Observer design and stabilization for linear neutral delay systems

This paper focuses on the state observer design problem as well as the observer-based stabilization problem for linear neutral delay systems. The purpose of the former problem is to design an observer that guarantees the asymptotic stability of the estimation error dynamics. The existence condition for such an observer is established. The latter problem, which is the main problem studied in this paper, aims at designing an observer-based feedback controller, such that the closed-loop system is asymptotically stabilized. It is shown that the desired controller can be easily designed if there are solutions to several linear matrix inequalities. Finally, two simulation examples are given to demonstrate the validity and effectiveness of the proposed approach.     

Robust observer-based absolute stabilization for Lur’e singularly perturbed systems with state delay

This paper is concerned with the problem of robust observer-based absolute stabilization for Lur’e singularly perturbed time-delay systems. The aim is to design a suitable observer-based feedback control law such that the resulting closed-loop system is absolutely stable. First, a full-order state observer is constructed. Based on the linear matrix inequality (LMI) technique, a delay-dependent sufficient condition is presented such that the observer error system is absolutely stable. Then, for observer-based feedback control, by introducing some slack matrices, a sufficient condition for input-to-state stability (ISS) of the closed-loop system with regard to the observer error is presented. Thus, the absolute stabilization of the closed-loop system can be guaranteed based on the ISS property. In addition, the criteria presented are both independent of the small parameter and the upper bound for the absolute stability can be obtained in a workable algorithm. Finally, two numerical examples are provided to illustrate the effectiveness of the developed methods.     

Static output feedback stabilization of networked control systems with a parallel-triggered scheme

This paper investigates the parallel-triggered static output feedback stabilization problem for linear networked control systems. A new parallel-triggered scheme is proposed by using both the relative error and the absolute error information. The scheme can reduce transmission rate while maintaining the global asymptotical stability. The linear parallel-triggered networked control system is modeled as a time-delay system. By employing Lyapunov stability theory, sufficient conditions are established for the closed-loop system to be globally asymptotically stable in terms of linear matrix inequalities. Moreover, a co-design algorithm is developed to obtain both the optimal trigger parameters and the output feedback controller gain in the sense that the transmission rate is minimized. Finally, two examples are given to illustrate the advantages of the proposed scheme.     

Robust and minimum norm partial quadratic eigenvalue assignment in vibrating systems: A new optimization approach

The partial quadratic eigenvalue assignment problem (PQEVAP) concerns reassigning a few undesired eigenvalues of a quadratic matrix pencil to suitably chosen locations and keeping the other large number of eigenvalues and eigenvectors unchanged (no spill-over). The problem naturally arises in controlling dangerous vibrations in structures by means of active feedback control design. For practical viability, the design must be robust, which requires that the norms of the feedback matrices and the condition number of the closed-loop eigenvectors are as small as possible. The problem of computing feedback matrices that satisfy the above two practical requirements is known as the Robust Partial Quadratic Eigenvalue Assignment Problem (RPQEVAP). In this paper, we formulate the RPQEVAP as an unconstrained minimization problem with the cost function involving the condition number of the closed-loop eigenvector matrix and two feedback norms. Since only a small number of eigenvalues of the open-loop quadratic pencil are computable using the state-of-the-art matrix computational techniques and/or measurable in a vibration laboratory, it is imperative that the problem is solved using these small number of eigenvalues and the corresponding eigenvectors. To this end, a class of the feedback matrices are obtained in parametric form, parameterized by a single parametric matrix, and the cost function and the required gradient formulas for the optimization problem are developed in terms of the small number of eigenvalues that are reassigned and their corresponding eigenvectors. The problem is solved directly in quadratic setting without transforming it to a standard first-order control problem and most importantly, the significant “no spill-over property” of the closed-loop eigenvalues and eigenvectors is established by means of a mathematical result. These features make the proposed method practically applicable even for very large structures. Results on numerical experiments show that the proposed method considerably reduces both feedback norms and the sensitivity of the closed-loop eigenvalues. A study on robustness of the system responses of the method under small perturbations show that the responses of the perturbed closed-loop system are compatible with perturbations.     

Decentralized output feedback stabilization for switched stochastic high-order nonlinear systems with time-varying state/input delays

This paper investigates decentralized output feedback stabilization problem for a class of switched stochastic high-order systems with time-varying state/input delays. With the help of coordinate transformations, a scaling gain is incorporated into the observers and controllers for the nominal system. Based on the homogeneous domination approach and stochastic Lyapunov–Krasovskii stability theorem, it is shown that global asymptotic stability in probability of the closed-loop system can be implemented by tuning the scaling gain. Two examples are given to demonstrate the feasibility of the proposed control method.     

