Linear Quadratic Regulator Control Algorithm Research Articles

GA-LQR for vehicle semi-active suspension with BiLSTM inverse model of magnetic rheological damper

This paper proposes a magnetic rheological (MR) semi-active control method based on bidirectional long short-term memory (BiLSTM) neural network, linear quadratic regulator (LQR) control algorithm, and genetic algorithm (GA). The LQR algorithm with GA optimizing the weight coefficients generates the expected damping force. Due to the nonlinear hysteresis characteristics of the magnetic rheological damper (MRD) and the fact that its input and output have certain time dependence, an inverse model of MRD is established by BiLSTM. The control current is predicted by BiLSTM and then the current is input to the MRD to obtain the damping force that is infinitely close to the expected damping force. The damping force is then applied to the suspension system to form a complete closed-loop feedback control, which realizes the damping effect and generates a real-time control. The simulation results show that the MRD inverse model can accurately predict the required control current, and the GA-optimized LQR control algorithm has a good suppression effect on the vertical vehicle acceleration, dynamic tire load, and suspension dynamic stroke.

Robust servo linear quadratic regulator controller based on state compensation and velocity feedforward of the spherical robot: Theory and experimental verification

There are few studies on the lateral motion of spherical robots. In this article, a new algorithm is proposed to solve the problem of low control accuracy of the lateral motion. A single lateral motion model is established, and the optimal solution of the linear quadratic regulator in infinite time domain is obtained. Aiming at the problems of longitudinal velocity and lateral angle coupling and low control precision, state compensation and velocity feedforward are carried out, and an improved robust servo linear quadratic regulator control algorithm is proposed. Experiments show that the proposed lateral control algorithm has strong adaptability and robustness to changing speeds and lateral angles, and the control effect is stable and reliable.

Seismic Response Control of Structures with Stiffness Irregularities through Optimally Placed Active Tendons using Multiobjective Genetic Algorithm

This paper studied the seismic response control of structural building with stiffness irregularities through active tendon system (ATS) using Linear Quadratic Regulator control algorithm. The various responses considered are the floor displacements, story drifts, and base shear. The optimal number and the optimal position of these active tendons are obtained through multiobjective optimization using Genetic Algorithm to reduce the responses and the cost of the control system simultaneously. The conflicting objectives minimized are the base shear of the irregular building and the number of active tendons to be used. The maximum story drift and maximum floor displacement are used as constraints. For numerical results, six combinations of stiffness irregularity in critical storys 1,2,and 10 of a ten story defecient shear building frame subjected to El Centro earthquake is considered. The results show that the optimized control system is capable of keeping the responses of the building frame to an earthquake within permissible limits and stiffness irregularity in the same defecient frame cost only the tendon in atmost one additional story.

New control strategy for suppressing the local vibration of sandwich beams based on the wave propagation method

The general vibration control strategy of beam structures is a global vibration control method based on the principle of modal superposition. However, the vibration wave control of beams can achieve local control of the vibration energy. This paper presents a wave control method for the local vibration control of fractional viscoelastic composite beams based on the operating principle of a piezoelectric sheet. To obtain better control performance, a particle swarm optimization algorithm was adopted to optimize the parameters of the piezoelectric sheet. A linear quadratic regulator control algorithm was designed to verify the validity of the proposed method. In addition, the effects of the piezoelectric sheet number and fractional order on the amplitude response and optimization parameters were investigated. We observed that the proposed method has a good control effect on the local area vibration, and it can control the flow direction of the vibration power. The proposed method can be used to directly design the voltage and phase of a piezoelectric sheet without real-time feedback computation. This method is suitable for reducing local vibration under single repetitive operating conditions in engineering and can provide a theoretical basis for a follow-up study on the acoustic black hole phenomenon.

Relative Performance of Linear Quadratic Regulator and Pole Placement Technique for Active Seismic Control of Structures

This paper presents the study conducted on the comparison of the performance of the two popular active control algorithms viz. Linear Quadratic Regulator (LQR) and Pole Placement technique in terms of their capability to alleviate the response of a structure to an earthquake. To compare the performance of the two control algorithms, a ten story regular shear building frame with three active tendons located in 1st, 4th and 5th Storys and subjected to an El Centro earthquake has been considered. A comparison of the numerical results shows that the reductions of maximum top floor displacement, maximum story drift and base shear obtained using LQR control algorithm are 71.48%, 59.70% and 62.7% while the reductions obtained using Pole Placement technique are 73.77%, 73.14% and 77% respectively. The percentage reduction of the three performance parameters per unit control force obtained using the two methods have also been estimated and compared. Pole placement technique gives higher reduction while the LQR algorithm gives more reduction per unit control force.

