Linear Control Algorithm Research Articles

Design of Buildings with Seismic Isolation Using Linear Quadratic Algorithm

Seismic isolation is a widely accepted control strategy to protect building against earthquakes. The seismic isolation control is a technique that employs a flexible element at the base of a building and allows the resonant frequency of this building being shifted away from the dominant frequency in earthquake excitations. However, large base displacements resulting from the increased flexibility of the seismic isolation system can potentially exceed the design limit of the building subjected to severe earthquake loading. Thus, design codes recommend equipping additive damping devices along with the seismic isolation bearings to lower the base displacements. In this study, a new design method of seismic isolation is developed using the linear quadratic algorithm that concurrently provides the terms of stiffness and damping coefficient. This design method facilitates the linear quadratic regulator control algorithm with output feedback. For a multiple-degree-of-freedom structure, the shear force provided by seismic isolation can be separated from the superstructure and formed as a control input. This control input is a function of the relative displacement and velocity at the isolation layer with a constant stiffness quantity and damping coefficient. This control algorithm provides the opportunity of deriving these two constants. Moreover, the derivation of isolation stiffness and damping coefficient depends on the user-defined weightings that allow adjusting performance of the isolated building in this control algorithm. One example is provided with eight-story buildings as the superstructures. As seen in the result, the root-mean-square responses are quite compatible between isolated buildings with linearly and nonlinearly isolated bearings. Therefore, the proposed method is useful for designing seismic isolation based on a multiple-degree-of-freedom building.

An input–output linearization algorithm‐based control for optimization of DFIG

This paper proposes an input–output linearization‐based active power control strategy to maximize the energy production of a doubly fed induction generator (DFIG)‐based wind energy conversion system (WECS). The DFIG‐based wind turbine is a nonlinear system, and the nonlinear behavior will result in tracking errors. The proposed control strategy utilizing state feedback successfully deals with the nonlinear behavior existing in the WECS. Such a control will linearize the system input and output first. Then, the control loop and parameters can be designed by the linear system control algorithm. The simulations carried in MATLAB/Simulink demonstrate that the proposed control strategy is effective and promising. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Adaptive positioning control of an ultrasonic linear motor system

A 3PRR parallel precision positioning system, driven by three ultrasonic linear motors, was designed for use as the object stage of a scanning electron microscope (SEM). To improve the tracking accuracy of the parallel platform, the positioning control algorithms for the drive joints needed to be studied. The dead-zone phenomenon caused by static friction reduces the trajectory tracking accuracy significantly. Linear control algorithms such as PID (Proportion Integration Differentiation) are unable to compensate effectively for the dead-zone nonlinearity. To address this problem, two types of feedforward compensation control algorithms have been investigated. One is constant feedforward with the integral separation PID; the other is adaptive feedback and feedforward based on the model reference adaptive control (MRAC). Simulations and experiments were conducted using these two control algorithms. The results demonstrated that the constant feedforward with integral separation PID algorithm can compensate for the time-invariant system after identifying the dead-zone depth, while the adaptive feedback and feedforward algorithm is more suitable for the time-varying system. The experimental results show good agreement with the simulation results for these two control algorithms. For the dead-zone nonlinearity caused by the static friction, the adaptive feedback and feedforward algorithm can effectively improve the trajectory tracking accuracy. A positioning system has been built for the driven joints of the 3-PRR in SEM.The dead-zone of the system has been identified and applied to compensation.The proposed control algorithm improves the tracking precision significantly.

Optimization of formation for multi-agent systems based on LQR

In this paper, three optimal linear formation control algorithms are proposed for first-order linear multiagent systems from a linear quadratic regulator (LQR) perspective with cost functions consisting of both interaction energy cost and individual energy cost, because both the collective object (such as formation or consensus) and the individual goal of each agent are very important for the overall system. First, we propose the optimal formation algorithm for first-order multi-agent systems without initial physical couplings. The optimal control parameter matrix of the algorithm is the solution to an algebraic Riccati equation (ARE). It is shown that the matrix is the sum of a Laplacian matrix and a positive definite diagonal matrix. Next, for physically interconnected multi-agent systems, the optimal formation algorithm is presented, and the corresponding parameter matrix is given from the solution to a group of quadratic equations with one unknown. Finally, if the communication topology between agents is fixed, the local feedback gain is obtained from the solution to a quadratic equation with one unknown. The equation is derived from the derivative of the cost function with respect to the local feedback gain. Numerical examples are provided to validate the effectiveness of the proposed approaches and to illustrate the geometrical performances of multi-agent systems.