Generalized predictor based active disturbance rejection control for non-minimum phase systems

In this paper, a generalized predictor based control scheme is proposed to improve system performance of set-point tracking and disturbance rejection for non-minimum phase (NMP) systems. By using a generalized predictor to estimate the system output without time delay, a model-based extended state observer (MESO) is designed to simultaneously estimate the system state and disturbance. Accordingly, an active disturbance rejection control design is developed which consists of a state feedback control and a feedforward control for the disturbance rejection. The MESO and feedback controllers are analytically derived by specifying the desired characteristic roots of MESO and closed-loop system poles, respectively. To improve the output tracking performance, a pre-filter is designed based on a desired closed-loop transfer function for the set-point tracking. A sufficient condition guaranteeing robust stability of the closed-loop system against time-varying uncertainties is established in terms of linear matrix inequalities (LMIs). Three illustrative examples from the literature are used to demonstrate the effectiveness and merit of the proposed control scheme.     

线性自抗扰气缸位置伺服控制研究

针对气动伺服系统复杂的非线性问题,提出了一种线性自抗扰控制策略对气动伺服系统进行位置控制。利用线性自抗扰控制器不依赖于被控对象精确数学模型的特点,解决被控气动系统内外各种不确定性,设计了线性扩张状态观测器来估计和补偿系统的全部干扰,同时给出了线性状态误差反馈控制器来保证系统的闭环响应性能。证明了线性扩张状态观测器的收敛性和闭环系统的镇定性。应用线性自抗扰控制策略与PID控制策略在气缸伺服系统中进行实验、比较,实验结果表明所设计的线性自抗扰控制器具有良好的控制效果。     

双星编队构形保持抗干扰容错控制

为解决系统模型误差、外部干扰以及执行器故障引起的双星编队轨道控制精度低、稳定性差问题,设计一种基于观测器的抗干扰容错线性二次型调节器(LQR)控制策略。首先,根据编队双星相对运动动力学模型,设计基于双比例积分自适应律的增广观测器,同时实现对系统状态、间歇故障与快速时变故障、可建模干扰的快速精确估计,并采用H∞优化技术抑制不可建模干扰对控制系统的影响。其次,采用Lyapunov稳定性理论,保证动态误差系统渐近稳定。然后,在控制器中引入未知动态估计信息的前馈补偿项,设计闭环反馈抗干扰容错LQR控制律。最后实验结果表明,相比文献中控制方法,本文所提方法的编队卫星相对位置控制精度提高49.93%,验证了所设计的抗干扰容错LQR控制律的优越性,能够为双星编队构形保持提供精确控制策略。     

Position control of a rodless cylinder in pneumatic servo with actuator saturation

In this paper, positioning control of a rodless cylinder in pneumatic servo systems with actuator saturation is investigated via an active disturbance rejection control. A linear extended state observer is designed to estimate and compensate strong friction force and other nonlinearities in the pneumatic rodless cylinder system. An actuator saturation linear feedback control law is developed to further improve the control performance. Furthermore, a linear matrix inequality-based optimization algorithm is employed to estimate a strictly invariance set for the closed-loop system. Experiment results with response time 0.5 s and accuracy 0.005 mm for a 200 mm step signal demonstrate the effectiveness of the proposed control strategy.     

A nonlinear updated gain observer for MIMO systems: Design,analysis and application to marine surface vessels

In this paper, the state estimation problem of a class of multi-input-multi-output nonlinear systems with measurement noise is studied. We develop an extended updated-gain high gain observer to make a tradeoff between reconstruction speed and measurement noise attenuation. The designed observer, whose gains are driven by nonlinear functions of the available output estimation errors, has the ability to reconstruct system states quickly and reduce the effect of measurement noise. We establish that, if there exists a state feedback law exponentially stabilizing the system with respect to an invariant set, the estimations and estimation errors are bounded. Besides, the trajectories of state- and output-feedback (based on the proposed observer) are sufficiently close, namely performance recovery. The observer performance is illustrated by various examples in marine control, including a case of transformation into the predefined structure.     

