风扰影响下的无人机非线性广义最小方差跟踪控制

本文以鱼鹰型固定翼无人机为研究对象,基于非线性广义最小方差(nonlinear generalized minimum variance,NGMV)最优控制理论,研究了受到非线性阵风干扰影响下的无人机跟踪控制问题.首先对鱼鹰型无人机动力学模型解耦,在解耦后的横向和纵向模型上分别实现跟踪控制;然后针对阵风非线性模型的特定形式,根据NGMV理论设计了增维的非线性广义最小方差控制器,使得模型充分考虑了阵风干扰的特性.所设计的NGMV最优控制器的主要优势在于它能处理带有干扰和时滞环节的非线性系统.多组阵风扰动的仿真试验结果表明,非线性广义最小方差最优控制器具有跟踪性和收敛性.     

线性混杂自动机的非线性广义最小方差控制

研究线性混杂自动机(LHA) 模型. 线性混杂自动机在一定条件下可以转化成与之等价的状态依赖空间模型, 等价性是指两个系统所产生的轨迹是相同的. 采用非线性广义最小方差算法对状态依赖空间模型进行控制器的设计, 非线性广义最小方差控制器的设计则基于更为一般的非线性模型, 模型中可含有时滞项和外界干扰, 控制器的计算过程简单且易于实现. 仿真结果表明, 非线性广义最小方差控制算法能够有效地控制线性混杂自动机, 而且在系统存在延时、干扰以及噪声的情况下能够得到较为理想的控制效果.     

GMV control of non-linear continuous-time systems including common delays and state-space models

A non-linear generalized minimum variance control law is proposed for the control of non-linear continuous-time multivariable systems with common delays on input and output channels. The quadratic cost index involves both error and control signal costing terms. The solution for the control law is obtained using a non-linear operator representation of the plant and a linear state-equation model for the disturbance and reference models. The reference and disturbance models are represented by linear subsystems. However, the plant model can be in a very general non-linear operator form, which could involve state-space, transfer operators or non-linear function look up tables. The structure of the system and criterion is chosen so that a simple controller structure and solution is obtained. The controller obtained is simple to implement, particularly in one form, which might be considered to be a state-space version of a non-linear Smith predictor. The results are related to those for discrete-time systems but the presence of the transport delay terms complicates the solution rather more in the continuous-time case.     

非线性广义最小方差控制律综述

如何设计简单的控制策略对复杂非线性系统进行控制是控制界还未解决的难题．非线性广义最小方差控制律的提出使得非线性控制器的设计可以基于更为一般的非线性模型，并且控制器易于实现．整个系统包含时滞环节，稳定的非线性输入子系统和一个可以用多项式或者状态空间描述的子系统．通过最小化由误差加权项、状态加权项和输入加权项组成的信号的方差得到优化控制器．在系统为开环稳定的情况下，可用史密斯预估器进行控制．本文首先介绍了非线性广义最小方差控制的发展进程，然后综述了基于状态空间和多项式描述的系统的非线性广义最小方差控制器的设计以及其现状和今后的发展方向．     

Robust nonlinear generalised minimum variance control and fault monitoring

The first part of this paper extends the Nonlinear Generalised Minimum Variance (NGMV) controller to improve the robustness of its control or set-point tracking performance. This is achieved by replacing the Kalman filter included in the original NGMV controller with an observer to minimise the effect of uncertainty, which includes unknown disturbance, modelling error, and faults. The observer design also allows the NGMV controller to be utilised in fault monitoring. More specifically, the second part of this paper obtains the observer gain by solving a multi-objective optimisation problem through the application of a genetic algorithm so that the residual signal becomes sensitive to faults and insensitive to any other uncertainty. The control and fault monitoring performance of the extended NGMV controllers is tested by application to a nonlinear tank model.     

基于LS-SVM的一类非线性系统的性能估计

控制系统性能估计的研究多数针对线性系统,但是非线性系统本质上更加复杂,用传统的方法进行估计存在局限性.对于一类可由非线性部分叠加线性干扰表示的非线性系统,首先分析了其反馈不变量的存在性,指出此类系统性能估计的关键在于构造超前预测模型.接着用最小二乘支持向量机辨识非线性模型,把最小方差性能估计问题转换成模型参数辨识问题,...     

Structured Singular Valued based robust nonlinear model predictive controller using Volterra series models

A methodology is proposed for designing a robust nonlinear model predictive controller based on a Volterra series model with uncertain coefficients. A key benefit of using the Volterra series model is that it can be split into a nominal and an uncertainty model thus permitting the application of robust analysis tools. The controller is based on the on-line solution of a robust performance test based on a Structured Singular Value norm. The cost function of the controller can be formulated to account for manipulated variable movement weighting, manipulated variable constraints and a terminal condition. Finally, the proposed methodology is applied to a single-input–single-output continuous stirred tank reactor problem and to a multiple-input–multiple-output pH neutralization process.     