Linear Matrix Inequality-Based Nonlinear Adaptive Robust Control of Quadrotor

In this paper, we propose a novel linear matrix inequality-based nonlinear adaptive robust control algorithm to design the attitude and position controllers for an X-configuration quadrotor helicopter. The inner loop of the autopilot controls the attitude and altitude of the quadrotor, and the outer loop controls its position in the Earth-fixed coordinate frame. By assuming knowledge of the bounds of the quadrotor’s uncertain parameters (e.g., mass and moments of inertia) and predetermined bounds on the external and unstructured disturbances (e.g., wind gusts and unmodeled dynamics), we attain a guaranteed transient and steady-state tracking performance. We demonstrate the performance of the controllers via two illustrative examples. In the first example mission, the quadrotor follows an altitude reference trajectory in the presence of wind gusts and delivers a package of uncertain mass midflight. The second example presents an autonomous waypoint flight in the presence of wind disturbances. The results of our simulations indicate that our controller design is useful for a variety of quadrotor applications, including precise trajectory tracking, autonomous waypoint navigation in the presence of disturbances, and package delivery without loss of performance.

Performance Evaluation of the Full-Scale Active MassDampers based on a Numerical Model and Test

In this study, the experimental test results are given to confirm the control efficiency of the linear control algorithm used for designing the active mass dampers(AMD) which are supposed to be installed at Incheon international airport control tower. The comparison between the results from test and numerical analysis is conducted and it was observed that the AMD showed the control performance expected by the numerical model. The effects of the gain scheduling and constant-velocity signal added to the control signal calculated by the algorithm is identified through the observation that the AMD always show behavior within the given stroke limit without any loss of the desired control performance. The phase difference between the accelerations of the structure and the AMD were almost close to 90 degree, which implies that the AMD absorbed the structural energy effectively.

Development of a Toolbox in Matlab for Designing Discrete and Continuous-Time Linear Controllers with System Control Application Using Software in the Loop

Throughout the career in Mechatronics Engineering, the necessity to apply control strategies allowing to obtain the desired behaviors in different processes is observed, to perform the design and application of the characteristic parameters of each linear strategies in continuous or discrete time and be implemented in a SISO-type final system. Therefore, the controller designer must spend a lot of time in developing algorithms to calculate these parameters quickly and efficiently, but these algorithms could be implemented mistakenly caused an application of erroneous controllers in the processes. For the previous reason, this paper describes the development and condensation of linear control algorithms in MATLAB® toolbox that allows the calculation of different control strategies in continuous and discrete time. Besides it has a number of features such as friendly graphical user interface, robust algorithms, robustness verification of the system and implementation of the designed control system in software in the loop to verify its efficacy and efficiency.

MFC Sensors and Actuators in Active Vibration Control of the Circular Plate

Abstract In this paper, the MFC sensor and actuators are applied to suppress circular plate vibrations. It is assumed that the system to be regulated is unknown. The mathematical model of the plate was obtained on the base of registration of a system response on a fixed excitation. For the estimation of the system’s behaviour the ARX identification method was used to derive the linear model in the form of a transfer function of the order nine. The obtained model is then used to develop the linear feedback control algorithm for the cancellation of vibration by using the MFC star-shaped actuator (SIMO system). The MFC elements location is dealt with in this study with the use of a laser scanning vibrometer. The control schemes presented have the ability to compute the control effort and to apply it to the actuator within one sampling period. This control scheme is then illustrated through some numerical examples with simulations modelling the designed controller. The paper also describes the experimental results of the designed control system. Finally, the results obtained for the considered plate show that in the chosen frequency limit the designed structure of a closed-loop system with MFC elements provides a substantial vibration suppression.

Sintonización de controladores Pareto-óptimo robustos para sistemas multivariables. Aplicación en un helicóptero de 2 grados de libertad

The tuning of Pareto-optimal robust controllers was applied to improve the performance of a helicopter with two-degrees-of-freedom with a linear control algorithm. The tuning procedure is based on the simultaneous minimization of the integral of square sum of errors and the integral of square sum of control action. A 2D Pareto front is built with these integrals. Afterwards, a decision-making process is carried out to select the most preferable controller. Experimental results on the physical platform validate the tuning procedure as practical and reliable.

Pole-placement self-tuning control of nonlinear Hammerstein system and its application to pH process control

By taking advantage of the separation characteristics of nonlinear gain and dynamic sector inside a Hammerstein model, a novel pole placement self tuning control scheme for nonlinear Hammerstein system was put forward based on the linear system pole placement self tuning control algorithm. And the nonlinear Hammerstein system pole placement self tuning control (NL-PP-STC) algorithm was presented in detail. The identification ability of its parameter estimation algorithm of NL-PP-STC was analyzed, which was always identifiable in closed loop. Two particular problems including the selection of poles and the on-line estimation of model parameters, which may be met in applications of NL-PP-STC to real process control, were discussed. The control simulation of a strong nonlinear pH neutralization process was carried out and good control performance was achieved.

