LQR Approach Research Articles

Path tracking control for autonomous vehicles using hybrid fault-tolerant approach

Signal delay, execution deviation and reference model mismatch are common faults in autonomous vehicles, resulting in reduced path tracking control performance. To improve the path tracking performance of autonomous vehicles under fault conditions, this paper proposes a hybrid fault-tolerant (HFT) path tracking control approach, in which passive fault-tolerant path tracking control and fault observer-based hybrid active fault-tolerant path tracking control are introduced. The probable usual errors in path tracking are first examined and analyzed, together with the vehicle kinematic model and a typical autonomous driving system. Then, a slide-mode-based passive fault-tolerant path tracking controller is designed and integrated with a fault observer to create a hybrid active fault-tolerant controller. Finally, simulations and experiments are conducted, and the results demonstrate that our proposal is effective. After convergence of the fault observations, the lateral tracking error is less than 0.2m and the root mean square of the tracking error is 44% smaller than the LQR approach.

Event-Based Attack Detection and Mitigation for DC Microgrids via Adaptive LQR Approach

Event-Based Attack Detection and Mitigation for DC Microgrids via Adaptive LQR Approach

Power System Stability Improvement by LQR Approach and PSS Considering Electric Vehicle as Disturbance

Low frequency oscillations result due to heavy loading conditions line faults, sudden change of generator output and also due to poor damping of interconnected power systems. There are different types of disturbances in the power system like sudden change of load, generation, faults, switching of lines. This hampers the power transmission capacity of the lines and the stability of the system There are significant impacts on the system stability during the charging and discharging operation of Electric Vehicle (EV). In the present work the charging operation of EV is considered as a load disturbance. The introduction of these vehicles in the system creates the problem of low frequency oscillation and endanger the system stability and security. In the present work the Single machine infinite bus system (SMIB) is first developed using mathematical modelling with consideration of EV disturbance. The LQR approach from optimal control theory is then applied in the system to damp the system oscillations, improving the system eigenvalues and enhancing the stability. The stability is seen in the system after LQR from various figures. In the second work the plotting of variation of different state variables is done using three different methods which are the transfer function model method, using code and then using state space representation of the system. The work is further extended by adding Power system stabilizer (PSS) to the system, again considering the EV disturbance. The time domain simulation results showed the improvement in stability using PSS device. Thus, in the present work the oscillations problems created due to the introduction of electric vehicles are solved by two methods. The first is implementing LQR approach from optimal control theory in the system and the second method is by adding PSS device in the same system.

Integration of Feedback Control with Feedforward Control for Trajectory Tracking Improvements for Very Fast Microscale Systems

Abstract— This article presents three control schemes: (i) feedback control method using LQR approach, (ii) inversionbased feedforward control method, and (iii) integration of the feedback control method with the feedforward control method, which is a control system that combines a feedback control method with a feedforward approach. Each control scheme is implemented to track two types of desired trajectories: triangle wave trajectory and sawtooth wave trajectory of the same frequency of 200 Hz and the same amplitude of 5 µm. The tracking is challenging in that the system is very fast, and the motion takes microscale amplitudes. The performance of tracking for each control method is evaluated by the quantifying tracking errors. The main contributions of this article are to show that: (i) the feedback control method cannot track the desired trajectories properly, and tracking errors are perhaps not acceptable in some applications, (ii) the feedforward method can substantially improve the performance of tracking as it is compared to that of the feedback approach, and (iii) integration of the feedback control scheme with the feedforward control scheme can further enhance the tracking of the trajectories and can achieve the best performance of tracking. The integration of the feedback control method with the feedforward control method can be effectively used in case good tracking is needed. Keywords— feedback control method, feedforward control method, LQR, reduced order inverse scheme, trajectory tracking, very fast microscale systems

Vibration reduction control by a cable actuation system for reflector antenna

Vibration deformation of a reflector antenna under a moving load will reduce pointing performance. Current vibration suppression technology for reflector antennas, such as the application of mesh reflector antennas, the construction of large radomes, the use of antennas with high stiffness, and the improvement of the shaft servo systems, can reduce the impact of vibrations. However, the disadvantages of high-frequency transmission, high cost, increased weight, and servo bandwidth limitations, are unavoidable. A cable actuation system is proposed as a method for reducing the vibration of reflector antennas while having little influence on the original structure. In this method, the acceleration of the reflector is measured, and an unbiased minimum variance estimator of the system state is introduced to observe the vibration state of the reflector. Then using the LQR approach, drivers on the slide rail pull the cables to suppress the vibration of the reflector. Moreover, the position of the drivers on the slide rail can be adjusted depending on the moving load condition. Finally, the experimental results show that the vibration time of the reflector without control was approximately 7 s, while the vibration time of the reflector with control was reduced to approximately 1 s when the pendulum fell from the same height to excite the reflector.

