Recursive Control Algorithm Research Articles

Study on discrete acceleration feedback control with time delay

This paper addresses the design problem of a discrete controller with time delay and acceleration feedback. The delta operator is firstly used to describe the discrete acceleration signal and convert the delayed continuous-time state equation into the delayed discrete-time system. Then the delayed discrete-time system is transformed into the delay-free one by applying a discrete reduction method. Based on the delay-free discrete-time system, the optimal output delta state feedback controller is designed by minimizing a discrete non-standard quadratic performance index and the feedback gain of the controller is obtained by a convergent algorithm. On the basis of the optimal output delta state feedback controller, the discrete time-delayed acceleration feedback controller is achieved by using the inverse reduction method, and the corresponding recursive control algorithm is developed. The controller saves the process of performing numerical integration and eliminating direct current and trend term in designing the displacement or velocity feedback control, so as to make the closed-loop system become simpler. Moreover, it can solve the problem of phase shift of the measured signal caused by time delay. The proposed controller with a low order model-based control algorithm is implemented on a smart cantilever beam with an accelerometer and piezoelectric actuator for different controller gain-delay combinations, and the control performance is evaluated. Simulation and experimental results demonstrate that the controller can effectively reduce the free vibration response of the smart cantilever beam.

Self-Tuning Predictive Control of Nonlinear Servo-Motor

Self-Tuning Predictive Control of Nonlinear Servo-MotorThe paper is focused on a design of a self-tuning predictive model control (STMPC) algorithm and its application to a control of a laboratory servo motor. The model predictive control algorithm considers constraints of a manipulated variable. An ARX model is used in the identification part of the self-tuning controller and its parameters are recursively estimated using the recursive least squares method with the directional forgetting. The control algorithm is based on the Generalised Predictive Control (GPC) method and the optimization was realized by minimization of a quadratic and absolute values objective functions. A recursive control algorithm was designed for computation of individual predictions by incorporating a receding horizon principle. Proposed predictive controllers were verified by a real-time control of highly nonlinear laboratory model — Amira DR300.

Optimal multi‐interval control of a cantilever beam by a recursive control algorithm

AbstractThe optimal‐distributed control of a transversely vibrating cantilever beam is studied with the objective of minimizing the deflection and velocity in a given period of time with the minimum possible expenditure of force. The beam undergoes transient vibrations and is subject to given displacement and velocity initial conditions. The control is exercised by means of a transversely distributed force referred to as the control force. In the present study, a multi‐interval optimal control method is developed with the application of a maximum principle. The method consists of dividing the control duration into several intervals and using the maximum principle to obtain the optimality conditions at each interval. The explicit solutions for a cantilever beam are obtained by a recursive algorithm that takes the final conditions of the last interval as the initial conditions of the next interval. The formulation and the method of solution are suitable and convenient for digital computation. Numerical results are given, which compare the deflections, velocities and the control force under the optimal multi‐interval control with those under the optimal single‐interval control. Copyright © 2008 John Wiley & Sons, Ltd.

MODELLING AND STABILIZING CONTROL LAWS DESIGN BASED ON BACKSTEPPING FOR AN UAV TYPE-QUADROTOR

In this paper; we are interested principally in dynamic modelling of the four rotor mini aircraft named as a quadrotor while taking into account the high-order nonholonomic constraints as well as the various physical phenomena, which can influence the dynamics of a flying structure. These permit us to introduce a new state-space representation. We present also the development and the synthesis of a recursive control algorithm based on backstepping technique ensuring Lyapunov stability and desired tracking trajectories. Finally simulation results are also provided in order to illustrate the performances of the proposed controller.

On a simple recursive control algorithm automated and applied to an electrochemical experiment.

We review a simple recursive proportional feedback (RPF) control strategy for stabilizing unstable periodic orbits found in chaotic attractors. The method is generally applicable to high-dimensional systems and stabilizes periodic orbits even if they are completely unstable, i.e., have no stable manifolds. The goal of the control scheme is the fixed point itself rather than a stable manifold and the controlled system reaches the fixed point in d+1 steps, where d is the dimension of the state space of the Poincare map. We provide a geometrical interpretation of the control method based on an extended phase space. Controllability conditions or special symmetries that limit the possibility of using a single control parameter to control multiply unstable periodic orbits are discussed. An automated adaptive learning algorithm is described for the application of the control method to an experimental system with no previous knowledge about its dynamics. The automated control system is used to stabilize a period-one orbit in an experimental system involving electrodissolution of copper. (c) 1997 American Institute of Physics.

Tracking unstable turing patterns through mixed-mode spatiotemporal chaos.

A method is presented for stabilizing and tracking unstable Turing patterns in reaction-diffusion systems. The Gray-Scott model is used to simulate a chemical system exhibiting spatiotemporal chaos arising from the interaction between Turing and Hopf bifurcations. The local behavior of the unstable pattern is first approximated with a single-input, single-output linear model constructed from a time series. A recursive control algorithm is then used to stabilize and track the unstable pattern by monitoring a single point in space and making small adjustments to a global parameter.

Optimal Predictive Control

In the paper a novel predictive control based on a quadratic cost function is presented. The system to be controlled is described by an input-output description, and a reference model that the system to be controlled will follow, is chosen. Then the quadratic cost function minimizes a sequence of the tracking errors between the desired future outputs of the reference model and those of the system. We present in the paper a new formulation of the future output prediction, which allows us to solve the cost function recursively, and achieve recursive control algorithms.

Adaptive control of a single-link flexible manipulator with unknown load

A new adaptive control scheme for the tip position control of a single-link flexible manipulator handling unknown loads and its experimental as well as simulative verification are presented here. The scheme essentially comprises a least-squares identification algorithm and a self-tuning pole placement controller. A novel recursive control algorithm with parameter estimate resetting is developed to eliminate a ‘ring effect’ transient during load release. A performance comparison of the new adaptive controller with a constant-gain pole placement controller as well as a standard self-tuning pole placement controller clearly demonstrates its superior ability in handling load changes in quiescent states. Simulation results also demonstrate that the new control scheme enables the load changes to be carried out in an active state without creating any transients.

The Tracking Capability of the Computed-Torque Type Robot Control Systems

The purpose of this paper is to study the boundedness of the tracking position error of robot controls based on the computed-torque method. It is seen that the nature of the input vector bears heavily on the results: only resolved-acceleration input permits to null the error. The later part of the Paper deals with the robustness of the conventional computed-torque structure and in particular, with a robust recursive control algorithm for robots proposed in a previous paper

The Reverse-Exchange Interconnection Network

Properties of the reverse-exchange interconnection network are used to develop a reconfiguration scheme and a two-pass structure for enhancing the efficiency of a class of multistage interconnection networks. Functional relationships among a class of multistage interconnection networks are first derived. According to the functional relationships, we propose a reconfiguration scheme which enables a network to accomplish various interconnection functions of other networks. Then the admissible permutations along with related recursive control algorithms of the reverse-exchange interconnection network are specified through a set of theorems. Using the reverse-exchange property, we also prove that the algorithms actually work. Finally, we prove that arbitrary permutations can be realized in two passes (or 2 · 1og2N switching steps where N is the network size). By taking advantage of Benes network control algorithms, a way to control the two-pass structure is also developed.