Infinite horizon optimal repetitive control of fractional-order linear systems

This paper presents a linear quadratic regulator-based repetitive control algorithm for fractional-order linear systems. First, a new repetitive control configuration for fractional-order linear system is proposed that contains a dynamic compensator and a state-feedback controller. Next, using fractional variational principle, the analytical solution for optimal repetitive controller is presented and the parameters of both the feedback controller and dynamic compensator are designed simultaneously. For the case of infinite time horizon, and under assumption of being in the middle of the control process the algorithm has the same form as for integer order case. Furthermore, new tuning parameters are introduced to modify the algorithm when the system is not exactly at the middle of the control process. Finally, a numerical example demonstrates the validity of the proposed approach.

Active vibration control of nanotube structures under a moving nanoparticle based on the nonlocal continuum theories

The active vibration control of nanotubes under action of a moving nanoscale particle is carried out using nonlocal elasticity theory of Eringen. The nanotube is simulated by an equivalent continuum structure under simply supported boundary conditions within the framework of nonlocal Rayleigh as well as Timoshenko beam theory. A Dirac-delta function is applied to model the location of the moving mass along the nanotube as well as its inertial effects. In the following a linear classical optimal control algorithm with a time varying gain matrix and displacement-velocity feedback is applied to vibration suppression in nanotube structure. The effects of the moving nanoparticle velocity, slenderness ratio of nanotube and small scale effect parameter on the dynamic deflection are studied in some detail for both the Rayleigh and Timoshenko theories. Finally the proficiency of the control algorithm in suppressing the response of the nanostructure under the effect of moving nanoparticle with different number of controlled modes and control forces is studied. The results of the present work can be used as a benchmark in future studies of nanomachines and nanosystems.

Development of a coupled analysis regarding the rotor/dynamic components of a rotorcraft

This paper presents a combined analysis for the rotor and dynamic components of a rotorcraft. The dynamic components consist of the following elements: a rotor shaft, a drive train, the engine shafts, and an engine and its governor. In this paper, the dynamic components were developed in a modularized fashion and combined with the rotor analysis. The present rotor structural analysis was derived based on the mixed variational formulation of moving beams and combined with finite-state dynamic inflow aerodynamics. A linear mass-spring-damper connection was used for a drive train representation and a simple linear control algorithm was used for an engine governor. To analyze the response of the components, a state-space equation was established based on the torque equilibrium. The present multi-component structural and aerodynamic analysis was solved for by measuring the steady-state trim and time-transient response. Numerical validation was performed using a sample hingeless rotor in a tiltrotor aircraft. The present prediction showed good agreement with CAMRAD II for both the trim analysis and the transient analysis with the trimmed state. And distinctions between the rotor with and without dynamic components were verified. Thus, an accurate framework for the rotor system including the dynamic components was developed, which would be useful during the preliminary design stage of creating a rotorcraft.

Passive control of along-wind response of tall building

Most of modern tall buildings using lighter construction materials with high strength and less stiffness are more flexible, which occurs excessive wind-induced vibration, resulting in occupant discomfort and structural unsafety. It is necessary to predict wind-induced vibration response and find out a method to mitigate such an excessive wind-induced vibration at the preliminary design stage. Recently, many studies have been conducted in using actuator control force based on the linear quadratic optimum control algorithm. It was accepted as a common knowledge that the performance of passive tuned mass damper (TMD) could increase by incorporating a feedback active control force in the design of TMD, which is called active tuned mass damper (ATMD). However, the fact that ATMD is superior to TMD to reduce wind-induced vibration of a tall building is still a question. The effectiveness of TMD for mitigating the along-wind vibration of a tall building was investigated. Optimum parameters of tuning frequency and damping ratio for TMD under a random load which has a white noise spectra were used. Fluctuating along-wind load acting on a tall building treated as a stationary Gaussian random process was simulated numerically using the along-wind load spectra. And using this simulated along-wind load, along-wind responses of a tall building with and without TMD were calculated and the effectiveness of TMD in mitigating the along-wind response of a tall building was found out.

Linear Motor Control Algorithm and Experimental Research Based on Feedforward Fuzzy PID

In this paper, theory analysis, the MATLAB research and experimental verification about feedforward fuzzy PID control have been performed by combining the characteristics of the PID, feedforward control and fuzzy control. Simulation results show that the feedforward fuzzy PID control could improve the response speed of the system and reduce the tracking error of the system which shows the obvious superiority compared with the PID, feedforward PID, and fuzzy PID. Load experiment for such four kinds of control modes is done on the linear motor platform, and the experimental results show that the accuracy of the feedforward fuzzy PID control is obviously higher than the other three kinds of control modes and the feedforward fuzzy PID control is easier to be implemented. The position error of feedforward fuzzy PID control is changeless during the load change, and the change of the speed tracking error is small, which proves that the feedforward fuzzy PID control is suitable for the condition of load change or the great disturbance.

