Disturbance decoupling for a class of nonlinear MIMO systems by static measurement feedback

In this paper, the disturbance decoupling problem for a square-invertible nonlinear system is stated and solved by static feedback of measured variables only, in contrast with standard solutions which assume that the full state is available for feedback. The results are valid for left-invertible systems as well.     

Variable high-gain disturbance observer design with online adaption of observer gains embedded in numerical integration

In this paper, a variable gain design approach for the high-gain disturbance observer, called Proportional-Integral-Observer (PI-Observer), is proposed to solve the problem of choosing suitable observer gains. The high-gain PI-Observer is successfully applied to estimate unknown inputs of systems together with the system states. It is known that reasonable estimations of unknown inputs can only be derived using high observer gains. On the other hand, extremely large gains will cause serious problems with respect to measurements noise and unmodeled dynamics. According to the analysis of the estimation quality regarding to the factors which influence the estimation results, the optimal level of observer gains is changing during the estimation, an online adaption for the observer gains is therefore developed. The designed PI-Observer, called Advanced PI-Observer (API-Observer), will use changing observer gains from the adaption algorithm, which is proved to give stable estimation error dynamics. Simulation results from an elastic beam example are shown to illustrate the implementation of the API-Observer.     

Variable structure output feedback control design for a class of uncertain dynamic systems

In this paper, we consider the problem of designing a variable structure output feedback control (VSOFC) law for a class of uncertain systems with mismatched uncertainty in the state matrix. We derive existence conditions of linear sliding surfaces in terms of constrained linear matrix inequalities (LMIs), and we give VSOFC strategies. We also give a simple design procedure and parameterizations of the linear switching surfaces, together with solvability conditions for the given constrained LMIs. Finally, we give a design example in order to show the effectiveness of our method.     

Almost non-interacting control by measurement feedback

Consider a linear system Σ that, apart from a control input and a measurement output, has two exogeneous inputs and two exogenous outputs. Controlling such a system by means of a measurement feedback compensator Σ_c results in a closed loop system with two inputs and two outputs. Hence, the closed loop transfer matrix can be partitioned as a two by two block matrix.The problem addressed in this paper consists of the following. Given Σ and any positive number ge, is it possible to find Σ_c such that the off-diagonal blocks of the closed transfer matrix, in a suitable norm, are smaller than ε?For the solvability of this problem necessary and sufficient conditons will be derived.     

Disturbance attenuation by dynamic output feedback for input-delay systems

This paper addresses the optimal disturbance attenuation problem by output feedback for multivariable linear systems with delayed inputs. The attenuation is optimal in the sense that the controller minimizes the maximal amplitude of the plant output in response to such a disturbance. The controller is a general feedback, involving an observer, a state predictor, and a predicted state feedback. The optimal disturbance attenuation problem is formulated in terms of an equivalent system without delay. The optimal bound of the disturbance attenuation is then characterized, and it is shown that the optimal controller tends to have high gains. A necessary and sufficient condition to guarantee the existence of an optimal solution is provided using the geometric approach.     

A model reference quantitative feedback design theory with application to turbomachinery

A new decentralized robust control design framework, model reference quantitative feedback design (MRQFD), is developed for the design of the MIMO parametric uncertain control systems. An internal model reference loop is proposed to obtain the achievement of generalized diagonal dominance (GDD) and the reduction of uncertainty in the resultant compensated internal loop system. Based on nonnegative matrix theory, a useful design guide is derived to achieve the GDD condition for the internal model reference loop. Then a sensitivity-based quantitative feedback design (QFD) method is developed and used to solve the resulting series of single-loop QFD problems. The MIMO quantitative specifications are guaranteed to be satisfied by the proposed design framework for largely uncertain systems. A successful application to the design of a robust multivariable controller for the Allison PD-514 aircraft turbine engine is presented to demonstrate the effectiveness of the methodology developed here.     

Design of CIC roll-off compensation filter in a W-CDMA digital IF receiver

In a digital intermediate frequency (IF) receiver, decimation is performed to reduce the computational complexity and cascaded integrated comb (CIC) filter is used together with the decimation as an anti-aliasing filter. However, the CIC filter generates the roll-off phenomenon in the pass-band, which causes the receiving performance to be considerably degraded due to the distorted pass-band flatness of the receiving filter. In this paper, we propose a design method of the CIC roll-off compensation filter to reduce the performance degradation due to the roll-off characteristics of the CIC filter for a W-CDMA digital IF receiver. The performance of the proposed CIC roll-off compensation filter is confirmed through computer simulation in such a way that bit error rate (BER) is minimized by compensating the roll-off characteristics. In addition, the proposed method can be used in the design of a digital-to-analog (DAC) compensation filter and interpolator in the transmitter.     

一类饱和非有理系统状态反馈设计

本文研究了一类饱和非有理系统状态反馈镇定问题.通过线性分式表示技术,这类非有理系统可以转化为带有两个非线性回路的线性时不变(linear time-invariant,LTI)系统.假设非有理函数项分别满足局部扇形区间不等式以及局部Lipschitz条件,提出了两种基于LMI条件的镇定方法.最后,举例证明了所提出方法的有效性.     

Adaptive output feedback tracking control of a nonholonomic mobile robot

An adaptive output feedback tracking controller for nonholonomic mobile robots is proposed to guarantee that the tracking errors are confined to an arbitrarily small ball. The major difficulties are caused by simultaneous existence of nonholonomic constraints, unknown system parameters and a quadratic term of unmeasurable states in the mobile robot dynamic system as well as their couplings. To overcome these difficulties, we propose a new adaptive control scheme including designing a new adaptive state feedback controller and two high-gain observers to estimate the unknown linear and angular velocities respectively. It is shown that the closed loop adaptive system is stable and the tracking errors are guaranteed to be within the pre-specified bounds which can be arbitrarily small. Simulation results also verify the effectiveness of the proposed scheme.     

