四旋翼飞行器的轨迹跟踪抗干扰控制

针对四旋翼飞行器轨迹跟踪问题中系统存在模型不确定和易受到外界扰动的情况,提出了基于切换函数的扩张状态观测器设计方法来对系统中的扰动进行估计,并将估计值与滑模控制器的设计相结合,实现了对系统中非匹配不确定性和匹配不确定性的抑制且实现了系统跟踪误差的一致最终有界.首先,根据变量间的耦合关系将飞行器系统模型分解为两个子系统模型,设计扩张状态观测器对子系统中的非匹配不确定性进行估计,并将估计值作为变量加入到切换函数的设计中;进而基于切换函数设计扩张状态观测器以估计经切换函数重构系统中的扰动,并在控制器中对扰动进行补偿.最后通过李雅普诺夫理论证明了控制系统的稳定性.通过仿真验证了本文提出的方法能够有效实现飞行器轨迹跟踪控制且能够抑止传统滑模控制的抖振现象.     

基于动态参考规划的鲁棒Tube模型预测跟踪控制

为实现扰动和约束作用下对系统的最优鲁棒跟踪, 提出一种动态参考规划(DRP)方法, 设计鲁棒Tube模型预测控制器(RTMPC)将系统状态驱动到以最优跟踪点为中心的扰动不变集内. 基于DRP的RTMPC控制方法, 以多步参考为决策变量, 确保在线优化递归可行性的同时, 增加在线优化的自由度; 另外, 通过设定目标函数惩罚标称状态轨迹和参考稳态之间、以及最后一步参考稳态和设定点之间的加权欧式距离, 可实现最优鲁棒跟踪.     

有界扰动下异质车辆队列分布式鲁棒经济预测控制

针对有界扰动下异质车辆队列节能与稳定分布式协同控制问题,提出一种新的分布式鲁棒经济模型预测控制(economic model predictive control, EMPC)策略.首先采用不确定误差模型描述有界扰动下异质车辆队列纵向行驶动态特性,再应用tube思想对系统约束进行紧缩设计,补偿有界扰动对系统造成的不确定性.其次,采用局部车辆行驶能耗模型描述车辆队列分布式经济性能优化的有限时域最优控制问题,并利用传统跟踪性能指标设计附加稳定收缩约束函数.进一步,基于系统收缩原理,建立车辆队列闭环系统关于有界扰动的输入-状态稳定性条件.最后,通过与车辆队列传统分布式鲁棒模型预测控制策略的数值仿真对比结果验证了所提出策略的有效性和优越性.     

精确估计下的多智能体系统漏斗复合控制

针对一类具有时变扰动的非线性多智能体系统, 研究其在有向拓扑下的一致性跟踪问题, 提出一种基于精 确估计的复合自适应预设有限时间(PFT)漏斗控制方法. 首先, 构建一种新的PFT漏斗控制, 使跟踪误差约束在PFT 漏斗边界内. 其次, 采用神经网络(NN)逼近系统的未知非线性, 并利用NN逼近信息设计扰动观测器, 建立基于NN和 扰动观测器的复合估计模型, 将得到的预测误差引入NN权值的复合更新律中, 实现对未知非线性和时变扰动的精 确估计. 然后, 利用动态面技术和误差补偿机制, 在解决传统反步法“计算爆炸”问题的同时, 消除滤波器误差对系 统的影响. 最后, 通过Lyapunov稳定性理论证明闭环系统所有信号均为有界的, 并通过仿真实验验证控制方法的有 效性.     

基于等价输入干扰滑模观测器的磁悬浮球系统模型预测控制

本文针对系统不确定性和外部干扰引起的磁悬浮球系统控制性能下降的问题,提出了一种基于等价输入干扰滑模观测器的模型预测控制(MPC+EIDSMO)方法.首先将原系统转化为EID系统,采用等价输入干扰滑模观测器对EID系统状态变量及等价输入干扰进行估计;然后基于状态估计值设计模型预测控制器,并将等价输入干扰估计值以前馈的方式补偿后得到最终的复合控制律,实现对参考位置跟踪的快速性,准确性以及对总扰动的鲁棒性.值得注意的是,与传统EID结构中的龙伯格观测器相比,等价输入干扰滑模观测器中增加的非线性观测误差反馈项有助于提高状态估计的快速性和精确性.从理论上证明了该系统是全局一致毕竟有界的.仿真和实验结果表明,相较于基于EID观测器的模型预测控制方法和基于龙伯格观测器的积分模型预测控制方法,所提方法提高了磁悬浮球系统的跟踪性能,并且有效的抑制了系统不确定性和外部干扰.     

