Nonlinear control algorithm for improving settling time in systems with friction

A nonlinear control algorithm that greatly reduces settling time in precision instruments with rolling element bearings is proposed. Reductions of 80.5%-87.4% in settling time were achieved when settling to within 3-100 nm of the commanded position. Final settling of such systems is typically impacted by the nonlinearity in the pre-rolling friction regime, which manifests as a hysteretic stiffness. Consequently, the integral term in the controller can take a long time to respond. In this paper, a nonlinear integral action settling algorithm is presented. The nonlinear integral gain takes the form of a Dahl friction model. Since the integral gain mimics hysteretic stiffness, the output of the integral control term is instantaneously set to a large value after each direction change, greatly improving settling response. A nearly first-order error dynamic results, which has a user-definable time constant. Before the algorithm can be implemented, the Coulomb friction and initial contact stiffness in the Dahl model must be experimentally determined for the stage. A sensitivity study is performed on the initial contact stiffness, which was found in other works to dictate the stability of the algorithm. © 1993-2012 IEEE

Theoretical analysis and experimental validation of a simplified fractional order controller for a magnetic levitation system

Fractional order (FO) controllers are among the emerging solutions for increasing closed-loop performance and robustness. However, they have been applied mostly to stable processes. When applied to unstable systems, the tuning technique uses the well-known frequency-domain procedures or complex genetic algorithms. This brief proposes a special type of an FO controller, as well as a novel tuning procedure, which is simple and does not involve any optimization routines. The controller parameters may be determined directly using overshoot requirements and the study of the stability of FO systems. The tuning procedure is given for the general case of a class of unstable systems with pole multiplicity. The advantage of the proposed FO controller consists in the simplicity of the tuning approach. The case study considered in this brief consists in a magnetic levitation system. The experimental results provided show that the designed controller can indeed stabilize the magnetic levitation system, as well as provide robustness to modeling uncertainties and supplementary loading conditions. For comparison purposes, a simple PID controller is also designed to point out the advantages of using the proposed FO controller

Bacterial foraging-optimized PID control of a two-wheeled machine with a two-directional handling mechanism

This paper presents the performance of utilizing a bacterial foraging optimization algorithm on a PID control scheme for controlling a five DOF two-wheeled robotic machine with two-directional handling mechanism. The system under investigation provides solutions for industrial robotic applications that require a limited-space working environment. The system nonlinear mathematical model, derived using Lagrangian modeling approach, is simulated in MATLAB/Simulink(®) environment. Bacterial foraging-optimized PID control with decoupled nature is designed and implemented. Various working scenarios with multiple initial conditions are used to test the robustness and the system performance. Simulation results revealed the effectiveness of the bacterial foraging-optimized PID control method in improving the system performance compared to the PID control scheme

Neurocontroller Alternatives for Fuzzy Ball-and-Beam Systems with Nonuniform Nonlinear Friction

The ball-and-beam problem is a benchmark for testing control algorithms. Zadeh proposed (1994) a twist to the problem, which, he suggested, would require a fuzzy logic controller. This experiment uses a beam, partially covered with a sticky substance, increasing the difficulty of predicting the ball\u27s motion. We complicated this problem even more by not using any information concerning the ball\u27s velocity. Although it is common to use the first differences of the ball\u27s consecutive positions as a measure of velocity and explicit input to the controller, we preferred to exploit recurrent neural networks, inputting only consecutive positions instead. We have used truncated backpropagation through time with the node-decoupled extended Kalman filter (NDEKF) algorithm to update the weights in the networks. Our best neurocontroller uses a form of approximate dynamic programming called an adaptive critic design. A hierarchy of such designs exists. Our system uses dual heuristic programming (DHP), an upper-level design. To our best knowledge, our results are the first use of DHP to control a physical system. It is also the first system we know of to respond to Zadeh\u27s challenge. We do not claim this neural network control algorithm is the best approach to this problem, nor do we claim it is better than a fuzzy controller. It is instead a contribution to the scientific dialogue about the boundary between the two overlapping disciplines

A New Self-Tuning Nonlinear PID Motion Control for One-Axis Servomechanism with Uncertainty Consideration

This paper introduces a new study for one-axis servomechanism with consideration the parameter variation and system uncertainty. Also, a new approach for high-performance self-tuning nonlinear PID control was developed to track a preselected profile with high accuracy. Moreover, a comparison study between the proposed control technique and the well-known controllers (PID and Nonlinear PID). The optimal control parameters were determined based on the COVID-19 optimization technique. The parameters of the servomechanism system changed randomly at a preselected range through the online simulation. The change of these parameters acts as the nonlinearity resources (friction, backlash, environmental effects) and system uncertainty. A comparative study between the linear and nonlinear models had been accomplished and investigated. The results show that the proposed controller can track several operating points with high accuracy, low rise time, and small overshoot

Iterative Feedback Tuning with Application to Robotics

Many control objectives can be expressed in terms of a criterion function. Generally, explicit solutions to such optimization problem require full knowledge of the plant and disturbances and complete freedom in the complexity of the controller. In practice, the plant and the disturbances are seldom known, and it is often desirable to achieve the best possible performance with a controller of prescribed complexity such as for example a PID controller. The optimization of such control performance criterion typically requires iterative gradient-based minimization procedures. The major stumbling block for the solution of this optimal control problem is the computation of the gradient of the criterion function with respect to the controller parameters: it is a fairly complicated function of the plant and disturbance dynamics. When these are unknown, it is not clear how this gradient can be computed. Iterative Feedback Tuning (IFT) is a input-output data-based design method for the tuning of restricted complexity controllers. It does not depend on the plant model, utilizes I/O data only. Therefore IFT is robust against the plant model uncertainty. At each iteration, an update for the parameters of the controller is estimated from data obtained partly from the normal operation of the closed loop system and partly from a special experiment. No identification procedure is involved. In this thesis tuning of robot joint controllers using IFT is considered. The different IFT-schemes have been verified in simulation and in real experiments on an industrial robot manipulator ABB Irb-2000

Impulse-Based Hybrid Motion Control

The impulse-based discrete feedback control has been proposed in previous work for the second-order motion systems with damping uncertainties. The sate-dependent discrete impulse action takes place at zero crossing of one of both states, either relative position or velocity. In this paper, the proposed control method is extended to a general hybrid motion control form. We are using the paradigm of hybrid system modeling while explicitly specifying the state trajectories each time the continuous system state hits the guards that triggers impulsive control actions. The conditions for a stable convergence to zero equilibrium are derived in relation to the control parameters, while requiring only the upper bound of damping uncertainties to be known. Numerical examples are shown for an underdamped closed-loop dynamics with oscillating transients, an upper bounded time-varying positive system damping, and system with an additional Coulomb friction damping.Comment: 6 pages, 4 figures, IEEE conferenc