H ∞ control of a Wiener-type system

A Wiener system is a system which can be modelled as a linear dynamic followed by a static gain. The goal of this paper is to develop a robust H _∞ compensator for controlling an SISO Wiener system. The controller also takes the form of a Wiener model. The design approach consists of the approximation of the non-linear gain using a piecewise linear (PWL) function and in using a linear controller for each sector obtained from this approximation. Therefore, the general controller structure can be stated as a linear dynamic compensator in series with a PWL static gain.

As an illustrative case, a neutralization pH reaction between a strong acid and a strong base in the presence of a buffer agent is dealt with. Computer simulations are developed for showing the performance of the proposed controller.     

MPC for discrete-event systems with soft and hard synchronization constraints

Discrete-event systems with only synchronization and no concurrency, also known as timed event graphs or (max, +)-linear systems, have been studied by several authors. The synchronization constraints that arise in these discrete-event systems are hard, i.e. they cannot be broken under any circumstances. In this paper we consider a more extended class of discrete-event systems with both hard and soft synchronization constraints, i.e. if necessary, some synchronization conditions may be broken, but then a penalty is incurred. We show how the model predictive control (MPC) framework, which is a very popular controller design method in the process industry, can be extended to this class of discrete-event systems. In general, the MPC control design problem for discrete-event systems with soft and hard synchronization constraints leads to a non-linear non-convex optimization problem. We show that the optimal MPC strategy can also be computed using an extended linear complementary problem.     

Identification for control: Optimal input intended to identify a minimum variance controller

It is well known that the quality of the parameters identified during an identification experiment depends on the applied excitation signal. Prediction error identification using full order parametric models delivers an ellipsoidal region in which the true parameters lie with some prescribed probability level. This ellipsoidal region is determined by the covariance matrix of the parameters. Input design strategies aim at the minimization of some measure of this covariance matrix. We show that it is possible to optimize the input in an identification experiment with respect to a performance cost function of a closed-loop system involving explicitly the dependence of the designed controller on the identified model. In the present contribution we focus on finding the optimal input for the estimation of the parameters of a minimum variance controller, without the intermediate step of first minimizing some measure of the model parameter accuracy. We do this in conjunction with using covariance formulas which are not asymptotic in the model order, which is rather new in the domain of optimal input design. The identification procedure is performed in closed-loop. Besides optimizing the input power spectrum for the identification experiment, we also address the question of optimality of the controller. It is a wide belief that the minimum variance controller should be the optimal choice, since we perform an experiment for designing a minimum variance controller. However, we show that this may not always be the case, but rather depends on the model structure.     

PID based nonlinear processes control model uncertainty improvement by using Gaussian process model

Proportional-integral-derivative (PID) controller design based on the Gaussian process (GP) model is proposed in this study. The GP model, defined by its mean and covariance function, provides predictive variance in addition to the predicted mean. GP model highlights areas where prediction quality is poor, due to the lack of data, by indicating the higher variance around the predicted mean. The variance information is taken into account in the PID controller design and is used for the selection of data to improve the model at the successive stage. This results in a trade-off between safety and the performance due to the controller avoiding the region with large variance at the cost of not tracking the set point to ensure process safety. The proposed direct method evaluates the PID controller design by the gradient calculation. In order to reduce computation the characteristic of the instantaneous linearized GP model is extracted for a linearized framework of PID controller design. Two case studies on continuous and batch processes were carried out to illustrate the applicability of the proposed method.     

基于支持向量机的参数自整定PID非线性系统控制

对非线性系统提出了一种基于支持向量机的自整定PID控制新方法.用支持向量机辨识系统的非线性关系,并对之进行线性化,提取出瞬时线性模型,采用最小方差的准则获取PID控制器的最优参数.为改善控制器的性能,提出了一些改进措施,包括使用一阶滤波器、控制器参数更新标准及惩罚系数的调整等.通过对典型非线性系统的仿真,验证了该方法的有效性和可行性.     

一类非线性系统的最小方差性能评估策略/

针对线性控制回路性能评估会因非线性因素的引入而出现过估计的问题,提出一种性能评估方法.通过计算输出信号的双相干系数对回路的非线性特征进行提前判断,然后使用Volterra级数将其最小方差性能评估问题转化为一类模型辨识问题.通过仿真实例,将所得结果和线性性能评估方法进行比较,比较结果验证了所提出算法的优越性.     

Minimum variance performance map for constrained model predictive control

A minimum variance performance map is introduced for constrained linear model predictive control (MPC). The minimum variance performance map provides a demonstration of the effect of constraints in an MPC on the best achievable controller performance. The constrained minimum variance controller is formulated for the MPC system to be monitored. Using multi-parametric quadratic programming (mp-QP), the linear, piecewise control law is obtained for the constrained minimum variance controller. The linear, piecewise control law is used with a Kalman filter to obtain the minimum output variance in each region of the state space partition. The minimum variance performance map is demonstrated on a second order process with a constraint on the input amplitude.     

