Dynamic Stability Analysis of Linear Time-varying Systems via an Extended Modal Identification Approach

The problem of linear time-varying(LTV) system modal analysis is considered based on time-dependent state space representations, as classical modal analysis of linear time-invariant systems and current LTV system modal analysis under the ‘‘frozen-time' assumption are not able to determine the dynamic stability of LTV systems.Time-dependent state space representations of LTV systems are first introduced, and the corresponding modal analysis theories are subsequently presented via a stabilitypreserving state transformation. The time-varying modes of LTV systems are extended in terms of uniqueness, and are further interpreted to determine the system's stability. An extended modal identification is proposed to estimate the time-varying modes, consisting of the estimation of the state transition matrix via a subspace-based method and the extraction of the time-varying modes by the QR decomposition. The proposed approach is numerically validated by three numerical cases, and is experimentally validated by a coupled moving-mass simply supported beam experimental case. The proposed approach is capable of accurately estimating the time-varying modes, and provides a new way to determine the dynamic stability of LTV systems by using the estimated time-varying modes.     

电液比例系统的H∞鲁棒性控制设计

针对电液比例系统中系统控制数学模型参数时变要求控制器鲁棒性强的特点,通过分析电液比例系统的物理模型,利用线性分式变换(LFT)方法,引入乘性不确定性参数,给出了参数时变的电液比例模型,并得出了具有参数不确定性系统状态空间函数模型。运用线性矩阵不等式(LM I)的H∞控制器的处理方法,设计出基于H∞控制的电液比例系统控制器。利用该控制器可有效的抑制参数时变对系统输出的影响。仿真表明该控制器在较大不确定参数的变动下,控制器仍然能够使系统具有较好的输出性能,结果说明该鲁棒控制器的有效性。     

Robust control application for a three-axis road simulator

This paper presents the design of a quantitative feedback control system for a three-axis hydraulic road simulator. The road simulator is a multiple input-output (MIMO) system with parameter uncertainties which should be compensated with a robust control method. The objective of the present paper is to reproduce the random input signal or real road vibration signal by three hydraulic cylinders. The replaced m ² MISO equivalent control system is suggested, which satisfies the design specification of the original m×m MIMO control system by decoupling each of the three axes. Quantitative Feedback Theory (QFT) is used to control the simulator. The QFT illustrates a tracking performance of the closed-loop controller with low order transfer function G (s) and pre-filter F (s) having the minimum bandwidth for the uncertain plant with parameter uncertainty. The efficacy of the designed controller is verified through dynamic simulation, which is co-simulated with hydraulic models of Matlab and Adams multi-body. The simulation and the experimental results show that the proposed control technique works well for uncertain hydraulic plant systems.     

基于定量反馈理论的液压机器人单关节鲁棒控制器

液压机器人单关节性能直接影响机器人整体控制性能,液压系统参数的不确定性和时变性降低了机器人单关节控制精度和响应速度,因此要求机器人单关节控制器具有鲁棒性。建立了伺服阀控制摆动液压缸数学模型,分析了系统参数的不确定性,应用定量反馈理论 (QFT)设计了单关节鲁棒控制器。仿真表明,该控制器对斜坡干扰和正弦干扰都具有较强的鲁棒性,实验验证了控制算法的正确性。     

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.     

Robust LQG controller design for lightly damped uncertain linear systems

In this note, we consider lightly damped uncertain linear systems with natural frequency variations. This type of uncertainty has multiple uncertain parameters with multiple rank structure. It is well known that the conventional LQG or LQG/LTR methods can not be applied to such system bccause of the instability and the design conservatism. To overcome such shortcomings, we propose a systematic method to design robust LQG controllers. The proposed method requires only the LQG tuning parameters and the structure information of uncertainty. It will be shown that our approach can be effectively applied to flexible structure control design problems. Center for Noise and Vibration Control (NoViC), Dept. of Mech Eng., Korea Advanced Institute of Science and Technology (KAIST)     

加工过程QFT控制及与自适应控制的结合

阐述了定量反馈理论（QFT）的基本原理和设计步骤。并给出了设计实例。为了进一步改善系统性能。在QFT的基础上提出了QFT与自适应控制相结合的方案。QFT能克服对象的不确定性。保障系统的鲁棒性。自适应控制可以提高系统的控制精度。仿真结果表明。这种方法适合高精度系统的鲁棒控制。     

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.     