An improved linear quadratic regulator control method through convolutional neural network–based vibration identification

An efficient vibration control can reduce negative effects induced by environmental vibrations and thereby improve the performance of precision instruments and the qualities of manufacture. The performance of the widely used linear quadratic regulator control algorithm, a classical active control methodology, depends on the parameters of the control algorithm. Consequently, a set of fixed parameters cannot satisfy the demand for controlling various types of environmental vibrations. Therefore, this study proposes a vibration identification method based on a convolutional neural network. This method helps to optimize the linear quadratic regulator algorithm by selecting corresponding optimal parameters according to the identification results, thereby achieving the objective of optimal control subjected to various types of vibration inputs. Specifically, environmental vibration signals are collected, and the preliminary features of the vibrations (i.e. wavelet coefficient matrices or images) are adopted as input samples for the convolutional neural network. A genetic algorithm is used to optimize the parameters of the linear quadratic regulator algorithm for each type of vibration; subsequently, the trained convolutional neural network model with the best performance is used to identify the vibration and select the corresponding optimal parameters of the linear quadratic regulator algorithm under different types of vibration inputs. Case studies show that the performance of the improved linear quadratic regulator control method is significantly better than that of the conventional linear quadratic regulator algorithm with fixed parameters.

Seismic control performance indices for magneto-rheological dampers considering simple soil-structure interaction

In this study, two instantaneous optimal control performance indices for seismic control of structures incorporating magneto-rheological (MR) dampers are analytically defined. One of the time dependent performance index uses conventional state vector considering simple soil structure interaction (SSI). However, absolute displacement and absolute velocities are added to the conventional state vector terms and eventually to the other one. SSI effects are also included simply in the second performance index. The response reduction performance of these simple indices is compared with the linear quadratic regulator control (LQR). A three story ¼-scaled structure incorporating an MR damper is taken into account as a numerical example. The power requirement of the MR damper is considered by using an MR damper model which is piece wise invertible. It is obtained from numerical results that the proposed performance indices are as effective as LQR algorithm in uncontrolled seismic structural response reduction performance. However taking SSI effects into account increases structural responses and decreases control effectiveness slightly.

LQR optimal control research for four-wheel steering forklift based-on state feedback

Taking the steering performance of four-wheel steering (4WS) forklift as the research object, based on two degrees of freedom (2DOF) model and three degree of freedom (3DOF) model of 4WS system, combined with the characteristics and steering requirements of forklift, the Linear Quadratic Regulator (LQR) optimization control algorithm based on state feedback is proposed, and the solution of LQR control algorithm for the 4WS forklift is presented. The simulation analyses of the steering performance of proportional control 4WS, LQR control 4WS and rear wheel steering (RWS) control are given. The simulation results show that the comprehensive effect of LQR optimal control is better, and it effectively improves the flexibility and the handling stability of 4WS forklift.

Use of active control algorithm for optimal design of base-isolated buildings against earthquakes

This study presents a new design method that concurrently determines the stiffness and damping coefficient in a base isolation system. This design method is developed based on the similarity between the active and passive control system. Then, the stiffness and damping coefficient are derived from the linear quadratic regulator control algorithm to a single degree of freedom superstructure and formed as a function of single weighting. The best design of a base isolation system is determined by optimizing this weighting from the minimum H∞-norm responses of base displacement and roof acceleration. A parametric study is performed to understand the influence of superstructures to the resulting optimized base isolation system. Moreover, this study also provides a numerical example to validate the optimal design of base isolation systems. The potential to design nonlinear lead-rubber bearings with added viscous dampers based on the proposed method is also investigated. As a result, the proposed method yields a high-performance base isolation system for a known superstructure.

Linear quadratic regulator for laser beam shaping

The performance of an adaptive optics system depends on multiple factors, including the quality of the laser beam before being projected to the mesosphere. In general, cumbersome procedures are required to optimize the laser beam in terms of amplitude and phase. However, aberrations produced by the optics of the laser beam system are still detected during the operations due to, for example, uncertainty in the utilized models. In this paper we propose the use of feedback to overcome the presence of model uncertainty and disturbances. In particular we use a Linear Quadratic Regulator (LQR) for closed loop laser beam shaping using a setup of two deformable mirrors. The proposed method is studied and simulated to provide an automatic optimization of the Amplitude of the laser beam. The performance of the LQR control algorithm is evaluated via numerical simulations using the root mean square error (RMSE). The results show an effective amplitude correction of the laser system aberrations after 20 iterations of the algorithm, a RMSE less than 0.7 was obtained, with about 140 actuators per mirror and a separation of z=3 [m] among the mirrors.

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.