Robust pole assignment using velocity–acceleration feedback for second-order dynamical systems with singular mass matrix

In this paper the robust pole assignment problem using combined velocity and acceleration feedback for second-order linear systems with singular mass matrix is illustrated. This is promising for better applicability in several practical applications where the acceleration signals are easier to obtain than the proportional ones. First, the explicit parametric expressions of both the feedback gain controller and the eigenvector matrix are derived. The parametric solution involves manipulations only on the original second-order model. The available degrees of freedom offered by the velocity–acceleration feedback in selecting the associated eigenvectors are utilized to improve robustness of the closed-loop system. Straight-forward computational algorithms are introduced to demonstrate the effectiveness of the proposed approach. These algorithms are applicable for a dynamical system with mass matrices that can be either singular or nonsingular. Numerical examples are provided to illustrate the application of the proposed procedure.     

Direct yaw moment control for distributed drive electric vehicle handling performance improvement

For a distributed drive electric vehicle (DDEV) driven by four in-wheel motors, advanced vehicle dynamic control methods can be realized easily because motors can be controlled independently, quickly and precisely. And direct yaw-moment control (DYC) has been widely studied and applied to vehicle stability control. Good vehicle handling performance: quick yaw rate transient response, small overshoot, high steady yaw rate gain, etc, is required by drivers under normal conditions, which is less concerned, however. Based on the hierarchical control methodology, a novel control system using direct yaw moment control for improving handling performance of a distributed drive electric vehicle especially under normal driving conditions has been proposed. The upper-loop control system consists of two parts: a state feedback controller, which aims to realize the ideal transient response of yaw rate, with a vehicle sideslip angle observer; and a steering wheel angle feedforward controller designed to achieve a desired yaw rate steady gain. Under the restriction of the effect of poles and zeros in the closed-loop transfer function on the system response and the capacity of in-wheel motors, the integrated time and absolute error (ITAE) function is utilized as the cost function in the optimal control to calculate the ideal eigen frequency and damper coefficient of the system and obtain optimal feedback matrix and feedforward matrix. Simulations and experiments with a DDEV under multiple maneuvers are carried out and show the effectiveness of the proposed method: yaw rate rising time is reduced, steady yaw rate gain is increased, vehicle steering characteristic is close to neutral steer and drivers burdens are also reduced. The control system improves vehicle handling performance under normal conditions in both transient and steady response. State feedback control instead of model following control is introduced in the control system so that the sense of control intervention to drivers is relieved.     

Attitude output feedback control for rigid spacecraft with finite-time convergence

The main problem addressed is the quaternion-based attitude stabilization control of rigid spacecraft without angular velocity measurements in the presence of external disturbances and reaction wheel friction as well. As a stepping stone, an angular velocity observer is proposed for the attitude control of a rigid body in the absence of angular velocity measurements. The observer design ensures finite-time convergence of angular velocity state estimation errors irrespective of the control torque or the initial attitude state of the spacecraft. Then, a novel finite-time control law is employed as the controller in which the estimate of the angular velocity is used directly. It is then shown that the observer and the controlled system form a cascaded structure, which allows the application of the finite-time stability theory of cascaded systems to prove the finite-time stability of the closed-loop system. A rigorous analysis of the proposed formulation is provided and numerical simulation studies are presented to help illustrate the effectiveness of the angular-velocity observer for rigid spacecraft attitude control.     

Active steering wheel shimmy control for electric vehicle by sampled-data output feedback

In this paper, a new two Degree of Freedom (DOF) shimmy dynamic model of an Electric Vehicle (EV) with independent suspension subject to uncertain disturbances is built via Lagrange’s theorem firstly. Secondly, Based on the built model, an active control method is proposed to solve the shimmy problem of the steering system via a sampled-data output feedback controller. The output feedback domination approach is also used to dominate uncertain disturbances by using a scaling gain. With the help of these tools, the sampling period and scaling gain are calculated to guarantee global stability and disturbance attenuation for the closed-loop control system. Finally, simulations and tests are conducted to verify the effectiveness of the sampled-data output feedback controller for the EV’s shimmy problem under different conditions.     

Full-order Luenberger observer based on fuzzy-logic control for sensorless field-oriented control of a single-sided linear induction motor

This paper investigates sensorless indirect field oriented control (IFOC) of SLIM with full-order Luenberger observer. The dynamic equations of SLIM are first elaborated to draw full-order Luenberger observer with some simplifying assumption. The observer gain matrix is derived from conventional procedure so that observer poles are proportional to SLIM poles to ensure the stability of system for wide range of linear speed. The operation of observer is significantly impressed by adaptive scheme. A fuzzy logic control (FLC) is proposed as adaptive scheme to estimate linear speed using speed tuning signal. The parameters of FLC are tuned using an off-line method through chaotic optimization algorithm (COA). The performance of the proposed observer is verified by both numerical simulation and real-time hardware-in-the-loop (HIL) implementation. Moreover, a detailed comparative study among proposed and other speed observers is obtained under different operation conditions.     

