Dynamic optimization of dual-mode hybrid systems with state-dependent switching conditions

This paper presents a computational approach for optimizing a class of hybrid systems in which the state dynamics switch between two distinct modes. The times at which the mode transitions occur cannot be specified directly, but are instead governed by a state-dependent switching condition. The control variables, which should be chosen optimally by the system designer, consist of a set of continuous-time input signals. By introducing an auxiliary binary-valued control function to represent the system's current mode, we show that any dual-mode hybrid system with state-dependent switching conditions can be transformed into a standard dynamic system subject to path constraints. We then develop a computational algorithm, based on control parameterization, the time-scaling transformation, and an exact penalty method, for determining the optimal piecewise constant input signals for the original hybrid system. A numerical example on cancer chemotherapy is included to demonstrate the effectiveness of the proposed algorithm.     

An adaptive generation method for electrophoretic display driving waveform design

Electrophoretic display (EPD) technology is attractive when used for reading devices such as e‐paper because of its paper‐like appearance. EPD driving is more complex than other display technologies such as liquid crystal display or organic light emission diode because the driving result of a pixel strongly depends on the initial display state. The particle size and distribution in the EPD film may vary, even if the initial state is the same. Therefore, the display devices vary between different manufacturing batches. Furthermore, different display modes such as videos, pictures or documents need different driving waveforms to achieve an optimal result. EPD manufacturers need to build a customized driving waveform for every manufacturing batch. This is very inconvenient if new applications on EPD are to be developed. And the workload is huge. In this work, an adaptive method is described for automatically creating EPD driving waveforms to fit different conditions. The central idea of this method is generally adjusting the driving time and the voltage state after getting the feedback from a measurement model. In this method, a new driving waveform is used to reduce refresh time and visual flicker. The experimental results show that the proposed approach can automatically and adaptively generate an EPD driving waveform with reasonable quality.     

车载TBTC-CBTC系统降级场景下的CPN建模与仿真

基于轨道电路的列车控制（TBTC）-基于通信的列车控制（CBTC）双模车载系统是实现轨道交通多网融合的关键,其模式间切换具有较强的随机性和并发性,并直接影响车载信号系统的运营可用性。然而,车载信号系统故障降级导致轨道交通资源利用率降低,表现为列车追踪的时间间隔增加,而间隔增加程度取决于区间长度和TBTC列车占用检测区段长度。从不同模式下资源分配、使用和释放角度,在列车运行过程中利用有色Petri网对TBTC-CBTC双模冗余车载信号系统的列车追踪运营场景进行建模,模拟CBTC车载信号系统故障发生的随机性和系统降级对后续列车的影响,精准描述并分析列车运营受影响的情况。将城市轨道交通项目的典型配置参数代入到有色Petri网模型中进行仿真,验证在不同线路下运营间隔受模式切换影响的程度。仿真结果表明,当区间长度小于1 500 m时,列车晚点时间可控制在180 s以内,晚点时间随着区间长度的增加而延长。     

Solving predictive control problem of fast-varying multivariable systems by incorporating unknown active dynamics generated by real-time adaptive learning machine

Not only adaptive predictive control of switched systems is a computationally intensive procedure, it also involves various challenges in addressing the problems of robust stabilization and precise tracking. This study proposes new strategies to deal with the aforementioned issues (namely safe and precise control alongside with reduction of computational burden). The first contribution of this work is reduction of conservatism for described class of systems. Control of switched systems with undetectable switching signals is often conducted in worst case switching configuration to ensure robustness, which potentially results in conservative design. The issue of conservativeness is intensified in multi input-multi output (MIMO) dynamical systems due to increased dimensions. However, attaining a robust control scheme for all switching configurations while ensuring precise response is inherently paradoxical. To overcome this issue, this study proposes a new dual-mode algorithm where control modes corresponding to safety and precision are activated at appropriate stages of system response. This is conducted based on incorporation of an adaptive fuzzy-wavelet neural network identification scheme in predictive control of MIMO switched systems. However, as convergence of the adaptive algorithm to actual system is attained after a finite period of time, a safe-mode control algorithm is proposed to maintain quality of transient response in convergence period. In other words, the proposed algorithm operates in safe and precise control modes to ensure robust stability in the convergence period and non-conservative design in steady-state. Second major contribution of the work is reduction of calculation burden based on incorporation of a suboptimal control algorithm. To this end, we propose a predictive control scheme based on a suboptimal gradient-descent based controller, calculating feasible stabilizing inputs instead of optimal inputs. Effects of dynamical variations are incorporated in the model predictive control framework for increased compatibility with high-speed switching dynamics. Then, based on incorporation of dual-mode algorithm, precise steady-state performance is attained while preventing notable perturbations in dynamical discontinuities at switching.     