综合定量反馈理论与特征结构配置的飞行控制系统优化设计

定量反馈理论(QFT)是一种新颖的频率域鲁棒控制技术,在N ichols图上开展分析与设计。针对大包线范围内系统模型变化大的特点,可采用QFT设计横航向控制器。由于QFT主要针对单输入单输出(SISO)系统进行分析,因此首先应采用特征结构配置(EA)理论将无人机的横航向模态进行近似解耦,将多输入多输出(M IMO)系统转化为SISO系统,再采用QFT进行控制系统设计。本文将两种控制方法结合起来,构成综合优化飞行控制方法,针对某型无人机包线范围内选取的18个状态点组成的控制对象模板进行控制设计,并进行非线性仿真。仿真结果表明设计的控制器使得无人机在全包线范围内具有较好的性能和鲁棒稳定性。     

Performance analysis of active disturbance rejection tracking control for a class of uncertain LTI systems

The paper considers the tracking problem for a class of uncertain linear time invariant (LTI) systems with both uncertain parameters and external disturbances. The active disturbance rejection tracking controller is designed and the resulting closed-loop system׳s characteristics are comprehensively studied. In the time-domain, it is proven that the output of closed-loop system can approach its ideal trajectory in the transient process against different kinds of uncertainties by tuning the bandwidth of extended state observer (ESO). In the frequency-domain, different kinds of parameters׳ influences on the phase margin and the crossover frequency of the resulting control system are illuminated. Finally, the effectiveness and robustness of the controller are verified through the actuator position control system with uncertain parameters and load disturbances in the simulations.     

基于QFT的开关阀控气动位置伺服系统鲁棒控制

考虑开关阀的滞后特性,建立了高速开关阀控气动位置控制系统的非线性模型,并在原模型的基础上,将系统模型处理为包含滞后环节的数学模型。针对该模型对象参数不确定、摄动量大和负载变化范围大等问题,采用包含小闭环的2自由度控制结构,用定量反馈理论,进行系统的鲁棒稳定性、干扰抑制和跟踪性能设计,设计了具有鲁棒性能的控制器,并且设计了有效的摩擦力补偿器。经过试验验证,系统不仅具有较好的稳定鲁棒性,还具有很好的动态性能和位置精度。     

Robust-optimal active vibration controllers design for the uncertain flexible mechanical systems possessing integrity via genetic algorithm

In this paper, a robust-optimal control approach is proposed to treat the active vibration control (or active vibration suppression) problem of flexible mechanical systems under mode truncation, linear time-varying parameter uncertainties in both the controlled and residual parts, feedback gain perturbations, estimator gain perturbations and partial actuator failures. A sufficient condition is proposed to ensure that the flexible mechanical systems with time-varying structured parameter uncertainties are asymptotically stable against partial actuator failures. Systems which have such a property of keeping stable under partial actuator failures are said to possess integrity, and this is an inherent property of MIMO systems. Based on the robust stability constraint and the minimization of a defined H₂ performance, a hybrid Taguchi-genetic algorithm (HTGA) is applied to solve the optimal state feedback controller and observer design problem of uncertain flexible mechanical systems. A design example of a flexible rotor system is given to demonstrate the applicability of the proposed approach. It is shown that the proposed approach can obtain satisfactory results.     

Identification of multivariable nonlinear systems in the presence of colored noises using iterative hierarchical least squares algorithm

This paper presents an efficient method for identification of nonlinear Multi-Input Multi-Output (MIMO) systems in the presence of colored noises. The method studies the multivariable nonlinear Hammerstein and Wiener models, in which, the nonlinear memory-less block is approximated based on arbitrary vector-based basis functions. The linear time-invariant (LTI) block is modeled by an autoregressive moving average with exogenous (ARMAX) model which can effectively describe the moving average noises as well as the autoregressive and the exogenous dynamics. According to the multivariable nature of the system, a pseudo-linear-in-the-parameter model is obtained which includes two different kinds of unknown parameters, a vector and a matrix. Therefore, the standard least squares algorithm cannot be applied directly. To overcome this problem, a Hierarchical Least Squares Iterative (HLSI) algorithm is used to simultaneously estimate the vector and the matrix of unknown parameters as well as the noises. The efficiency of the proposed identification approaches are investigated through three nonlinear MIMO case studies.     

Robust control for a class of time varying systems via switching hypersurface design with output signals

Sliding mode control methods have been used widely since they provide robustness against parameter variations and disturbances. This paper focuses on the problem of a robust output-sliding control design for linear uncertain multi-input multi-output time-varying systems with norm-bounded uncertainty. Output signals are used for the definition of switching hypersurfaces. The formulation of a control law is emphasized. Output tracking can be achieved against a class of time varying parameter variations and external disturbances. The effectiveness of the proposed output-sliding control is confirmed by an application example.     

