PID Control of Planar Nonlinear Uncertain Systems in the Presence of Actuator Saturation

This paper investigates PID control design for a class of planar nonlinear uncertain systems in the presence of actuator saturation. Based on the bounds on the growth rates of the nonlinear uncertain function in the system model, the system is placed in a linear differential inclusion. Each vertex system of the linear differential inclusion is a linear system subject to actuator saturation. By placing the saturated PID control into a convex hull formed by the PID controller and an auxiliary linear feedback law, we establish conditions under which an ellipsoid is contractively invariant and hence is an estimate of the domain of attraction of the equilibrium point of the closed-loop system. The equilibrium point corresponds to the desired set point for the system output. Thus, the location of the equilibrium point and the size of the domain of attraction determine, respectively, the set point that the output can achieve and the range of initial conditions from which this set point can be reached. Based on these conditions, the feasible set points can be determined and the design of the PID control law that stabilizes the nonlinear uncertain system at a feasible set point with a large domain of attraction can then be formulated and solved as a constrained optimization problem with constraints in the form of linear matrix inequalities (LMIs). Application of the proposed design to a magnetic suspension system illustrates the design process and the performance of the resulting PID control law.      

Accounting for the uncertainties in the estimation of average shear wave velocity using V S– N correlations

Site-specific seismic hazard analysis is crucial for designing earthquake resistance structures, particularly in seismically active regions. Shear wave velocity ( V _S) is a key parameter in such analysis, although the economy and other factors restrict its direct field measurement in many cases. Various V _S–SPT– N correlations are routinely incorporated in seismic hazard analysis to estimate the value of V _S. However, many uncertainties question the reliability of these estimated V _S values. This paper comes up with a statistical approach to take care of such uncertainties involved in V _S calculations. The measured SPT– N values from all the critical boreholes were converted into statistical parameters and passed through various correlations to estimate V _S at different depths. The effect of different soil layers in the boreholes on the Vs estimation was also taken into account. Further, the average shear wave velocity of the top 30 m soil cover ( V _S30) is estimated after accounting for various epistemic and aleatoric uncertainties. The scattering nature of the V _S values estimated using different V _S– N correlations was reduced significantly with the application of the methodology. Study results further clearly demonstrated the potential of the approach to eliminate various uncertainties involved in the estimation of V _S30 using general and soil-specific correlations.     

Adaptive backstepping repetitive learning control design for nonlinear discrete‐time systems with periodic uncertainties

This paper addresses a tracking problem for uncertain nonlinear discrete‐time systems in which the uncertainties, including parametric uncertainty and external disturbance, are periodic with known periodicity. Repetitive learning control (RLC) is an effective tool to deal with periodic unknown components. By using the backstepping procedures, an adaptive RLC law with periodic parameter estimation is designed. The overparameterization problem is overcome by postponing the parameter estimation to the last backstepping step, which could not be easily solved in robust adaptive control. It is shown that the proposed adaptive RLC law without overparameterization can guarantee the perfect tracking and boundedness of the states of the whole closed‐loop systems in presence of periodic uncertainties. In addition, the effectiveness of the developed controller is demonstrated by an implementation example on a single‐link flexible‐joint robot. Copyright © 2014 John Wiley & Sons, Ltd.     

Filtered adaptive constrained sampled-data control for uncertain multivariable nonlinear systems

A filtered adaptive constrained sampled-data controller for uncertain multivariable nonlinear systems in the presence of various constraints is synthesized in this paper. A piecewise constant adaptive law drives that estimation error dynamics to zero at each sampling time instant yields adaptive parameters. The filtered control scheme consists of two components. Based on an estimation/cancellation strategy, a disturbance rejection control law is designed to compensate the nonlinear uncertainties within the bandwidth of low-pass filters, whereas a constraint violation avoidance control law is designed to solve an online constrained optimization problem. Although a reduced sampling time helps to minimize the estimation error caused by the neglect of unknowns, the resulting aggressive signals put more restrictions on the control law. Greater sacrifice of tracking performance is required to satisfy the constraints. The constraints violation avoidance control law is in favor of a larger sampling time. Sufficient conditions are given to guarantee the stability of the closed-loop system with the sampled-data controller, where the input/output signals are held constant over the sampling period. Numerical examples are provided to validate the theoretical results, comparisons between the constrained sampled-data controller and unconstrained adaptive controller with the implementation of different sampling times are carried out.     

A suitable computational strategy for the parametric analysis of problems with multiple contact

The aim of the present work is to develop an application of the LArge Time INcrement (LATIN) approach for the parametric analysis of static problems with multiple contacts. The methodology adopted was originally introduced to solve viscoplastic and large‐transformation problems. Here, the applications concern elastic, quasi‐static structural assemblies with local non‐linearities such as unilateral contact with friction. Our approach is based on a decomposition of the assembly into substructures and interfaces. The interfaces play the vital role of enabling the local non‐linearities, such as contact and friction, to be modelled easily and accurately. The problem on each substructure is solved by the finite element method and an iterative scheme based on the LATIN method is used for the global resolution. More specifically, the objective is to calculate a large number of design configurations. Each design configuration corresponds to a set of values of all the variable parameters (friction coefficients, prestress) which are introduced into the mechanical analysis. A full computation is needed for each set of parameters. Here we propose, as an alternative to carrying out these full computations, to use the capability of the LATIN method to re‐use the solution to a given problem (for one set of parameters) in order to solve similar problems (for the other sets of parameters). Copyright © 2003 John Wiley & Sons, Ltd.     

