solutions in terms of cost and feasibility of machine integration, but they need to be optimized for each machine and customer requirements to achieve the required calibration uncertainty and minimize machine occupation time.This paper introduces a digital twin-based methodology to simulate all relevant effects in an artefact-based machine tool calibration procedure, from the machine itself with its expected error ranges, to the artefact geometry and uncertainty, artefact positions in the workspace, probe uncertainty, compensation model, etc. By parameterizing all relevant variables in the design of the calibration procedure, this simulation methodology can be used to analyse the effect of each design variable on the error mapping uncertainty, which is of great help in adapting the procedure to each specific machine and user requirements. The simulation methodology and the analysis possibilities are illustrated by applying it on a 3-axis milling machine tool.     

Context-free grammars to detect straight segments and a novel polygonal approximation method

A new method for the polygonal approximation is presented. The method is based on the search for break points through a context-free grammar, that accepts digital straight segments with loss of information, as well as the decrease in the error committed employing the comparison of a tolerable error. We present an application of our method to different sets of objects widely used, as well as a comparison of our results with the best results reported in the literature, proving that our method achieves better values of error criteria. Besides, a new way to find polygonal approximations, with context-free grammars to recognize digital straight segments without loss of pixels, it is also addressed.     

Optimal design of nonlinear model predictive controller based on new modified multitracker optimization algorithm

The controller design for the robotic manipulator faces different challenges such as the system's nonlinearities and the uncertainties of the parameters. Furthermore, the tracking of different linear and nonlinear trajectories represents a vital role by the manipulator. This paper suggests an optimal design for the nonlinear model predictive control (NLMPC) based on a new improved intelligent technique and it is named modified multitracker optimization algorithm (MMTOA). The proposed modification of the MTOA is carried out based on opposition-based learning (OBL) and quasi OBL approaches. This modification improves the exploration behavior of the MTOA to prevent it from becoming trapped in a local optimum. The proposed method is applied on the robotic manipulator to track different linear and nonlinear trajectories. The NLMPC parameters are tuned by the MMTOA rather than the trial and error method of the designer. The proposed NLMPC based on MMTOA is compared with the original MTOA, genetic algorithm, and cuckoo search algorithm in literature. The superiority and effectiveness of the proposed controller are confirmed to track different linear and nonlinear trajectories. Furthermore, the robustness of the proposed method is emphasized against the uncertainties of the parameters.     

Unreliable numbers: error and harm induced by bad design can be reduced by better design

Number entry is a ubiquitous activity and is often performed in safety- and mission-critical procedures, such as healthcare, science, finance, aviation and in many other areas. We show that Monte Carlo methods can quickly and easily compare the reliability of different number entry systems. A surprising finding is that many common, widely used systems are defective, and induce unnecessary human error. We show that Monte Carlo methods enable designers to explore the implications of normal and unexpected operator behaviour, and to design systems to be more resilient to use error. We demonstrate novel designs with improved resilience, implying that the common problems identified and the errors they induce are avoidable.     

Robust predictive extended state observer for a class of nonlinear systems with time-varying input delay

ABSTRACT

This paper deals with asymptotic stabilisation of a class of nonlinear input-delayed systems via dynamic output feedback in the presence of disturbances. The proposed strategy has the structure of an observer-based control law, in which the observer estimates and predicts both the plant state and the external disturbance. A nominal delay value is assumed to be known and stability conditions in terms of linear matrix inequalities are derived for fast-varying delay uncertainties. Asymptotic stability is achieved if the disturbance or the time delay is constant. The controller design problem is also addressed and a numerical example with an unstable system is provided to illustrate the usefulness of the proposed strategy.     

On the performance of improved quadrature spatial modulation

Quadrature spatial modulation (QSM) utilizes the in‐phase and quadrature spatial dimensions to transmit the real and imaginary parts of a single signal symbol, respectively. The improved QSM (IQSM) transmits two signal symbols per channel use through a combination of two antennas for each of the real and imaginary parts. The main contributions of this study can be summarized as follows. First, we derive an upper bound for the error performance of the IQSM. We then design constellation sets that minimize the error performance of the IQSM for several system configurations. Second, we propose a double QSM (DQSM) that transmits the real and imaginary parts of two signal symbols through any available transmit antennas. Finally, we propose a parallel IQSM (PIQSM) that splits the antenna set into equal subsets and performs IQSM within each subset using the same two signal symbols. Simulation results demonstrate that the proposed constellations significantly outperform conventional constellations. Additionally, DQSM and PIQSM provide a performance similar to that of IQSM while requiring a smaller number of transmit antennas and outperform IQSM with the same number of transmit antennas.     

Nonlinear dynamic behaviors and control based on simulation of high-purity heat integrated air separation column

In this paper, the dynamic behaviors on the basis of simulation for high-purity heat integrated air separation column (HIASC) are studied. A nonlinear generic model control (GMC) scheme is proposed based on the nonlinear behavior analyses of a HIASC process, and an adaptive generic model control (AGMC) scheme is further presented to correct the model parameters online. Related internal model control (IMC) scheme and multi-loop PID (M-PID) scheme are also developed as the comparative base. The comparative researches are carried out among these linear and nonlinear control schemes in detail. The simulation research results show that the proposed AGMC schemes present advantages in both servo control and regulatory control for the high-purity HIASC.     

Adaptive robust boundary control of shaft vibrations under perturbations with unknown upper bounds

This paper presents robust and adaptive boundary control designs to stabilize the two‐dimensional vibration of hybrid shaft model. The hybrid shaft is mathematically represented by a set of partial differential equations, governing the shaft vibrations, coupled to ordinary differential equations, describing rigid body spinning and dynamic boundary conditions. The control objective is to stabilize the transverse vibrations of the perturbed shaft while regulating the spinning rate. To achieve this, the paper first establishes robust boundary control laws that fulfil the control objective in the presence of modeling uncertainties and external disturbances operating over the shaft domain and boundary. Lyapunov‐based analyses show that the proposed robust control exponentially stabilizes the shaft with vanishing distributive perturbations, while assuring ultimately bounded vibrations in the case of nonvanishing perturbations. Then, adaptive control philosophy is utilized to achieve redesigned robust controllers that only use online adaptation of control gains without acquiring the knowledge of bounds on perturbations, as well as dynamic parameters. An advantage of this design is avoiding an overconservative robust control law, which may induce poor stability and chattering in tackling system perturbations with unknown upper bounds. Simulations through finite element method illustrate the results. Copyright © 2014 John Wiley & Sons, Ltd.