基于模型预测的PHEV模式切换协调控制

针对混合动力汽车在模式切换过程中,由于离合器的结合/分离易产生较大冲击度和滑磨功,提出一种模型预测切换协调控制方法。在进行动力学分析基础上,建立预测模型。以电机驱动下的速度响应作为目标转速,构造目标函数,考虑其非可行解问题、动力部件物理约束以及最大冲击度限制要求,引入松弛因子,设计状态约束条件,保证其解的可行性与切换平顺性,实现较小冲击度与滑磨功。同时,引入预测误差,对预测值进行反馈校正,以提高控制精度;将所提策略转化为在线二次规划问题,便于计算机实现。仿真验证结果表明,所提协调控制策略与传统策略相比,冲击度与滑磨功明显降低,保证了切换平顺性,提高了驾驶性能。     

切换非线性系统全局优化运行的经济预测控制

切换非线性系统在不同模式间平稳切换和经济切换是全局优化运行的主要需求.针对不同模式有限时域下控制算法可行域未必存在交集的系统,提出了对应的经济预测控制算法（Economic model predictive control,EMPC）及切换策略.切换发生时,该方法在实时优化层求解和更新可行中间点,并构造基于耗散的局部EMPC辅助性能指标,在考虑中间点稳定性问题上使其尽可能逼近原经济性能.在先进控制层,利用局部EMPC将状态逐次稳定至中间点,同时利用中间点问题得到的最优轨迹保证模式间的经济切换.最后,分析了切换过程的暂态经济性.该方法实际可操作性强,仿真结果说明了方法的有效性.     

Experimental two-axis vibration suppression and control of a flexible robot arm

This article focuses on the implementation of a dual-mode controller for the maneuver of a two-axis flexible robotic arm. The joint angle trajectory tracking is accomplished by proportional and derivative and feedforward controllers. Based on the pole placement technique, a linear stabilizer is designed for elastic mode stabilization in the plane perpendicular to each joint axis. The stabilizer is switched on when the trajectory reaches the vicinity of the terminal state. The effect of switching time of the stabilizer and varying payload on arm vibration are investigated. With the proposed control system, accurate joint angle tracking and elastic mode stabilization can be accomplished. © 1993 John Wiley & Sons, Inc.     

一类时滞复杂动态网络的鲁棒自适应同步问题

针对一类耦合时滞复杂网络,基于变结构控制研究其同步问题.首先,利用系统的左特征向量函数设计切换面,使网络的运动轨线在期望的同步轨道保持稳定;然后,针对网络中的非线性项已知和未知时,分别设计相应的滑模控制器,使从任意时刻出发的动态网络轨线都能在有限时间内同步到达期望的轨道;最后,利用所设计的控制器对两个算例进行仿真,仿真结果说明了所设计控制器的有效性.     

Finite data-rate feedback stabilization of switched and hybrid linear systems

We study the problem of asymptotically stabilizing a switched linear control system using sampled and quantized measurements of its state. The switching is assumed to be slow enough in the sense of combined dwell time and average dwell time, each individual mode is assumed to be stabilizable, and the available data rate is assumed to be large enough but finite. Our encoding and control strategy is rooted in the one proposed in our earlier work on non-switched systems, and in particular the data-rate bound used here is the data-rate bound from that earlier work maximized over the individual modes. The main technical step that enables the extension to switched systems concerns propagating over-approximations of reachable sets through sampling intervals, during which the switching signal is not known; a novel algorithm is developed for this purpose. Our primary focus is on systems with time-dependent switching (switched systems) but the setting of state-dependent switching (hybrid systems) is also discussed.     

