LQ Control Research Articles

Resilient Predictive Control for Cyber–Physical Systems Under Denial-of-Service Attacks

In this brief, we investigate the Cyber-Physical Systems (CPSs) with measurement channels under Denial-of-Service (DoS) attacks. An equivalent predictive control system model and attack model are constructed firstly. To compensate for the data loss due to the attacks, the predictive controller is designed based on linear quadratic form. Furthermore, through the design of an observer-based output predictor, a novel resilient observer-based predictive control framework is presented to improve the robustness of the LQ controller. By constructing the closed-loop system with proposed controller, the states of the control system are theoretically proved to be asymptotically stable under the influence of DoS attacks. Finally, the efficacy of the proposed control strategy is illustrated through a comparative simulation example.

Comparison of Control Algorithms by Simulating Power Consumption of Differential Drive Mobile Robot Motion Control in Vineyard Row

Abstract The paper deals with comparing electricity power consumption of various control algorithms by simulating differential mobile robot motion control in a vineyard row. In field of autonomous mobile robotics, the quality of control is a crucial aspect. Besides the precision of control, the energy consumption for motion is becoming an increasingly demanding characteristic of a controller due to the increasing costs of fossil fuels and electricity. A simulation model of a differential drive mobile robot motion in a vineyard row was created, including robot dynamics for evaluating motion consumption, and there were implemented commonly used PID, Fuzzy, and LQ control algorithms, the task of which was to navigate the robot through the centre of vineyard row section by measuring distances from trellises on both robot sides. The comparison was carried out using Matlab software and the best results in terms of both power consumption and control accuracy were achieved by LQI controller. The designed model for navigating the robot through the vineyard row centre and optimized controllers were implemented in a real robot and tested under real conditions.

The difference and unity of irregular LQ control and standard LQ control and its solution

Irregular linear quadratic control (LQ, was called Singular LQ) has been a long-standing problem since 1970s. This paper will show that an irregular LQ control (deterministic) is solvable (for arbitrary initial value) if and only if the quadratic cost functional can be rewritten as a regular one by changing the terminal cost x′(T)Hx(T) to x′(T)[H + P1(T)]x(T), while the optimal controller can achieve P1(T)x(T) = 0 at the same time. In other words, the irregular controller (if exists) needs to do two things at the same time, one thing is to minimize the cost and the other is to achieve the terminal constraint P1(T)x(T) = 0, which clarifies the essential difference of irregular LQ from the standard LQ control where the controller is to minimize the cost only. With this breakthrough, we further study the irregular LQ control for stochastic systems with multiplicative noise. A sufficient solving condition and the optimal controller is presented based on Riccati equations.

Adaptive LQ Control Using Reduced Hamiltonian for Continuous-Time Systems with Unmatched Input Disturbances

Adaptive LQ Control Using Reduced Hamiltonian for Continuous-Time Systems with Unmatched Input Disturbances

Methods of Weighting Matrices Determination of Moving Double Poles with Jordan Block to Real Poles By LQ Control

Methods of Weighting Matrices Determination of Moving Double Poles with Jordan Block to Real Poles By LQ Control

LW-RCP와 Odroid 기반의 Machine Vision을 이용한 Ball and Plate 시스템 구현에 관한 연구

In this paper, we propose the architecture of a ball-and-plate system as an educational platform that can help students comprehensively study control engineering, robotics, machine vision, and embedded systems. In addition, we describe how to implement the sub-systems and present an example of an education plan using the proposed system. In the proposed system, we use an LW-RCP(Light Weight-Rapid Control Prototyping) system, which is lab-built, to help students implement the control algorithm. An RCP system makes it easy for students who are not familiar with u-Controller or the C language to implement controllers. We also use Odroid, a low-cost SBC (single-board computer), and a single camera to calculate the position of ball using a machine vision algorithm. In this structure, the measurement subsystem is more durable compared with contact-based sensing systems and student can test their own machine vision algorithms for better measurements. We adopt the Stewart platform, a type of parallel robot, to generate roll-and-pitch actuation for the ball-and-plate system. By adopting the Stewart platform, we can handle more complicated control problems for movement that requires more than two degrees of freedom. Additionally, we implement an LQ controller, which is a typical model-based controller, and apply it to the ball-plate system. Finally, through experiments, we illustrate the usefulness of the proposed system.