Global optimization control for nonlinear full‐car active suspension system with multi‐performances

In this article, based on feedback linearized approach and linear quadratic regulator optimization control approach using particle swarm optimization, the almost disturbance decoupling, input amplitude reduction, tuning parameter optimization, controllable convergence rate, improved suspension and globally exponential stability multi-performances of highly nonlinear multi-input multi-output full-car uncertain system are simultaneously achieved without applying any nonlinear function approximator including neural network approach and fuzzy logic approach. The article proposes a new method to achieve the optimal control matrices of LQR such that the composite controller can reduce the amplitudes of system control inputs. Determination of the LQR tuning parameters is conventionally determined via trial and error approach. In addition to being very troublesome, it is difficult to find the globally best tuning matrices with LQR method. This study has first proposed the convergence rate formula of the nonlinear system response as the fitness function of LQR approach by using PSO optimization algorithm to take the place of the conventional trial and error method and locally Jacobian linearized approach under the guarantee of globally exponential stability. The simulation results show how the full-car system can be controlled optimally and satisfactorily and confirm the superiority of the proposed method.

Protection from overturning of rigid block‐like objects with linear quadratic regulator active control

In recent years, several studies proposed new techniques aimed at improving the performances of rigid block-like objects under base excitation. The majority of these studies considered passive control methods, such as base isolation or other techniques based on the tuned mass damper principle. Only few studies considered active and semi-active control methods applied to the dynamics of rigid blocks. This paper proposes an active control method for symmetric rigid blocks that is based on the LQR approach. The optimal control law is obtained starting from the linearized equation of motion. The effectiveness of the proposed control method is investigated comparing the behaviour of rigid blocks with and without active control under harmonic and seismic excitation. The results are summarized in overturning spectra, in the case of harmonic excitation, and rocking maps, in the case of seismic excitation. Although the proposed active control method is expected to work well for slender blocks, specific analyses show that the method also improves the dynamics of no-slender blocks and is effective for blocks with different geometrical characteristics. Moreover, the results show that the control law has a good robustness with respect to the sampling time and the time delay.

Robust finite‐horizon optimal control of autonomous helicopters in aggressive maneuvering

AbstractThere has been an increasing need for autonomous helicopters to have the ability to perform aggressive maneuvers. To achieve this, robust and high performance controllers are required to accurately drive the helicopters. In this paper, the robust compensator (RC) technique is applied to the classic finite‐horizon LQR approach to deal with the uncertainties, including nonlinearities, external disturbances, and other interference. The robust properties of the proposed method are analyzed, and it is proved that the RC can eliminate the effects of the uncertainties as expected. The effectiveness of the proposed method is shown through simulations and real experiments of a prototype helicopter.

Improve Linear Quadratic Regulator by Particle Swarm Optimization Algorithms for Two Wheeled Self Balancing Mobile robot

The aim of this paper is to suggest a methodical smooth control method for improving the stability of two wheeled self-balancing robot under effect disturbance. To promote the stability of the robot, the design of linear quadratic regulator using particle swarm optimization (PSO) method and adaptive particle swarm optimization (APSO). The computation of optimal multivariable feedback control is traditionally by LQR approach by Riccati equation. Regrettably, the method as yet has a trial and error approach when selecting parameters, particularly tuning the Q and R elements of the weight matrices. Therefore, an intelligent numerical method to solve this problem is suggested by depending PSO and APSO algorithm. To appraise the effectiveness of the suggested method, The Simulation result displays that the numerical method makes the system stable and minimizes processing time.