四旋翼飞行器自适应动态面轨迹跟踪控制

针对具有未知外界扰动和系统不确定性集总未知非线性的四旋翼飞行器,提出了一种采用自适应不确定性补偿器的自适应动态面轨迹跟踪方法.通过将四旋翼飞行器系统分解为位置、欧拉角和角速率3个动态子系统,使各子系统虚拟控制器设计能充分考虑欠驱动约束;结合动态面控制技术,通过采用一阶低通滤波器,避免对虚拟控制信号求导;进而设计自适应不确定性补偿器,处理未知外界扰动和系统不确定性,最终确保闭环控制系统的稳定性、跟踪误差一致最终有界和系统所有状态信号有界.仿真研究和实验结果验证了本文提出控制方法的有效性和优越性.     

基于鲁棒正不变集的传感器故障区间估计

针对具有传感器故障和未知扰动与测量噪声的线性离散系统, 提出了一种传感器故障区间估计方法. 将传感器故障视为增广状态, 原始系统转化为一个等效的广义系统. 为了得到故障的点估计同时抑制扰动和噪声的影响, 基于有界实引理设计了一个针对广义系统的鲁棒状态观测器. 然后, 通过中心对称多胞体技术实现对故障的区间估计并基于鲁棒正不变集给出了一种降低区间估计计算量的方法. 最后, 通过一个垂直起降(Vertical take-off and landing, VTOL)飞行器线性化模型的仿真算例验证了所提出方法的有效性与优越性.     

自由漂浮空间机器人轨迹跟踪的模型预测控制

针对传统控制方法难以解决自由漂浮空间机器人(free-floating space robot, FFSR)轨迹跟踪过程中的各类约束的问题,采用模型预测控制对自由漂浮空间机器人的轨迹跟踪问题进行了研究.在自由漂浮空间机器人拉格朗日动力学模型的基础上,建立了系统伪线性化的扩展状态空间模型;在给定系统的性能指标和各类约束的情况下,基于拉盖尔模型设计相应的离散模型预测控制器,并证明控制器的稳定性,控制器中引入任务空间滑模变量实现了对末端期望位置和期望速度的同时跟踪;以平面二杆自由漂浮空间机器人为例,对无约束末端轨迹跟踪和有约束末端轨迹跟踪两种情况进行对比仿真验证.仿真结果表明,该模型预测控制器不仅可以实现对末端期望轨迹的有效跟踪,还能满足各类约束.     

基于干扰观测器的机械臂广义模型预测轨迹跟踪控制

为实现对多自由度机械臂关节运动精确轨迹跟踪,提出一种基于非线性干扰观测器的广义模型预测轨迹跟踪控制方法。针对机械臂轨迹跟踪运动学子系统,采用广义预测控制（Generalized Predictive Control,GPC）方法设计期望的虚拟关节角速度。对于机械臂轨迹跟踪动力学子系统,考虑机械臂的参数不确定性和未知外界扰动,利用GPC方法设计关节力矩控制输入,基于非线性干扰观测器方法实时估计和补偿系统模型中的不确定性。在李雅普诺夫稳定性理论框架下证明了机械臂关节角位置和角速度的跟踪误差最终收敛于零的小邻域。数值仿真验证了所提出控制方法的有效性和优越性。     

基于收缩约束模型预测控制的无人车辆路径跟踪

针对存在有界扰动的非线性无人驾驶车辆避障过程中最优路径规划跟踪问题,提出一种基于预测时域内系统输入输出收缩约束(PIOCC)的模型预测控制(MPC)方法.首先在构建目标函数时,为扩大可行性解的范围引入软约束思想,将最优规划路径的跟随问题转化为对模型预测控制优化问题的求解;其次为避免短预测时域造成闭环系统发散而导致在约束条件限定下出现无可行性解的情况,采用预测时域内系统输入输出收缩约束的方法,设计模型预测控制器;再次基于Lyapunov稳定性理论证明所设计的模型预测闭环控制系统是渐近稳定的;最后通过仿真实例验证了所提出基于PIOCC的控制策略在解决扩大可行解范围和避免闭环系统发散问题时的有效性,实现了无人驾驶车辆在路径跟踪时具有良好的快速性和稳定性.     