Study on LQR control algorithm using superelement model

The conventional linear quadratic regulator (LQR) control algorithm is one of the most popular active control algorithms. One important issue for LQR control algorithm is the reduction of structure’s degrees of freedom (DOF). In this work, an LQR control algorithm with superelement model is intended to solve this issue leading to the fact that LQR control algorithm can be used in large finite element (FE) model for structure. In proposed model, the Craig-Bampton (C-B) method, which is one of the component mode syntheses (CMS), is used to establish superelement modeling to reduce structure’s DOF and applied to LQR control algorithm to calculate Kalman gain matrix and obtain control forces. And then, the control forces are applied to original structure to simulate the responses of structure by vibration control. And some examples are given. The results show the computational efficiency of proposed model using synthesized models is higher than that of the classical method of LQR control when the DOF of structure is large. And the accuracy of proposed model is well. Meanwhile, the results show that the proposed control has more effects of vibration absorption on the ground structures than underground structures.

Development of Frequency-dependent Optimal Control in Independent Modal Space

In this study, a frequency dependent algorithm is proposed in the independent modal space as an improvement to the linear quadratic regulator control algorithm. The passive control parameters such as mass, stiffness and damping of a dynamic system are sensitive to different frequency ratio when subjected to external excitation. Depending upon the sensitivity of these parameters, the algorithm is developed in such a way that the similar response reduction as that of a linear quadratic regulator can be achieved with a significantly smaller gain. The optimal gain is obtained by optimizing the H 2 norm of the transfer function. It is observed from the results that the algorithm works well for high frequency ratio and near resonance regimes. The efficiency of the proposed algorithm is demonstrated by considering a base isolated structure when subjected to a narrow band base excitation. By comparing with the results from linear quadratic regulator control, it is observed that the proposed algorithm is more efficient in terms of displacement response and optimal gain. It is envisioned that the proposed algorithm will be highly useful for response control of base isolated structures.

Control of structures under uniform hazard earthquake excitation via wavelet analysis and pattern search method

A new methodology for optimal control of structures under uniform hazard earthquake excitation has been presented in this study. The proposed method for generation of uniform hazard earthquake accelerograms is based on the sets of ground motions developed for the SAC Steel Project. The proposed controller employs the decomposing capabilities of wavelet analysis on uniform hazard earthquake accelerograms and the ability of the pattern search method to optimize a cost function to control response of structure. The performance and effectiveness of the presented method are applied to both single degree of freedom and multiple degree of freedom systems for the response control of uniform hazard earthquake-excited systems. The results are compared with the linear quadratic regulator control algorithm; performance of the proposed control system has been found to be better than the linear quadratic regulator controller. Copyright © 2012 John Wiley & Sons, Ltd.

On modal energy in civil structural control

A new control strategy based on modal energy criterion is proposed to demonstrate the effectiveness of the control system in reducing structural earthquake responses. The modal control algorithm combining LQR (linear quadratic regulator) control algorithm is adopted in the discrete time-history analysis. The various modal energy forms are derived by definition of the generalized absolute displacement vector. A preliminary numerical study of the effectiveness of this control strategy is carried out on a 20-storey framed steel structural model. The controlled performance of the model is studied from the perspectives of both response and modal energy. Results show that the modal energy-based control strategy is very effective in reducing structural responses as well as in consuming a large amount of modal energy, while augmentation of additional generalized control force corresponding to the modes that contain little modal energy is unnecessary, as it does little help to improve the controlled structural performance.

Design of a stability augmentation system for a helicopter using LQR control and ADS‐33 handling qualities specifications

Purpose – This paper aims to present the design of a stability augmentation system (SAS) in the longitudinal and lateral axes for an unstable helicopter. Design/methodology/approach – The feedback controller is designed using linear quadratic regulator (LQR) control with full state feedback and LQR with output feedback approaches. SAS is designed to meet the handling qualities specification known as Aeronautical Design Standard (ADS-33E-PRF). A helicopter having a soft inplane four-bladed hingeless main rotor and a four-bladed tail rotor with conventional mechanical controls is used for the simulation studies. In the simulation studies, the helicopter is trimmed at hover, low speeds and forward speeds flight conditions. The performance of the helicopter SAS schemes are assessed with respect to the requirements of ADS-33E-PRF. Findings – The SAS in the longitudinal axis meets the requirement of the Level 1 handling quality specifications in hover and low speed as well as for forward speed flight conditions. The SAS in the lateral axis meets the requirement of the Level 2 handling quality specifications in both hover and low speed as well as for forward speed flight conditions. The requirements of the inter axis coupling is also met and shown for the coupled dynamics case. The SAS in lateral axis may require an additional control augmentation system or adaptive control to meet the Level 1 requirements. Originality/value – The study shows that the design of a SAS using LQR control algorithm with full state and output feedbacks can be used to meet ADS-33 handling quality specifications.