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.      

Distributionally robust optimization of home energy management system based on receding horizon optimization

This paper investigates the scheduling strategy of schedulable load in home energy management system (HEMS) under uncertain environment by proposing a distributionally robust optimization (DRO) method based on receding horizon optimization (RHO-DRO). First, the optimization model of HEMS, which contains uncertain variable outdoor temperature and hot water demand, is established and the scheduling problem is developed into a mixed integer linear programming (MILP) by using the DRO method based on the ambiguity sets of the probability distribution of uncertain variables. Combined with RHO, the MILP is solved in a rolling fashion using the latest update data related to uncertain variables. The simulation results demonstrate that the scheduling results are robust under uncertain environment while satisfying all operating constraints with little violation of user thermal comfort. Furthermore, compared with the robust optimization (RO) method, the RHO-DRO method proposed in this paper has a lower conservation and can save more electricity for users.     

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.     

Adaptive robust control of fully-constrained cable driven parallel robots

In this paper, adaptive robust control (ARC) of fully-constrained cable driven parallel robots is studied in detail. Since kinematic and dynamic models of the robot are partly structurally unknown in practice, in this paper an adaptive robust sliding mode controller is proposed based on the adaptation of the upper bound of the uncertainties. This approach does not require pre-knowledge of the uncertainties upper bounds and linear regression form of kinematic and dynamic models. Moreover, to ensure that all cables remain in tension, proposed control algorithm benefit the internal force concept in its structure. The proposed controller not only keeps all cables under tension for the whole workspace of the robot, it is chattering-free, computationally simple and it does not require measurement of the end-effector acceleration. The stability of the closed-loop system with proposed control algorithm is analyzed through Lyapunov second method and it is shown that the tracking error will remain uniformly ultimately bounded (UUB). Finally, the effectiveness of the proposed control algorithm is examined through some experiments on a planar cable driven parallel robot and it is shown that the proposed controller is able to provide suitable tracking performance in practice.     

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.     

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.     

模糊讯息分析法评估砂性土液化潜能

本文以Ｓｅｅｄ和Ｉｄｒｉｓｓ简化法为机率分析法的基础，利用模糊讯息分析的基本理论并考虑砂性土基本动态特性所建立的模糊关系，进行砂性土液化潜能评估。计算结果与机率分析及蒙地卡罗模拟法结果互相对比、验证，表明模糊讯息分析对砂性土液化潜能可提供明确评估。     

Probabilistic seismic damage assessment of reinforced concrete buildings considering directionality effects

Most of buildings and structures are usually projected according to two main axes. However, the geographical position of these buildings varies randomly. Such random distributions of the azimuthal positions of structures, in most of the cities, generally, are not accounted for when assessing their seismic risk; certainly, the direction of the seismic loads is another highly random variable. Moreover, an additional important source of uncertainty is related to the structural response, mainly due to the random character of the mechanical properties. There is a consensus that uncertainties must be considered for adequately assessing the seismic risk of structures, but these directionality effects have not been deeply explored so far. In this article, the influence of the high uncertainty involved in these input variables on the expected seismic damage is analysed. Thus, an actual earthquake, which affected the southern part of Spain, is studied. Notably, damages on a group of affected buildings, located close to the epicentre, are analysed and discussed in detail. The results show that the influence of the random azimuthal position of structures is an important source of uncertainty and that it should be taken into account when estimating the expected seismic risk in urban areas.     

An adaptive control scheme using multiple reference models

This paper develops an extended model reference adaptive control scheme to expand the capacity of state feedback state tracking adaptive control to handle the plant‐model matching uncertainties for single‐input LTI systems. The extended scheme is developed, using multiple reference model systems (only one of which is required to be able to match the controlled plant), and multiple controllers (which are updated from adaptive laws generated from multiple reference model systems based estimation errors), as two key features of such design to relax a plant‐model matching condition. A switching mechanism is constructed using those multiple estimation errors, capable of selecting the suitable control input from the multiple control signals, to achieve the desired system performance. An aircraft flight control example is presented to show the capacity of such design in relaxing a practical design condition. Copyright © 2013 John Wiley & Sons, Ltd.