Left eigenstructure assignment via Sylvester equation

An effective and disturbance suppressible controller can be designed by assigning a left eigenstructure (eigenvalues/left eigenvectors) of a system. In this note, a novel left eigenstructure assignment scheme via Sylvester equation is proposed. The biorthogonality property between the right and left modal matrices of a system is utilized to develop the scheme.     

A fault isolation filter design using left eigenstructure assignment scheme

This paper presents a novel fault isolation filter design method using left eigenstructure assignment scheme proposed by the first author et al. The proposed method shows good performance of fault isolation with an exact eigenstructure assignment and guarantees that the corrupted γ faults can be isolated simultaneously when the number of available output measurements are equal to or larger than (γ+l). A numerical example for the fault isolation filter is also included.     

QFT Parameter-Scheduling control design for linear Time-Varying systems based on RBF networks

For most of linear time-varying (LTV) systems, it is difficult to design time-varying controllers in analytic way. Accordingly, by approximating LTV systems as uncertain linear time-invariant, control design approaches such as robust control have been applied to the resulting uncertain LTI systems. In particular, a robust control method such as quantitative feedback theory (QFT) has an advantage of guaranteeing the frozen-time stability and the performance specification against plant parameter uncertainties. However, if these methods are applied to the approximated linear time-invariant (LTI) plants with large uncertainty, the resulting control law becomes complicated and also may not become ineffective with faster dynamic behavior. In this paper, as a method to enhance the fast dynamic performance of LTV systems with bounded time-varying parameters, the approximated uncertainty of time-varying parameters are reduced by the proposed QFT parameter-scheduling control design based on radial basis function (RBF) networks.     

A new SSI algorithm for LPTV systems: Application to a hinged-bladed helicopter

Many systems such as turbo-generators, wind turbines and helicopters show intrinsic time-periodic behaviors. Usually, these structures are considered to be faithfully modeled as linear time-invariant (LTI). In some cases where the rotor is anisotropic, this modeling does not hold and the equations of motion lead necessarily to a linear periodically time-varying (referred to as LPTV in the control and digital signal field or LTP in the mechanical and nonlinear dynamics world) model. Classical modal analysis methodologies based on the classical time-invariant eigenstructure (frequencies and damping ratios) of the system no more apply. This is the case in particular for subspace methods. For such time-periodic systems, the modal analysis can be described by characteristic exponents called Floquet multipliers. The aim of this paper is to suggest a new subspace-based algorithm that is able to extract these multipliers and the corresponding frequencies and damping ratios. The algorithm is then tested on a numerical model of a hinged-bladed helicopter on the ground.     

Performance analysis of two-degree of freedom fractional order PID controllers for robotic manipulator with payload

The robotic manipulators are multi-input multi-output (MIMO), coupled and highly nonlinear systems. The presence of external disturbances and time-varying parameters adversely affects the performance of these systems. Therefore, the controller designed for these systems should effectively deal with such complexities, and it is an intriguing task for control engineers. This paper presents two-degree of freedom fractional order proportional-integral-derivative (2-DOF FOPID) controller scheme for a two-link planar rigid robotic manipulator with payload for trajectory tracking task. The tuning of all controller parameters is done using cuckoo search algorithm (CSA). The performance of proposed 2-DOF FOPID controllers is compared with those of their integer order designs, i.e., 2-DOF PID controllers, and with the traditional PID controllers. In order to show effectiveness of proposed scheme, the robustness testing is carried out for model uncertainties, payload variations with time, external disturbance and random noise. Numerical simulation results indicate that the 2-DOF FOPID controllers are superior to their integer order counterparts and the traditional PID controllers.     

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.     

IDENTIFICATION OF TIME-VARYING MODAL PARAMETERS USING LINEAR TIME-FREQUENCY REPRESENTATION

A new method of parameter identification based on linear time-frequency representation andHilbert transform is proposed to identify modal parameters of linear time-varying systems frommeasured vibration responses. Using Gabor expansion and synthesis theory measured responses arerepresented in the time-frequency domain and modal components are reconstructed by time-frequencyfiltering. The Hilbert transform is applied to obtain time histories of the amplitude and phase angle ofeach modal component, from which time-varying frequencies and damping ratios are identified. The     

Robust control of feedback linearizable large-scale systems

The design of decentralized controllers for a class of uncertain interconnected nonlinear systems is considered. The uncertainty considered here is time-varying and appears at each subsystem and interconnections. Two control techniques are explored. The first one, namely, the feedback linearization control, involves a known and autonomous nonlinear system. The second one, namely, the robust control, is especially suitable if any uncertainty and/or time-varying factors are involved in the nonlinear dynamics. These two controllers are combined to stabilize a class of large-scale nonlinear uncertain systems. Two decentralized robust controllers, nonadaptive and adaptive, are proposed and those results are proved.     