Relative Stability Analysis of Perturbed Cart Inverted Pendulum: An Experimental Approach

ABSTRACTIn this paper, generalized form of transfer function model of a cart inverted pendulum system is presented. Furthermore, robustness analysis of PID-based cart inverted pendulum using LQR approach and SBL approach are carried out using Krishnamurthi's corollary on Routh criterion by considering variations in cart mass, pendulum length, and also applied force to the cart. Here, the mathematical formula is developed which provides limit for the mass of cart before the pendulum becomes unstable. The most important advantage of the proposed approach is that the analysis is carried using classical approach without using advanced robust control techniques. The results have been verified on a hardware set-up of cart inverted pendulum system. Finally, practical issues have been identified by comparing simulation and hardware results. The results can be expected to be useful in other real-time applications.

Guaranteeing Constraints of Disturbed Nonlinear Systems Using Set-Based Optimal Control in Generator Space

We address the problem of finding an optimal solution for a nonlinear system for a set of initial states rather than just for a single initial state. In addition, we consider state and input constraints as well as a set of possible disturbances. While previous optimal control techniques typically ignore the fact that the current state of a system is not exactly known, future safety-critical systems demand that all uncertainties including the initial state are considered; this is required for e.g. automated vehicles, surgical robots, or human-robot interaction. We present a new method that obtains optimal control inputs by finding optimal weights for generators that span the space reachable by the considered system. This solution routine can be used not only for a single initial state but also for a set of initial states - this is not possible using classical optimization techniques. We ensure that all constraints are met by using reachability analysis, which provides formal bounds for all possible system trajectories. We demonstrate the applicability of our approach with an example from automated driving; for this example, the result is obtained within a few seconds and outperforms a classical LQR approach.

Reduced-Order Distributed Consensus Controller Design via Edge Dynamics

This paper proposes a novel approach to design reduced-order distributed consensus controllers for multi-agent systems (MASs) with identical linear dynamics of agents. A new model namely edge dynamics representing the differences on agents' states is first presented. Then the distributed consensus controller design is shown to be equivalent to the synthesis of a distributed stabilizing controller for this edge dynamics. Consequently, based on LQR approach, the globally optimal and locally optimal distributed stabilizing controller designs are proposed, of which the locally distributed stabilizing controller for the edge dynamics results in a distributed consensus controller for the MAS with no conservative bound on the coupling strength. This approach is next further developed to obtain reduced-order distributed consensus controllers for linear MASs. Several numerical examples are introduced to illustrate the theoretical results.

Digital and analog integer delayed modeling and control for multivariable systems with multiple time delays in states, inputs and outputs

This paper presents a new approximated integer delayed modeling and control technique for Continuous-time Fractional Delay Differential Equations (CFDDEs). Using the impulse response sequences of the CFDDE and the balanced model-reduction method, a delay-free discrete-time state-space model is constructed. Then, an equivalent Discrete-time Integer Delay Difference Equation (DIDDE) is obtained by transforming the obtained discrete-time state-space model into a controller-type block companion form. Furthermore, based on the obtained DIDDE, an equivalent Continuous-time Integer Delay Differential Equation (CIDDE) is determined by means of the newly developed Chebyshev's bilinear approximation method. For digital control of the CFDDE, an optimal Discrete-time Integer Delayed Control Law (DIDCL) is designed using the conventional discrete-time LQR approach together with the obtained delay-free discrete-time state-space model. On the other hand, for continuous-time control of the CFDDE, a Continuous-time Integer Delayed Control Law (CIDCL) is determined from the designed DIDCL by means of the inverse Chebyshev's bilinear approximation method. Finally, digital and analog integer delayed observers are constructed for the implementations of the developed DIDCL and CIDCL, respectively. An illustrative example is given to demonstrate the effectiveness of the proposed method.

A sub-optimal consensus design for multi-agent systems based on hierarchical LQR

This paper presents a new and systematic procedure to design sub-optimal hierarchical feedback controllers for the leader–follower consensus problem in homogeneous multi-agent systems. First, the given multi-agent system is treated as a two-layer hierarchical system where the agents perform local actions in the lower layer and interact with others in the upper layer to achieve some global goals. Then the consensus controller design is formulated as a hierarchical state feedback control problem. Employing LQR approach with an appropriately selected performance index, an optimal hierarchical state feedback controller is derived which includes two terms namely local and global terms. Consequently, by removing the local term, the remaining global term is proved to make the multi-agent system consensus which results in a sub-optimal hierarchical consensus controller. Finally, some numerical examples are introduced to illustrate the effectiveness of the proposed method.