A novel nonlinear observer‐based LQ control system design for wind energy conversion systems with single measurement

AbstractThe issue of tracking the optimal power for wind energy conversion systems (WECSs) via regulating the rotor speed of the generator is taken into account in this study. Additionally, a novel polynomial observer is proposed for estimating not only aerodynamic torque in WECSs but also d‐axis and electromagnetic torque. Therefore, in this new approach, only the rotor speed of the generator is required to be measured instead of measuring all state variables. With the new observer form, the aerodynamic torque does not need to satisfy any constraints, which are mandatory in the previous methods. It should be noted that this methodology has not been investigated for the WECSs in any previous papers. To design a complete control system, a linear optimal control method cooperated with the polynomial observer is employed to track the optimal trajectory of a generator. Moreover, in this paper, the permanent magnet synchronous generator is used. In addition, on the basis of the Lyapunov theory and sum‐of‐square (SOS) technique, the conditions for observer synthesis are derived in the main theorems. Finally, the simulation results are provided to prove the effectiveness and merit of the proposed method.

Linear quadratic stochastic optimal control problems with operator coefficients: open-loop solutions

An optimal control problem is considered for linear stochastic differential equations with quadratic cost functional. The coefficients of the state equation and the weights in the cost functional are bounded operators on the spaces of square integrable random variables. The main motivation of our study is linear quadratic (LQ, for short) optimal control problems for mean-field stochastic differential equations. Open-loop solvability of the problem is characterized as the solvability of a system of linear coupled forward-backward stochastic differential equations (FBSDE, for short) with operator coefficients, together with a convexity condition for the cost functional. Under proper conditions, the well-posedness of such an FBSDE, which leads to the existence of an open-loop optimal control, is established. Finally, as applications of our main results, a general mean-field LQ control problem and a concrete mean-variance portfolio selection problem in the open-loop case are solved.

Dynamical Modeling and LQR Control of a Gyroscopically Stabilized Bicycle

AbstractThis contribution focuses on the dynamical modeling and control of a self‐balancing bicycle. The bicycle is equipped with two flywheels rotating at constant speed mounted via a hinge that is actuated by an additional motor and allows for rotation about the vertical axis. Due to the balance of angular momentum, a torque is generated around the axis perpendicular to the hinge and spinning axis, i.e. an axis along the forward motion direction. This gyroscopic effect is exploited for the stabilization of the bicycle. Two cases are distinguished: 1) For the stabilization of the non‐moving bicycle an LQ–controller based on a linear model is used. 2) For the moving bicycle, a non‐linear dynamic model in terms of non‐holonomic velocities is derived and based on the linearized model at constant driving speeds the stability of the bicycle is analyzed. The model reveals the self‐stabilization behavior of a bicycle without flywheels. At a speed of about 17km/h, the linearized model has only eigenvalues with negative real parts and is hence stable. Experimental as well as simulation results are presented.

Distributed Observer-based LQ Controller Design and Stabilization for Discrete-time Multi-agent Systems

This paper will investigate the distributed observer-based LQ controller design and stabilization problem for uncoupled identical linear time-invariant multi-agent systems with a performance index coupling the behavior between the multi-agents. A design method is proposed by applying the decomposition of the global discrete-time algebraic Riccati equations. A computationally tractable solution can be obtained by solving four local algebraic Riccati equations which have the same dimensions as a single agent. The stability condition is given in terms of the spectrum of two matrices representing the desired sparsity pattern of the distributed controller and distributed observer. A limited overall performance can also be guaranteed by the proposed distributed controller which is parameterized by two scalars. To illustrate the effectiveness of the algorithm, a numerical example is provided.

High‐order observers‐based LQ control scheme for wind speed and uncertainties estimation in WECSs

SummaryTip speed ratio control is a popular method in wind energy conversion systems in order to capture the maximum power. This method, however, requires wind speed information, which is difficult in practice to accurately measure it. Therefore, estimation methods are usually applied, where a high‐precision estimate leads to a high‐efficient system. Based on the fact that the wind speed varies in a random way, this paper proposes a generalized high‐order observer to estimate the aerodynamic torque and the wind speed accordingly. This observer algorithm releases the assumption that the wind speed should be slowly varying, which is required in previous observer designs. Moreover, two other generalized high‐order observers are also applied to estimate the uncertainties, which depend on state variables and cannot be considered as slow‐varying disturbances. Using the outputs of these observers, a robust high‐performance optimal control system is developed for the rotor speed to keep the optimal tip speed ratio. The stability analysis of the designed control system is fully presented. The effectiveness of the proposed technique is validated via simulation studies.