FINITE-ELEMENT MODEL UPDATING,EIGENSTRUCTURE ASSIGNMENT AND EIGENVALUE EMBEDDING TECHNIQUES FOR VIBRATING SYSTEMS

This paper presents a brief overview of the existing direct methods for the finite-element model (FEM) updating problem and reviews the recently developed ‘direct and partial modal’ approach for the partial eigenstructure assignment problem and the ‘eigenvalue embedding’ techniques for vibrating systems, in the context of the solution of this problem.     

A global optimal sliding-mode control for the minimum time trajectory tracking with bounded inputs

A new design of the sliding mode control is proposed for the uncertain linear time-varying second order system. The proposed control drives system states to the target point in the minimum time with specified ranges of parametric uncertainties and disturbances, One of the advantages of the proposed control scheme is that the control inputs do not go beyond saturation limits of the actuators. The other advantage is that the minimum arrival time and the acceleration of the second order actuators system can be estimated with given parametric bounds and can be expressed in the closed form; conversely, the designer can select actuators based on the condition of the minimum arrival time to the target point. The superior performance of the proposed control scheme to other sliding mode controllers is validated by computer simulations.     

考虑时变输入时滞及频段约束的车辆主动悬架预瞄控制

针对预瞄控制中存在的输入时滞现象,提出一种时滞相关的有限频域线性变参数控制器设计方法,用于解决存在输入时滞及时变速度的汽车主动悬架预瞄控制问题。在控制器设计中,应用Padé方法将控制方程扩维为含路面预瞄信息的状态空间形式。用有限顶点的多胞形结构处理速度的时变性。以线性不等式的形式给出了控制器设计准则。区别于传统的全频域时滞相关的H∞控制,以车身加速度的有限频域H∞范数为优化性能指标,使其在关心频段内取得最小的能量增益值,同时保证相关的时域约束条件。通过数值算例及试验表明,在存在输入时滞的情况下,该方法能取得比无预瞄控制保守性更小的结果,舒适性得到了显著的提高。     

An improved auto-tuning scheme for PI controllers

Ziegler-Nichols tuned PI and PID controllers are usually found to provide poor performances for high-order and nonlinear systems. In this study, an improved auto-tuning scheme is presented for Ziegler-Nichols tuned PI controllers (ZNPICs). With a view to improving the transient response, the proportional and integral gains of the proposed controller are continuously modified based on the current process trend. The proposed controller is tested for a number of high-order linear and nonlinear dead-time processes under both set-point change and load disturbance. It exhibits significantly improved performance compared to ZNPIC, and Refined Ziegler-Nichols tuned PI controller (RZNPIC). Robustness of the proposed scheme is established by varying the controller parameters as well as the dead-time of the process under control.     

Smith predictor based-sliding mode controller for integrating processes with elevated deadtime

An approach to control integrating processes with elevated deadtime using a Smith predictor sliding mode controller is presented. A PID sliding surface and an integrating first-order plus deadtime model have been used to synthesize the controller. Since the performance of existing controllers with a Smith predictor decrease in the presence of modeling errors, this paper presents a simple approach to combining the Smith predictor with the sliding mode concept, which is a proven, simple, and robust procedure. The proposed scheme has a set of tuning equations as a function of the characteristic parameters of the model. For implementation of our proposed approach, computer based industrial controllers that execute PID algorithms can be used. The performance and robustness of the proposed controller are compared with the Matausek-Mici? scheme for linear systems using simulations.     

Frequency domain properties of EALQR with indefinite weighting matrix

EALQR (Linear Quadratic Regulator design with Eigenstructure Assignment capability) has the capability of exact assignment of eigenstructure with the guaranteed margins of the LQR for MIMO (Multi-Input Multi-Output) systems. However, EALQR undergoes a restriction on the state-weighting matrixQ in LQR to be indefinite with respect to the region of allowable closed-loop eigenvalues. The definiteness of the weighting matrix is closely related to the robustness property of a given system. In this paper, we derive a relation between the indefinite weighting matrix Q and the robustness property for EALQR. The modified frequency domain inequality, that could be guaranteed by EQLQR with an indefinite weighting matrix, is presented.     