Combined Design of Disturbance Model and Observer for Offset-Free Model Predictive Control

This note presents a method for the combined design of an integrating disturbance model and of the observer (for the augmented system) to be used in offset-free model predictive controllers. A dynamic observer is designed for the original (nonaugmented) system by solving an H_prop control problem aimed at minimizing the effect of unmeasured disturbances and plant/model mismatch on the output prediction error. It is shown that, when offset-free control is sought, the dynamic observer is equivalent to choosing an integrating disturbance model and an observer for the augmented system. An example of a chemical reactor shows the main features and benefits of the proposed method.     

Disturbance modeling for offset-free linear model predictive control

An offset-free controller is one that drives controlled outputs to their desired targets at steady state. In the linear model predictive control (MPC) framework, offset-free control is usually achieved by adding step disturbances to the process model. The most widely-used industrial MPC implementations assume a constant output disturbance that can lead to sluggish rejection of disturbances that enter the process elsewhere. This paper presents a general disturbance model that accommodates unmeasured disturbances entering through the process input, state, or output. Conditions that guarantee detectability of the augmented system model are provided, and a steady-state target calculation is constructed to remove the effects of estimated disturbances. Conditions for which offset-free control is possible are stated for the combined estimator, steady-state target calculation, and dynamic controller. Simulation examples are provided to illustrate trade-offs in disturbance model design.     

Linear offset-free Model Predictive Control

This work addresses the problem of offset-free Model Predictive Control (MPC) when tracking an asymptotically constant reference. In the first part, compact and intuitive conditions for offset-free MPC control are introduced by using the arguments of the internal model principle. In the second part, we study the case where the number of measured variables is larger than the number of tracked variables. The plant model is augmented only by as many states as there are tracked variables, and an algorithm which guarantees offset-free tracking is presented. In the last part, offset-free tracking properties for special implementations of MPC schemes are briefly discussed.     

Output tracking of constrained nonlinear processes with offset-free input-to-state stable fuzzy predictive control

This paper develops an efficient offset-free output feedback predictive control approach to nonlinear processes based on their approximate fuzzy models as well as an integrating disturbance model. The estimated disturbance signals account for all the plant-model mismatch and unmodeled plant disturbances. An augmented piecewise observer, constructed by solving some linear matrix inequalities, is used to estimate the system states and the lumped disturbances. Based on the reference from an online constrained target generator, the fuzzy model predictive control law can be easily obtained by solving a convex semi-definite programming optimization problem subject to several linear matrix inequalities. The resulting closed-loop system is guaranteed to be input-to-state stable even in the presence of observer estimation error. The zero offset output tracking property of the proposed control approach is proved, and subsequently demonstrated by the simulation results on a strongly nonlinear benchmark plant.     

Tuning SISO offset-free Model Predictive Control based on ARX models

In this paper, we present a tuning methodology for a simple offset-free SISO Model Predictive Controller (MPC) based on autoregressive models with exogenous inputs (ARX models). ARX models simplify system identification as they can be identified from data using convex optimization. Furthermore, the proposed controller is simple to tune as it has only one free tuning parameter. These two features are advantageous in predictive process control as they simplify industrial commissioning of MPC. Disturbance rejection and offset-free control is important in industrial process control. To achieve offset-free control in face of unknown disturbances or model-plant mismatch, integrators must be introduced in either the estimator or the regulator. Traditionally, offset-free control is achieved using Brownian disturbance models in the estimator. In this paper we achieve offset-free control by extending the noise model with a filter containing an integrator. This filter is a first order ARMA model. By simulation and analysis, we argue that it is independent of the parameterization of the underlying linear plant; while the tuning of traditional disturbance models is system dependent. Using this insight, we present MPC for SISO systems based on ARX models combined with the first order filter. We derive expressions for the closed-loop variance of the unconstrained MPC based on a state space representation in innovation form and use these expressions to develop a tuning procedure for the regulator. We establish formal equivalence between GPC and state space based off-set free MPC. By simulation we demonstrate this procedure for a third order system. The offset-free ARX MPC demonstrates satisfactory set point tracking and rejection of an unmeasured step disturbance for a simulated furnace with a long time delay.     