基于改进型全维观测器的 BLDC 无传感器控制

对基于全维观测器的无刷直流电机无传感器控制算法进行了研究,针对现有的传统全维观测器存在响应慢的问题,提出了一种改进型全维观测器,在传统全维观测器基础上,通过引入反馈增益,以提高动态响应能力和系统稳定性。为了验证提出方案的正确性,搭建相应的测试平台进行了传统和新型观测器的性能对比测试。由实验结果可知,所提出的改进型全维观测器无传感器控制算法能使系统响应更快,是实现无刷直流电机无传感器高速高响应控制的一种有效方法。     

A robust algorithm for a class of optimal control problems subject to regional stability constraints and disturbances

A robust globally convergent algorithm for solving the optimization control problem (OCP) in both state feedback controller and observation control system is investigated. Finding the OCP adjoint parameter for computing the optimal observer gain and feedback gain vectors are desired. First, the optimal control problem considering stability of degree constrains and disturbance that affects the dynamics of system is converted into a two-point boundary value problem (TPBVP). Then, we apply the He’s polynomials based on homotopy perturbation method (HPM) as an efficient method to find both optimal gains. The algorithm will be modified do decrease the number of iterations required to attain a desired control problem cost function. As a result lower computational complexity is required when compared with other state of the art methods. Applying the HPM makes the solution procedure become easier, simpler and more straightforward. In the proposed method the control problem can be solved with lower amplitudes of the input signal (control effort), comparing with analytical method. Lower control efforts may also help to avoid saturation effects, and to restrain the system to work within linear operating areas of the state space. On the other hand, there is a tradeoff between control effort and the degree of optimality obtained. For demonstrating the simplicity and efficiency of the proposed optimal control method, the algorithm is compared with a control architecture using the Kalman filter estimator and a controller gain designed by the Lyapunov’s second method.     

Adaptive NN output-feedback stabilization for a class of stochastic nonlinear strict-feedback systems

In this paper, the adaptive neural network output-feedback stabilization problem is investigated for a class of stochastic nonlinear strict-feedback systems. The nonlinear terms, which only depend on the system output, are assumed to be completely unknown, and only an NN is employed to compensate for all unknown upper bounding functions, so that the designed controller is more simple than the existing results. It is shown that, based on the backstepping method and the technique of nonlinear observer design, the closed-loop system can be proved to be asymptotically stable in probability. The simulation results demonstrate the effectiveness of the proposed control scheme.     

Failure-tolerant performance stabilization of the generic large-scale system by decentralized linear output feedback

Most of the existing results on the decentralized stabilization of large-scale systems consider systems in the input-output-decentralized form, i.e., systems whose input and output matrices are block diagonal. The controller synthesis for such systems is less involved than that for input-output-centralized ones. In this paper, a transformation is proposed for the input-output decentralization of the generic large-scale system. Using the transformed system, a sufficient condition for failure-tolerant performance stabilization of the original large-scale system in a desirable performance region under decentralized linear output feedback is established. The problem is then reformulated as a constrained nonlinear optimization problem. The proposed methodology results in the optimal reconciliation of failure-tolerant performance stabilization of the overall system, and reliability and low actuator gains of the isolated subsystems. The effectiveness of the proposed approach is demonstrated by an example.     

Finite-time sliding mode controller for perturbed second-order systems

This paper presents a novel finite-time sliding mode controller applied to perturbed second order systems. The proposed scheme employs a disturbance observer that can identify growing in time disturbances. Then, the observer is combined with a sliding mode controller to achieve finite-time stabilization of the second-order system. The convergence of the observer as well as the finite-time stability of the closed-loop system is theoretically demonstrated. Besides, it is also shown that the finite-time convergence properties of a given controller can be enhanced when using a compensation term based on the disturbance observer. The proposed controller is compared with a twisting algorithm and a finite-time sliding mode controller with disturbance estimation. Also, a conventional proportional integral derivative (PID) controller is combined with the proposed disturbance observer in a trajectory tracking task. Numerical simulations indicate that the proposed controller attains finite-time stabilization of the second order system by requiring a less amount of power than that demanded by the other control schemes and without being affected by the peaking phenomenon. Besides, the performance of the PID technique is enhanced by applying the proposed control methodology.