Output feedback control of switched nonlinear systems using multiple Lyapunov functions

This work presents a hybrid nonlinear control methodology for a broad class of switched nonlinear systems with input constraints. The key feature of the proposed methodology is the integrated synthesis, via multiple Lyapunov functions, of “lower-level” bounded nonlinear feedback controllers together with “upper-level” switching laws that orchestrate the transitions between the constituent modes and their respective controllers. Both the state and output feedback control problems are addressed. Under the assumption of availability of full state measurements, a family of bounded nonlinear state feedback controllers are initially designed to enforce asymptotic stability for the individual closed-loop modes and provide an explicit characterization of the corresponding stability region for each mode. A set of switching laws are then designed to track the evolution of the state and orchestrate switching between the stability regions of the constituent modes in a way that guarantees asymptotic stability of the overall switched closed-loop system. When complete state measurements are unavailable, a family of output feedback controllers are synthesized, using a combination of bounded state feedback controllers, high-gain observers and appropriate saturation filters to enforce asymptotic stability for the individual closed-loop modes and provide an explicit characterization of the corresponding output feedback stability regions in terms of the input constraints and the observer gain. A different set of switching rules, based on the evolution of the state estimates generated by the observers, is designed to orchestrate stabilizing transitions between the output feedback stability regions of the constituent modes. The differences between the state and output feedback switching strategies, and their implications for the switching logic, are discussed and a chemical process example is used to demonstrate the proposed approach.     

网络控制系统的模型依赖平均驻留时间调度与控制

针对具有随机短时延的资源受限网络控制系统,提出了一种新的模型依赖平均驻留时间的调度策略与反馈控制联合设计方法.该调度策略由模型依赖平均驻留时间和动态试一次就丢弃(try-once-discard,TOD)调度策略共同决定,将系统建模成带有参数不确定性的离散切换系统,基于多Lyapunov函数方法及线性矩阵不等式(linear matrix inequality,LMI)技术,给出了使闭环系统指数稳定的控制器设计和TOD调度策略下的各模态平均驻留时间条件.该联合设计方法降低了保守性,在一定程度上减少了系统模态之间的切换频率.最后通过仿真验证所提方法的有效性.     

Experimental analysis of occupational whole-body vibration exposure of agricultural tractor with large square baler

This study investigates longitudinal whole-body vibration in agricultural tractors powering a large square baler. The aim is to test the hypothesis that four-wheel drive has an influence on the longitudinal dynamic response. A number of experimental measurements are carried out on a specific vehicle combination driving uphill and downhill. The whole-body vibration exposure is measured at the operator seat under different conditions.The statistic results show a significant difference on the whole-body vibration exposure depending on operating conditions. Driving uphill and downhill with four-wheel drive activated showed the highest difference with increased vibration level at downhill driving.The results indicate that four-wheel drive influences the longitudinal dynamics and hence the whole-body vibration exposure on tractors with large square balers.Relevance to industryThe findings of this work are highly relevant to the manufacturers of agricultural tractors and machinery as well advisers within occupational health. The paper demonstrates potential in reducing damaging vibrations by simple manual or automatic control of four-wheel drive.     

考虑输入饱和的农用拖拉机路径跟踪有限时间控制

针对农用拖拉机的路径跟踪控制问题,提出基于有限时间和饱和技术的路径跟踪控制策略.首先,建立农机路径跟踪运动学模型,并通过有限时间控制技术,构造有限时间路径跟踪控制方法;其次,考虑到农用拖拉机的转向系统物理限制,将饱和技术与有限时间控制结合,给出复合的路径跟踪控制方法,通过严格的理论分析验证闭环系统在该控制器下的有限时间稳定性;最后,通过仿真结果表明,所设计的制导方法可以保证农用拖拉机快速、稳定地完成路径跟踪目标.     

Connection of nonlinear model predictive controllers for smooth task switching in autonomous driving

Motion planning, decision making, and control are vital functions in autonomous driving for accomplishing the desired driving task while considering passenger comfort, road infrastructure, and surrounding traffic participants. Model predictive control (MPC) is a promising method for simultaneously realizing these functions. However, formulating a single MPC that can run through all driving scenarios is difficult, and previous research has often been conducted to design an MPC for a specific driving task. To extend the availability of MPC for all driving tasks, smooth switching between different MPCs designed for each driving task must be addressed. One of the difficulties in switching between MPCs is guiding the state to a feasible set of optimization problems after switching. In this paper, we present a new framework to realize the smooth connection of MPCs, that is, to reduce the optimization infeasibility at the time of MPC switching. In our proposed method, two general nonlinear MPCs with different state spaces, cost functions, constraints, and formulations can be systematically switched via automatically generated intermediate-MPCs without requiring any particular alterations. This can help reduce the system complexity of the hybrid MPC system.     