A Biologically-Inspired Micro Aerial Vehicle

This paper introduces a novel framework for the design, modeling and control of a Micro Aerial Vehicle (MAV). The vehicle’s conceptual design is based on biologically-inspired principles and emulates a dragonfly (Odonata–Anisoptera). We have taken inspiration from the flight mechanism features of the dragonfly and have developed indigenous designs in creating a novel version of a Flapping Wing MAV (FWMAV). The MAV design incorporates a complex mechanical construction and a sophisticated multi-layered, hybrid, linear/non-linear controller to achieve extended flight times and improved agility compared to other rotary wing and FWMAV Vertical Take Off and Landing (VTOL) designs. The first MAV prototype will have a ballpark weight including sensor payload of around 30 g. The targeted lifting capability is about twice the weight. The MAV features state of the art sensing and instrumentation payload, which includes integrated high-power on-board processors, 6DoF inertial sensors, 3DoF compasses, GPS, embedded camera and long-range telemetry capability. A 3-layer control mechanism has been developed to harness the dynamics and attain complete navigational control of the MAV. The inner-layer is composed of a ‘quad hybrid-energy controller’ and two higher layers are at present, implementing a linear controller; the latter will be replaced eventually with a dynamic adaptive non-linear controller. The advantages of the proposed design compared to other similar ones include higher energy efficiency and extended flight endurance. The design features elastic storage and re-use of propulsion energy favoring energy conservation during flight. The design/modeling of the MAV and its kinematics & dynamics have been tested under simulation to achieve desired performance. The potential applications for such a high endurance vehicle are numerous, including air-deployable mass surveillance and reconnaissance in cluster and swarm formations. The efficacy of the design is demonstrated through a simulation environment. The dynamics are verified through simulations and a general linear controller coupled with an energy based non-linear controller is shown to operate the vehicle in a stable regime. In accordance with specified objectives a prototype is being developed for flight-testing and demonstration purposes.     

Discrete minimax linear quadratic regulation of continuous-time systems

In this paper, the statistical cyclostationary characteristics of a controlled continuous-time system which result as a consequence of implementing a digital controller are investigated. A minimax quadratic cost function which takes into account the periodic nature of the statistics is defined and optimized. The resulting linear state feedback law improves the intersample behavior of the controlled system when compared to discrete-time optimization. In particular, the minimax variance regulator which is proposed as a new design method for regulating the output variance offers a significant improvement over the classical minimum variance regulator.     

Conditions when minimum variance control is the optimal experiment for identifying a minimum variance controller

It is well known that if we intend to use a minimum variance control strategy, which is designed based on a model obtained from an identification experiment, the best experiment which can be performed on the system to determine such a model (subject to output power constraints, or for some specific model structures) is to use the true minimum variance controller. This result has been derived under several circumstances, first using asymptotic (in model order) variance expressions but also more recently for ARMAX models of finite order. In this paper we re-approach this problem using a recently developed expression for the variance of parametric frequency function estimates. This allows a geometric analysis of the problem and the generalization of the aforementioned finite model order ARMAX results to general linear model structures.     

Non-fragile robust optimal guaranteed cost control of uncertain 2-D discrete state-delayed systems

This paper is concerned with the problem of non-fragile robust optimal guaranteed cost control for a class of uncertain two-dimensional (2-D) discrete state-delayed systems described by the general model with norm-bounded uncertainties. Our attention is focused on the design of non-fragile state feedback controllers such that the resulting closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible parameter uncertainties and controller gain variations. A sufficient condition for the existence of such controllers is established under the linear matrix inequality framework. Moreover, a convex optimisation problem is proposed to select a non-fragile robust optimal guaranteed cost controller stabilising the 2-D discrete state-delayed system as well as achieving the least guaranteed cost for the resulting closed-loop system. The proposed method is compared with the previously reported criterion. Finally, illustrative examples are given to show the potential of the proposed technique.     

基于Volterra级数的一类非线性系统性能评估

化工过程多具有非线性特征,针对用线性系统性能评估方法处理非线性系统会存在过估计的情况,研究了一类叠加线性干扰的非线性系统的性能评估问题。通过使用Volterra级数近似非线性环节,把最小方差性能评估问题转化成一类模型辨识问题,并从辨识误差中得到非线性系统的最小方差估计值。通过数值仿真,将新方法所得结果和现有线性性能评估方法进行了比较,验证了设计算法的优越性。     

Recursive identification of linear and non-linear systems

The paper develops recursive techniques for off-line identification of linear and nonlinear systems. It is shown that if the system is linear and time invariant, impulse response characterization of the system coupled with an orthogonal series approximation can be utilized for the purpose stated above. The techniques of adaptive Kalman filtering are shown to be applicable, which besides permitting recursive evaluation of the coefficients, lead to a number of important advantages. In the second part of the study, the proposed method is extended for recursive identification of a class of non-linear systems which can be represented as a cascade combination of a linear dynamical system and a non-linear zero memory system. The method of Volterra series representation of such systems is utilized. Results are illustrated through numerical examples in each case.