LQ control design for the containment of the HIV/AIDS diffusion

An optimal control design approach is applied to a novel HIV/AIDS model to reduce the infection diffusion. Two classes of susceptible subjects, the wise one and the incautious ones, and three classes of infectious subjects, the ones not aware of their condition and the subjects in the pre-aids or in the aids status, are considered. The control input, represented by information campaigns and the medication action, is designed by means of a linear quadratic approach on the linearized model. Moreover, a preliminary state observer for the unmeasurable number of the unconscious infectious subjects is introduced. Numerical results show the effectiveness of the solution, and its robustness with respect to the approximations introduced by the linearization.

Adaptive rejection of unmatched input disturbances for output tracking using a control separation LQ method

SummaryIn this paper, an adaptive disturbance rejection scheme is developed for output tracking of multivariable nonminimum‐phase systems in the presence of uncertain unmatched input disturbances. Using a new cost function, a control separation–based LQ control framework is established for desired disturbance rejection and output tracking. The finite‐time and infinite‐time control separation–based LQ solutions are derived in an explicit composite controller structure, which has enhanced disturbance compensation and output tracking properties, as compared with a traditional LQ solution. An adaptive parameter update algorithm is used for estimation of uncertain disturbances, based on which an adaptive control separation–based LQ control solution is developed for plants in the presence of uncertain disturbances. Simulation results are presented to verify the desired adaptive disturbance rejection control system performance.

Control and estimation of a quadcopter dynamical model

The main motivation for this paper is to apply LQ and LQG methodologies for quadcopter control system. The developed control system is for both the rectangular position (xy) and altitude (z) as well as the orientation (attitude - angles around the axes) based on 6-Degree of Freedom (6DOF) mathematical model. 6DOF refers to the model with 3 linear and 3 angular motions. The altitude and attitude controllers are designed and the results presented in both the continuous and the discrete time cases. For the controller design, a nonlinear mathematical model was obtained first for 6DOF. The next step was to linearize the nonlinear model in hovering mode, and the final step was the reduction of the resulted linear model to be used as starting model for the controller design. The reduced linear model was tested for controllablity and observability. The control goal was to track a spatial trajectory with the quadcopter center of gravity under environment disturbances and sensor measurement errors. For this purpose, designed LQ controller was augmented by Kalman Filter state observer. The resultant controllers provide precise and robust performance for an input reference signal and for a regulation problem. After the transient response (of order of few seconds) the tracking error is acceptable which provides safe handling even under disturbances and measurement noises. The transient response can be further reduced by controllers fine tuning.

Implementation of a Ball and Plate Control System Using Sliding Mode Control

In this paper, we propose a cost-effective implementation method of a ball and plate system as an educational kit and present the application of sliding mode control to achieve better control performance. We choose a Stewart platform with rotary actuators to manipulate the plate. We explain the construction method of the platform in detail. We use a touch panel as a sensor to obtain the positional data at a high sample rate and to make the system compact. As a main control unit, we use a Nucleo-32 board, which is a small and powerful open source hardware with a built-in floating point unit. For controller synthesis, we show a mathematical model of the ball and plate system and explain the kinematics analysis of the Stewart platform. We design a sliding mode controller that includes error integration, which makes the system robust against external disturbances. We describe the results of the simulations and the experiments and then illustrate the advantage of the applied sliding mode control compared to LQ control. The proposed system is cost-effective, can be easily built, has good control performance, and occupies a small space. For these reasons, we expect that the system can be efficiently used as an educational tool.