基于径向基神经网络的直线超声电机位置控制

针对直线超声电机的精密位置控制,提出了一种基于径向基神经网络的自适应控制机制。鉴于直线超声电机工作原理,其运行状态必然受到摩擦、强非线性和时变等不确定性因素的干扰,为了对这些不确定性因素进行有效的逼近,采用了径向基神经网络。为了提高控制机制的自适应能力,首先利用来自试验数据的训练样本按正交最小二乘算法确定径向基神经网络的隐层单元的个数和相关参数,再按递推最小二乘法在线调整隐层与输出层之间的权重。试验结果表明,基于径向基神经网络的自适应控制器的性能不仅优于传统的PID控制和误差反向传播神经网络控制,而且具有很好的抗干扰能力。     

Adaptive backstepping sliding mode control of flexible ball screw drives with time-varying parametric uncertainties and disturbances

This paper presents a method to model and design servo controllers for flexible ball screw drives with dynamic variations. A mathematical model describing the structural flexibility of the ball screw drive containing time-varying uncertainties and disturbances with unknown bounds is proposed. A mode-compensating adaptive backstepping sliding mode controller is designed to suppress the vibration. The time-varying uncertainties and disturbances represented in finite-term Fourier series can be estimated by updating the Fourier coefficients through function approximation technique. Adaptive laws are obtained from Lyapunov approach to guarantee the convergence and stability of the closed loop system. The simulation results indicate that the tracking accuracy is improved considerably with the proposed scheme when the time-varying parametric uncertainties and disturbances exist.     

Decentralized robust control for interconnected nonlinear systems

Decentralized robust control of strongly interconnected uncertain systems is addressed in this paper. The uncertainties we consider here may include parameter uncertainty and input disturbance that may be nonlinear and (possibly fast) time-varying. We show specially how both internal and external uncertainties are taken into considerations. This work covers a broad class of large-scale systems since the current consideration renders all previous settings as special cases. Stability analysis with the proposed controllers is provided.     

Generalized characteristic ratios assignment for commensurate fractional order systems with one zero

In this paper, a new method for determination of the desired characteristic equation and zero location of commensurate fractional order systems is presented. The concept of the characteristic ratio is extended for zero-including commensurate fractional order systems. The generalized version of characteristic ratios is defined such that the time-scaling property of characteristic ratios is also preserved. The monotonicity of the magnitude frequency response is employed to assign the generalized characteristic ratios for commensurate fractional order transfer functions with one zero. A simple pattern for characteristic ratios is proposed to reach a non-overshooting step response. Then, the proposed pattern is revisited to reach a low overshoot (say for example 2%) step response. Finally, zero-including controllers such as fractional order PI or lag (lead) controllers are designed using generalized characteristic ratios assignment method. Numerical simulations are provided to show the efficiency of the so designed controllers.     

Eigenstructure assignment for linear systems with probabilistic uncertainties

In this paper, S (stochastic)-eigenvalue concept and its S-eigenvector for linear continuous-time systems with probabilistic uncertainties is proposed. The proposed concept is concerned with the perturbation of eigenvalues due to the probabilistic variable parameters in the dynamic model of a plant. S-eigenstructure assignment scheme via the Sylvester equation approach based on the S-eigenvalue concept is also proposed. The proposed design schemes are illustrated by numerical examples, and applied to the longitudinal dynamics of open-loop-unstable aircraft with possible uncertainties in aerodynamic and thrust effects as well as separate dynamic pressure. These results explicitly characterize how S-eigenvalues in the complex plane may impose stability on S-eigenstructure assignment.     

Discrete-time setpoint-triggered reset integrator design with guaranteed performance and stability

According to Bode's gain-phase relationship, in linear time-invariant controllers, introducing an integral action to eliminate the steady-state error has an adverse effect of increased phase delay and overshoot, leading to performance deterioration. Moreover, increasing the bandwidth of the closed-loop system to enhance the low-frequency disturbance rejection invariably amplifies the sensitivity to high-frequency disturbances. Hence, the performance of the linear controllers is always limited due to these fundamental frequency- and time-domain limitations. Motivated by the desire to address the fundamental limitations of linear controllers and improve the time-varying closed-loop performance, we put forward a novel setpoint-triggered reset integrator strategy that varies the integrator cut-off frequency based on the setpoint information. Particularly, to tackle the time-varying disturbances and setpoint profiles, the proposed controller consists of a nominal linear controller and a variable-gain reset integrator. We show the global asymptotic stability of the proposed methodology using positive-real lemma along with the LaSalle's invariance principle and experimentally validate using measured frequency response function. Moreover, the efficacy of the proposed technique compared to that of the linear controller is experimentally demonstrated on a benchmark rotary servo system. Experimental results assessed using the tracking error and cumulative power spectral density substantiate that the proposed control strategy can not only improve the low-frequency disturbance rejection but also augment the high-frequency trajectory tracking performance.