Uncertainty modeling and predicting the probability of stability and performance in the manufacture of dynamic systems

In this work, a method for determining the reliability of dynamic systems is discussed. Using statistical information on system parameters, the goal is to determine the probability of a dynamic system achieving or not achieving frequency domain performance specifications such as low frequency tracking error, and bandwidth. An example system is considered with closed loop control. A performance specification is given and converted into a performance weight transfer function. The example system is found to have a 20% chance of not achieving the given performance specification. An example of a realistic higher order system model of an electro hydraulic valve with spring feedback and position measurement feedback is also considered. The spring rate and viscous friction are considered as random variables with normal distributions. It was found that nearly 6% of valve systems would not achieve the given frequency domain performance requirement. Uncertainty modeling is also considered. An uncertainty model for the hydraulic valve systems is presented with the same uncertain parameters as in the previous example. However, the uncertainty model was designed such that only 95% of plants would be covered by the uncertainty model. This uncertainty model was applied to the valve control system example in a robust performance test.     

Identification of uncertain nonlinear systems for robust fuzzy control

In this paper, we consider fuzzy identification of uncertain nonlinear systems in Takagi-Sugeno (T-S) form for the purpose of robust fuzzy control design. The uncertain nonlinear system is represented using a fuzzy function having constant matrices and time varying uncertain matrices that describe the nominal model and the uncertainty in the nonlinear system respectively. The suggested method is based on linear programming approach and it comprises the identification of the nominal model and the bounds of the uncertain matrices and then expressing the uncertain matrices into uncertain norm bounded matrices accompanied by constant matrices. It has been observed that our method yields less conservative results than the other existing method proposed by S?krjanc et al. (2005) [11] and [12]. With the obtained fuzzy model, we showed the robust stability condition which provides a basis for different robust fuzzy control design. Finally, different simulation examples are presented for identification and control of uncertain nonlinear systems to illustrate the utility of our proposed identification method for robust fuzzy control.     

Improved results on delay-interval-dependent robust stability criteria for uncertain neutral-type systems with time-varying delays

In this paper, we consider the problem of delay-interval-dependent robust stability and stabilization of a class of linear uncertain neutral-type systems with time-varying delay. By constructing a candidate Lyapunov–Krasovskii functional (LKF), that takes into account the delay-range information appropriately, less conservative robust stability criteria are proposed in terms of linear matrix inequalities (LMIs) to compute the maximum allowable upper bounds (MAUB) for the delay-interval within which the uncertain neutral-type system under consideration remains asymptotically stable. The verifiable stabilizability conditions and memoryless state feedback control design are stated. Finally, numerical examples are also designated to demonstrate the effectiveness and reduced conservatism of the developed results.     

Resilient guaranteed cost control for uncertain T–S fuzzy systems with time-varying delays and Markov jump parameters

This paper aims to investigate the problem of resilient guaranteed cost control for uncertain Takagi–Sugeno fuzzy systems with Markov jump parameters and time-varying delay. A resilient mode-dependent fuzzy controller is designed and a weak sufficient condition is developed to ensure that the resulting closed-loop system is robust almost surely asymptotically stable with guaranteed cost index not exceeding the specified upper bound. Subsequently, the controller gain and upper bound of the guaranteed cost index can be obtained by solving a set of linear matrix inequalities. Finally, numerical and practical examples of the single-link robot arm system are provided to demonstrate the performance of the proposed approach.     

Robust extended Kalman filter of discrete-time Markovian jump nonlinear system under uncertain noise

This paper examines the problem of robust extended Kalman filter design for discrete-time Markovian jump nonlinear systems with noise uncertainty. Because of the existence of stochastic Markovian switching, the state and measurement equations of underlying system are subject to uncertain noise whose covariance matrices are time-varying or un-measurable instead of stationary. First, based on the expression of filtering performance deviation, admissible uncertainty of noise covariance matrix is given. Secondly, two forms of noise uncertainty are taken into account: Non-Structural and Structural. It is proved by applying game theory that this filter design is a robust mini-max filter. A numerical example shows the validity of the method.     

Machining force control with intelligent compensation

Force control is an effective means of improving the quality and efficiency of machining operations, so various approaches for force control have been proposed. However, due to the nonlinear, time-varying and uncertain characteristics of machining processes, it is difficult to develop force control systems that are stable and robust over the full range of operating conditions. This study proposed two control schemes to address such difficulties in the field of nonlinear force control by using a linear feedback proportional-derivate (PD) controller respectively with two different nonlinear intelligent compensators: fuzzy logic compensator (FLC) and neural network compensator (NNC). The PD controller is used to improve the transient response while maintaining the stability of the process system, and the FLC or NNC is employed to eliminate the steady-state error and compensate for the system nonlinearity (or uncertainty). The applications of the proposed schemes in machining processes show that the controllers adapt well to nonlinearity under time-varying cutting conditions in comparison to PID, PD, and FLC. The online updating of the NNC parameters through the Feedback-Error Learning can further improve the system performance.