Systematic Transformation of Chemical Catalyst Models for Control Design

Common system analysis and controller design methods are based on state-space models. However, most physical-chemical catalyst models are not represented in a state-space. In this paper, we present an approach to transform simplified physical–chemical models into the state-space, and hereby, we introduce the concept of weighting functions. The weighting functions represent the catalyst model in a compact form and are a convenient way for system analysis. The weighting functions will be analyzed from the system theoretical and chemical point of view. The generalization of this approach will be demonstrated. Exemplarily, three reaction mechanisms will be transformed into nonlinear state-space models. Based on the first model, the nonlinear state-space model will be linearized and a linear quadratic controller will be designed. Contrarily to the LQ controllers in the literature, the weighting matrix for the state vector is chosen in the model-based form. The only few design parameters are intuitive to choose.

Solutions of differential–algebraic equations as outputs of LTI systems: Application to LQ control problems

In this paper we propose a unified geometric framework for representing all solutions of a Linear Time Invariant Differential–Algebraic Equation (DAE-LTI) as outputs of classical Linear Time Invariant Ordinary Differential Equations (ODE-LTI). The proposed framework is then used to solve an LQ optimal control problem for DAE-LTIs with rectangular matrices.

Improved linear quadratic and proportional control system for improved liquid level system regulation in a coke fractionation tower

A new linear quadratic regulation (LQ) control plus a proportional (P) control system is proposed for the level regulation in an industrial coke fractionation tower. The process is first stabilized using a P controller and then a subsequent LQ controller is designed for the P control system. The P control system is modeled as a generalized first order plus dead time (FOPDT) process using step-response test and the LQ-P controller is designed through a new state space structure. Performance in terms of regulatory and servo issues were investigated. Simulation results showed that the proposed method is more robust and improves performance than traditional model predictive control.

New Minmax Linear Quadratic Fault-Tolerant Tracking Control for Batch Processes

A new design of linear quadratic control (LQ) is proposed for batch processes with partial actuator faults and unknown disturbance. The autoregressive model built through input-output process data is transformed into a new non-minimal state space (NMSS) model in which the process state variables and tracking error are combined, then a new LQ control scheme is derived based on minimax optimization. Unlike LQ based on traditional NMSS model (TNMSSLQ), the process state variables and tracking error can both be regulated in the proposed method. Monotonic situations of optimal performance cost are further derived to yield sufficient conditions for both nominal and robust system stability. Finally, an injection velocity control example is illustrated to show the effectiveness.

Abstract CT127: Results from a phase II clinical study in Chinese population: treatment with Chinese medicine cocktail LQ for patients with stage IIIB/IV advanced non-small cell lung cancer

Abstract OBJECTIVES: To estimate the response of Chinese medicine “cocktail” LQ in patients with advanced non-small cells lung cancer, a phase II multicenter, double-blind, randomized clinical trial was conducted. Patients with IIIB/IV stage received LQ and natural product control Spirulina. The end points for this study included overall survival (OS), progression free survival (PFS), safety of the regimen, disease control rate (DCR) and other criteria. METHODS: Patients with stage IIIB/IV advanced NSCLC cancer received LQ treatment and Spirulina. Toxicity was assessed. Quality of life was assessed. The primary objective was overall survival. RESULTS: A hundred and twenty patients were enrolled and 80 were treated. Median age was 60 years (range, 42-75). The median overall survival rate in LQ group and Spirulina group is 10.9 months vs 7.4 months respectively (p<0.0001). Median progression survival free survival is 3.84 months vs 1.97 months in LQ and Spirulina group (p<0.01). There is no side effect were found in there. There were 42 patients with stable disease with the disease control rate of 59.15% in LQ treatment group, Compare with Spirulina group, there were only 4 standard disease, for disease control rate of 11.76% (p<0.001). There are no notable toxicities were found in LQ treatment group. CONCLUSIONS: This first-in-human phase II study of Chinese medicine cocktail LQ used as first-line therapy in patients with advanced NSCLC. LQ, a promising new drug, provides a safer and high effective therapy for late-stage lung cancer patients. Citation Format: Lei Zhang, Chengyu Wu. Results from a phase II clinical study in Chinese population: treatment with Chinese medicine cocktail LQ for patients with stage IIIB/IV advanced non-small cell lung cancer. [abstract]. In: Proceedings of the 107th Annual Meeting of the American Association for Cancer Research; 2016 Apr 16-20; New Orleans, LA. Philadelphia (PA): AACR; Cancer Res 2016;76(14 Suppl):Abstract nr CT127.