Modeling and active vibration suppression of a single-walled carbon nanotube subjected to a moving harmonic load based on a nonlocal elasticity theory

This paper investigates active vibration suppression of a single-walled carbon nanotube (SWCNT) under the action of a moving harmonic load using Eringen’s nonlocal elasticity theory. The SWCNT is modeled according to the nonlocal Euler–Bernoulli beam theory. A Dirac-delta function is used to describe the position of the moving load along the SWCNT. Next, a linear classical optimal control algorithm with displacement-velocity feedback is used to suppress vibration in the SWCNT with control forces acting as actuators. The effects of a small-scale parameter, slenderness ratio, moving load velocity, and the excitation frequency of a moving load on the dynamic deflection of the SWCNT are examined. Finally, the ability of the control algorithm to suppress the response of the SWCNT under the effects of a moving load with a number of controlled modes and control forces is surveyed.

Integrated Multimodel Control of Nonlinear Systems Based on Gap Metric and Stability Margin

To avoid linear model redundancy and simplify the structure of a multimodel controller, two general integrated multimodel control design frameworks, which integrate the multimodel decomposition and the multimodel combination of a nonlinear system, are proposed based on the gap metric and stability margin criteria. One method uses the maximum stability margin (which is comparatively controller-independent) while the other uses the actual stability margin of a given controller design. For a prescribed linear control algorithm for local controller design, a smaller and better linear model bank that provides necessary information for multimodel controller design is obtained systematically without model redundancy. Besides, the local robust stability and performance of the system in each subregion can be achieved by the corresponding local controller. Many linear control techniques can be used in the proposed design frameworks, and H∞ control algorithm is employed as an example and applied to two benchmark nonlinear chemical processes for set point tracking and disturbance rejection control. Closed-loop simulations demonstrate that the proposed approaches are both systematic and effective and are better than the traditional multimodel control methods in terms of robust performance.

A Simplified Finite-Control-Set Model-Predictive Control for Power Converters

Finite-control-set model-predictive control (FCS-MPC) requires a large amount of calculation, which is an obstacle for its application. However, compared with the classical linear control algorithm, FCS-MPC requires a shorter control loop cycle time to reach the same control performance. To resolve this contradiction, this paper presents an effective method to simplify the conventional FCS-MPC. With equivalent transformation and specialized sector distribution method, the computation load of FCS-MPC is greatly reduced while the control performance is not affected. The proposed method can be used in various circuit topologies and cases with multiple constraints. Experiments on two-level converter and three-level NPC converter verify the good performance and application value of the proposed method.

A new active control performance index for vibration control of three-dimensional structures

Remarkable results have been reported about conventional active control algorithms during the last 30years, but nearly all the existing literature considers 2-dimensional in plane structures to implement and verify the active control algorithms. To simulate the behavior of real buildings more accurately, more realistic and complex models should be used in the performance evaluation and design of controllers and their control algorithms. This paper presents a new performance index for active vibration control of three-dimensional structures. To analytically validate the proposed performance index, a six story three-dimensional structure is considered as an example with a fully active tendon controller system implemented in one direction of the building. Tier building formulation is used for three-dimensional dynamic analysis. The building is modeled as a structure composed of members connected by a rigid floor diaphragm such that it has three degrees of freedom at each floor, i.e., lateral displacements in two perpendicular directions and a rotation with respect to a vertical axis for the third dimension. The performance of the building with the active tendons controlled using a classical linear optimal control algorithm is compared to the performance of the proposed control algorithm under several far-fault and near-fault earthquakes using several performance measures. Comparison between the computational results shows that the proposed algorithm outperforms the performance of the classical linear optimal control algorithm for the actively controlled building.

Design of the Embedded Control System of Laser Engraving Machine

The control system of laser engraving machine based on ARM processor realize the precise control of the two-dimensional stepping motor and the laser head. This article focuses on the proposed stepping motor speed and trajectory control algorithm, and meanwhile, the speed control adopt linear acceleration and deceleration control algorithm; Trajectory control, based on the traditional point by point comparison arc interpolation method, puts forward the improved algorithm which can effectively improve the interpolation speed and interpolation accuracy. The experimental results show that the method can improve the machining precision and machining efficiency of laser engraving machine, and also can realize the high precision carving.