Predictive control of switched nonlinear systems with scheduled mode transitions

In this work, a predictive control framework is proposed for the constrained stabilization of switched nonlinear systems that transit between their constituent modes at prescribed switching times. The main idea is to design a Lyapunov-based predictive controller for each constituent mode in which the switched system operates and incorporate constraints in the predictive controller design which upon satisfaction ensure that the prescribed transitions between the modes occur in a way that guarantees stability of the switched closed-loop system. This is achieved as follows: For each constituent mode, a Lyapunov-based model predictive controller (MPC) is designed, and an analytic bounded controller, using the same Lyapunov function, is used to explicitly characterize a set of initial conditions for which the MPC, irrespective of the controller parameters, is guaranteed to be feasible, and hence stabilizing. Then, constraints are incorporated in the MPC design which, upon satisfaction, ensure that: 1) the state of the closed-loop system, at the time of the transition, resides in the stability region of the mode that the system is switched into, and 2) the Lyapunov function for each mode is nonincreasing wherever the mode is reactivated, thereby guaranteeing stability. The proposed control method is demonstrated through application to a chemical process example.     

Finite-time Sliding Mode Control Design for a Class of Uncertain Conic Nonlinear Systems

This paper studies the sliding mode controller design problems for a class of nonlinear system. The nonlinear function is considered to satisfy conic-type constraint condition. A novel finite-time boundedness (FTB) based sliding mode controller design theory is proposed. And then a sufficient condition is obtained in terms of linear matrix inequalities (LMIs), which guarantees the resulted sliding mode dynamics to be FTB wrt some predefined scalars. Thereafter, a FTB-based sliding mode control (SMC) law is synthesized to ensure the state of the controlled system is driven into a novel desired switching surface s(t)=c (c is a constant) in a finite time. Simulation results illustrate the validity of the proposed FTB-based SMC design theory.      

PHEV由纯电动向混合驱动模式切换协调控制设计

针对并联混合动力汽车模式切换过程中动力中断和扭矩波动对车辆驾驶性能的影响,提出一种由纯电动向混合驱动模式切换的协调控制方法.首先,根据切换过程动力学分析及控制目标,将该过程分为离合器接合前后两部分.然后,对前者设计干扰观测器估计并补偿扭矩干扰和模型不确定性,提出基于干扰补偿的协调控制策略,以消除干扰,实现发动机的快速起动、同步;对后者引入发动机扭矩延迟变量,并利用电机扭矩补偿发动机扭矩误差,设计基于电机补偿的扭矩切换协调控制策略,实现平滑切换.仿真结果表明,该控制策略与传统控制方法相比,冲击度降低50.5%,有效减小了扭矩波动,确保了模式切换的平顺性,提高了驾驶性能.     

Synchronization and tracking control for multi‐motor driving servo systems with backlash and friction

This paper presents a novel switching controller incorporated with backlash and friction compensations, which is utilized to achieve speed synchronization among multi‐motor and load position tracking. The proposed controller consists of two parts: synchronization and tracking control in contact mode and robust control in backlash mode, where a function characterizing whether backlash occurs is used for switching between two modes. Using the proposed switching controller, several control objectives are achieved. Firstly, the coupling problem of speed synchronization and load tracking in contact mode is addressed by introducing a switching plane. Secondly, based on the switching plane, an improved prescribed performance function is introduced to attain load tracking with prescribed performances, and L_∞ performance of speed synchronization is guaranteed by initialization method, maintaining the transient performance of synchronization behavior. Thirdly, the lumped uncertain nonlinearity including friction and other uncertain functions is compensated by Chebyshev neural network in contact mode. Furthermore, a robust control is adopted in backlash mode to make system traverse backlash at an exponential rate and simultaneously eliminate low‐speed crawling phenomenon of LuGre friction. Finally, comparative simulations on four‐motor driving servo system are provided to verify the effectiveness and reliability. Copyright © 2015 John Wiley & Sons, Ltd.     

时滞系统的输出反馈滑模控制的一种奇异系统方法

利用一种奇异系统方法讨论了时滞系统的输出反馈滑模控制问题. 时滞系统的非线性项满足范数有界约束.首先,将滑动模态与线性切换面作为一个奇异时滞系统,基于奇异时滞系统的稳定性理论, 给出滑动模态稳定及切换面存在的线性矩阵不等式(Linear matrix inequality, LMI)充分条件.然后,给出使得系统闭环渐近稳定的静态输出反馈滑模控制器的设计方法,此控制器保证闭环 系统有限时间到达切换面.最后,用数值算例验证本文方法的有效性和正确性.