Offset-free model predictive control of a vapor compression cycle

This work describes the application of an offset-free model predictive controller (OF-MPC) to a vapor compression cycle (VCC). To this end, first a linear model is identified from data generated from a first-principle model of a VCC, interfaced with a building model implemented in EnergyPlus. Next, a model predictive controller is designed that includes an augmented model (including disturbance states) and an associated Luenberger observer to estimate the disturbance (plant-model mismatch) at steady state and eliminate it. Tuning guidelines are presented that enable partial ‘decoupling’ of the Luenberger design and choice of MPC parameters, leading to offset elimination and superior tracking performance while reducing the energy demand on the VCC, relative to traditional control approaches. The superior closed-loop performance of the OF-MPC strategy is demonstrated for a VCC model in isolation, subject to realistic disturbances and subject to measurement noise.     

Parsimonious cooperative distributed MPC algorithms for offset-free tracking

We propose in this paper novel cooperative distributed MPC algorithms for tracking of piecewise constant setpoints in linear discrete-time systems. The available literature for cooperative tracking requires that each local controller uses the centralized state dynamics while optimizing over its local input sequence. Furthermore, each local controller must consider a centralized target model. The proposed algorithms instead use a suitably augmented local system, which in general has lower dimension compared to the centralized system. The same parsimonious parameterization is exploited to define a target model in which only a subset of the overall steady-state input is the decision variable. Consequently the optimization problems to be solved by each local controller are made simpler. We also present a distributed offset-free MPC algorithm for tracking in the presence of modeling errors and disturbances, and we illustrate the main features and advantages of the proposed methods by means of a multiple evaporator process case study.     

Constrained nonlinear MPC for accelerated tracking piece-wise references and its applications to thermal systems

In this paper, we propose a model predictive control (MPC) strategy for accelerated offset-free tracking piece-wise constant reference signals of nonlinear systems subject to state and control constraints. Some special contractive constraints on tracking errors and terminal constraints are embedded into the tracking nonlinear MPC formulation. Then, recursive feasibility and closed-loop convergence of the tracking MPC are guaranteed in the presence of piece-wise references and constraints by deriving some sufficient conditions. Moreover, the local optimality of the tracking MPC is achieved for unreachable output reference signals. By comparing to traditional tracking MPC, the simulation experiment of a thermal system is used to demonstrate the acceleration ability and the effectiveness of the tracking MPC scheme proposed here.     

Nonlinear offset-free model predictive control

This paper addresses offset-free reference tracking of asymptotically constant reference signals using Model Predictive Control. Existing results for linear models are extended to general nonlinear models. The core of the proposed method employs a disturbance model and an observer to estimate its state. Typical disturbance models are shown and the implications of using them are discussed. Conditions are given for which this setup eliminates the tracking error asymptotically. Basically, we prove that error free output estimation and error free nominal tracking imply offset-free Model Predictive Control.     

Nonlinear control of constrained linear systems via predictivereference management

A method based on conceptual tools of predictive control is described for solving set-point tracking problems wherein pointwise-in-time input and/or state inequality constraints are present. It consists of adding to a primal compensated system a nonlinear device, called command governor (CG), whose action is based on the current state, set-point, and prescribed constraints. The CG selects at any time a virtual sequence among a family of linearly parameterized command sequences, by solving a convex constrained quadratic optimization problem, and feeds the primal system according to a receding horizon control philosophy. The overall system is proved to fulfill the constraints, be asymptotically stable, and exhibit an offset-free tracking behavior, provided that an admissibility condition on the initial state is satisfied. Though the CG can be tailored for the application at hand by appropriately choosing the available design knobs, the required online computational load for the usual case of affine constraints is well tempered by the related relatively simple convex quadratic programming problem