NIST 0:45 reflectometer

The NIST 0:45 reflectometer measures the spectral reflectance factor at an influx angle of 0° and an efflux angle of 45° of colored, nonfluorescent specimens at room temperature, with widths ranging from 3 to 10 cm and heights from 3 to 20 cm and with an uncertainty of less than 0.5 in color difference units. Published in 2008 by John Wiley & Sons, Inc. Col Res Appl, 33, 94–99, 2008     

SGCMGs驱动的挠性航天器有限时间自适应鲁棒控制

针对挠性航天器系统中同时存在单框架控制力矩陀螺群(Single gimbaled control moment gyroscopes, SGCMGs) 摩擦非线性、电磁干扰力矩、惯量摄动以及外部干扰等问题, 提出了一种有限时间自适应鲁棒控制(Finite-time adaptive robust control, FTARC) 方法. 针对系统中存在未知参数的情况, 分别设计自适应更新律, 使得控制器的设计不依赖参数信息, 同时减小外部干扰对系统的不利影响. 应用Lyapunov稳定性理论证明了闭环系统姿态角误差和姿态角速度误差可在有限时间内收敛到原点附近的邻域内. 仿真结果表明, 所提控制律可实现挠性航天器姿态快速机动, 并获得甚高指向精度.     

An Intelligent Robust Tracking Control for a Class of Electrically Driven Mobile Robots

This paper addresses the problem of designing robust tracking control for a class of uncertain wheeled mobile robots actuated by brushed direct current motors. This class of electrically‐driven mechanical systems consists of the robot kinematics, the robot dynamics, and the wheel actuator dynamics. Via the backstepping technique, an intelligent robust tracking control scheme that integrates a kinematic controller and an adaptive neural network‐based (or fuzzy‐based) controller is developed such that all of the states and signals of the closed‐loop system are bounded and the tracking error can be made as small as possible. Two adaptive approximation systems are constructed to learn the behaviors of unknown mechanical and electrical dynamics. The effects of both the approximation errors and the unmodeled time‐varying perturbations in the input and virtual‐input weighting matrices are counteracted by suitably tuning the control gains. Consequently, the robust control scheme developed here can be employed to handle a broader class of electrically‐driven wheeled mobile robots in the presence of high‐degree time‐varying uncertainties. Finally, a simulation example is given to demonstrate the effectiveness of the developed control scheme.     

考虑不确定性的高速公路光储充电站选址定容

针对高速公路并网光储充电站选址定容中存在的不确定性,提出了一种基于数据驱动的分布式鲁棒优化的两阶段选址定容方法.阶段1基于蒙特卡洛模拟方法得到充电点的位置,利用整数规划模型确定充电站的位置;阶段2兼顾充电站利益及用户满意度,建立基于数据驱动的分布式鲁棒优化定容模型,通过KL(Kullback-Leibler)散度构建以经验概率分布为中心的概率分布模糊集合描述不确定量,利用风险理论将分布式鲁棒优化模型转化为混合整数线性规划问题,进而对充电站内的充电桩数量及光储容量进行优化.最后,通过环形路网对所提方法进行验证并进行敏感度分析.结果表明:所提方法可行、有效;配置光储设备能降低年均寿命成本;通过控制KL散度公差、样本数量、续航里程、充电功率等能有效平衡系统的经济性与鲁棒性.     

A stochastic controller for a scalar linear system with additive Cauchy noise

A stochastic control scheme is developed for scalar, discrete-time, and linear-dynamic systems driven by Cauchy distributed process and measurement noises. When addressing the optimal control problem for such systems, the standard quadratic cost criteria cannot be used. In this study we introduce a new objective function that is functionally similar to the Cauchy probability density function. The performance index, defined as the expectation of this objective function with respect to the Cauchy densities, exists. The dynamic programming solution to the fixed and finite horizon optimal control problem that uses this performance index appears to be intractable. Therefore, a moving horizon optimal model predictive control problem is implemented, for which the conditional expected value of the objective function and its gradients can be computed in closed   form and without assumptions such as certainty equivalence. Numerical results are shown for this m$m$-step model predictive optimal controller and compared to a similar, Linear-Exponential-Gaussian model predictive controller. An essential difference between the Cauchy and Gaussian controllers when applied to a system with Cauchy noises is that, while the Gaussian controller is linear and reacts strongly to all noise pulses, the Cauchy controller can differentiate between measurement and process noise pulses by ignoring the former while responding to the latter. This property of the Cauchy controller occurs when an impulsive measurement noise is more likely than an impulsive process noise. The Cauchy and Gaussian controllers react similarly when applied to a system with Gaussian noises, demonstrating the robustness of the proposed control scheme.