Fault-Tolerant Control of FWIA Electric Ground Vehicles with Differential Drive Assisted Steering

This paper investigates a novel fault-tolerant control approach against active steering system failure based on differential drive assisted steering (DDAS) on four-wheel independently actuated (FWIA) electric ground vehicles. The front-wheel steering angle can be generated with the front-wheel differential driving torque when the steering motor fails. DDAS being the only steering power source is a potential alternative to replace the regular steering system in defective situation. On this issue, this paper deploys a hierarchical control method to utilize DDAS for automatic steering. The higher-level controller is dedicated to generate the desired control input including the yaw moments based on a robust LQR approach, and the lower-level controller is responsible for control allocation and giving out the respective desired tire forces and the desired steering angle. Simulation based on a high-fidelity and full-car model indicates that DDAS-based fault-tolerant control design for FWIA electric vehicle is effective to achieve equal handling and maneuverability performance in case of the steering failure.

ACTIVE DISTURBANCE REJECTION CONTROL TUNING EMPLOYING THE LQR APPROACH FOR DECOUPLING UNCERTAIN MULTIVARIABLE SYSTEMS

The ADRC tuning is essentially a pole-placement technique and the desired performance is indirectly achieved through the location of the closed-loop poles. However, the final choice of these poles becomes a trial-and-error strategy. In contrast with pole-placement, in the LQR method, the desired performance objectives are directly and globally addressed by minimizing a quadratic function of the state and control input. ADRC tuning employing the LQR approach is then applied for decoupling uncertain MIMO systems. This is done by considering all the coupling and interference interactions between the channels of the system as disturbances, using an ESO to estimate them in real time and then canceling its effect employing the estimate as part of the control signal.

ADRC Tuning Employing the LQR Approach for Decoupling Uncertain MIMO Systems

Active Disturbance Rejection Control (ADRC) tuning employing the LQR approach is applied for decoupling uncertain MIMO systems. This is done by considering all the coupling and interference interactions between the channels of the system as disturbances, using an Extended State Observer (ESO) to estimate them in real time and then canceling its effect employing the estimate as part of the control signal. The ADRC tuning is essentially a pole-placement technique and the desired performance is indirectly achieved through the location of the closed-loop poles. However, the final choice of these poles becomes a trial-and-error strategy. In contrast with pole-placement, in the LQR method, the desired performance objectives are directly and globally addressed by minimizing a quadratic function of the state and control input. DOI: http://dx.doi.org/10.5755/j01.itc.43.2.4059

Robust Tracking of Linear Systems for Matched Uncertainty using LQR Approach

Robust Tracking of Linear Systems for Matched Uncertainty using LQR Approach

Hierarchical Decentralized Stabilization for Networked Dynamical Systems by LQR Selective Pole Shift

This paper proposes a systematic method to design hierarchical, decentralized, stabilizing controllers for homogeneous hierarchical dynamical networks. Based on LQR approach with a properly chosen performance index including global and local objectives with control input penalty, an obtained optimal LQR feedback gain gives the closed-loop system a prescribed desirable hierarchical structure. In addition, the undesirable eigenvalues of the given homogeneous network can be selectively shifted by further selecting the weighting matrices based on the left eigenvectors associated with those eigenvalues. Finally, the proposed method is summarized into a systematic design procedure with an illustrative numerical example to show its effectiveness.

Control of Flexible Beam with Unmodelled Dynamics Using Second-Order Pole Placement and LQR Techniques

Control of a flexible beam such as that in flexible-link robot manipulators in many mechanical devices is very challenging, due in part to its intrinsic nature of unmodelled dynamics in a system. Such a system is said to be subjected to nonholonomic constraints, hence its feedback control is difficult to realize. This paper presents the application of control design based on second-order pole placement and LQR approaches to a single-link flexible robotic arm. In this case, a controller considering the flexibility of highly-flexible arm is employed to suppress the tip vibration of the manipulator. The effectiveness of the method is verified through computer simulations and consequently, the adequateness of the control performance and the feasibility of the system with a super-light link are shown.