Fault diagnosis based on high-gain observer with an update law for a class of nonlinear systems

In this paper, by using the well-known high-gain observer design, an update law for the gain and an adaptive estimation of parameters, a new method of fault diagnosis for a class of nonlinear systems is presented. Without resort to any transformation for the parameters, the estimation errors of the states and the parameters are guaranteed to be globally exponentially convergent by a persistent excitation condition. Compared to the existing results, it can be applied to nonlinear systems with nonlinear terms admitting an incremental rate depending on the measured output. A case study further verifies the validity of the proposed research.     

Almost disturbance decoupling for a class of nonlinear systems via sampled‐data output feedback control

This paper addresses the problem of almost disturbance decoupling (ADD) using sampled‐data output feedback control for a class of continuous‐time nonlinear systems. Under a lower‐triangular linear growth condition, a sampled‐data output feedback controller is constructed based on the output feedback domination approach, and a Gronwall–Bellman‐like inequality is established in the presence of disturbances. Even though a sampled‐data controller is employed for easy computer implementation, the proposed controller is still able to achieve ADD under the commonly used continuous‐time requirement, that is, the disturbances' effect on the output is attenuated to an arbitrary degree of accuracy in the L₂ gain sense. Copyright © 2015 John Wiley & Sons, Ltd.     

Peaking free variable structure control of uncertain linear systems based on a high-gain observer

An output-feedback model-reference variable structure controller based on a high-gain observer (HGO) is proposed and analyzed. For single-input-single-output (SISO) linear plants with relative degree greater than one, the control law is generated using the HGO signals only to drive the sign function of the variable structure control component while the sign function gain, also called modulation, as well as the other components of the control signal are generated using signals from state variable filters which do not require high gain and are free of peaking. This scheme achieves global exponential stability with respect to a small residual set and does not generate peaking in the control signal.     

Acceleration feedback in a lithographic tool

Acceleration feedback increases the mass of a system as experienced by disturbance forces. A high bandwidth is required to avoid phase lag in the position control loop. This article splits the acceleration controller in a forward and backward path to create the original process behavior for the position controller, removing the high-bandwidth requirement. Digital controller effects, incorporation of plant dynamics, and implications for setpoint feedforward are discussed. The method is implemented in the stage of a lithographic scanner operating at nanometer accuracy in semiconductor manufacturing. It is shown that the low-frequent disturbance rejection is considerably improved without impacting higher-frequency performance.     

状态反馈预测控制干扰解耦的研究

讨论状态反馈预测控制系统设计中的干扰解耦设计问题，给出了状态反馈预测控制系统干扰可解耦设计的充分必要条件。基于状态空间模型，给出了状态反馈预测控制系统设计参数——预测时域按干扰解耦设计的选取方法。它可改善控制系统的性能，提高控制系统的抗干扰能力。仿真结果表明了状态反馈预测控制系统干扰解耦设计的有效性。     

H∞-control by state feedback: An iterative algorithm and characterization of high-gain occurence

We present an iterative algorithm to compute the achievable H_∞-norm by state feedbak for a standard regular problem and give a characterization when high-gain feedback is necessary to approach the optimal value.

If there is no need for high-gain components to approximate the optimal value, we can reduce the problem to the computation of the H_∞-norm of a certain stable transfer matrix.     

Computational complexity of a problem arising in fixed order output feedback design

This paper is concerned with a matrix inequality problem which arises in fixed order output feedback control design. This problem involves finding two symmetric and positive definitive matrices X and Y such that each satisfies a linear matrix inequality and that XY=I. It is well-known that many control problems such as fixed order output feedback stabilization, H_∞ control, guaranteed H₂ control, and mixed H₂/H_∞ control can all be converted into the matrix inequality problem above, including static output feedback problems as a special case. We show, however, that this matrix inequality problem is NP-hard.     

输出反馈实现一类带不确定输入动态非线性系统的鲁棒几乎干扰解耦

研究一类带不确定输入动态非线性系统的输出反馈干扰抑制问题并基于观测器给出了输出反馈控制器 构造性的设计方法.所设计的控制器具有对可允许不确定动态的鲁棒性.不仅在L₂增益意义上抑制了干扰对输出 的影响,同时在ISS镇定意义上抑制了干扰对状态的影响.     

一类非线性时滞广义系统的状态反馈控制

利用线性矩阵不等式(LMI),讨论了一类非线性时滞广义系统的状态反馈控制问题.通过对非线性映射Frechet导数的逆矩阵的估计,给出了系统渐近稳定的充分条件.这一条件与时滞相关,可归结为一个线性矩阵不等式的可解性.在LMI有解的条件下,可得到系统状态反馈控制器的参数表示.数值实例表明该方法是有效的.     

Adaptive λ-tracking for a class of infinite-dimensional systems

For a class of high-gain stabilizable multivariable linear infinite-dimensional systems we present an adaptive control law which achieves approximate asymptotic tracking in the sense that the tracking error tends asymptotically to a ball centred at 0 and of arbitrary prescribed radius λ>0. This control strategy, called λ-tracking, combines proportional error feedback with a simple nonlinear adaptation of the feedback gain. It does not involve any parameter estimation algorithms, nor is it based on the internal model principle. The class of reference signals is W^1,∞, the Sobolev space of absolutely continuous functions which are bounded and have essentially bounded derivative. The control strategy is robust with respect to output measurement noise in W^1,∞ and bounded input disturbances. We apply our results to retarded systems and integrodifferential systems.