基于能量控制与近似输出调节的二级倒立摆起摆和跟踪控制

二级倒立摆是一个典型的欠驱动非线性系统,其控制问题具有一定的挑战性.为了解决时变参考信号下二级倒立摆的起摆和跟踪控制问题,本文提出了一种基于能量控制与近似输出调节方法的起摆和三阶控制器设计方案.首先,采用能量控制方法将第1级摆杆从下垂位置摆起到倒立位置附近;其次,采用滑模控制方法将第1级摆杆稳定在倒立位置,同时,采用等效小车与能量控制相结合的方法将第2级摆杆摆起到倒立位置附近;最后,采用基于近似输出调节理论的多项式近似方法设计三阶控制器实现二级倒立摆的位置跟踪控制.仿真和实验结果均验证了该控制方案的有效性.     

基于混合遗传算法的力矩受限圆轨二级倒立摆摆起控制

为了实现力矩受限时圆轨二级倒立摆非线性系统的摆起控制,提出了一种新的开环优化控制策略.该策略通过在规定的时间内向系统施加一前馈控制序列,使上、下摆杆从自然悬垂位置摆到倒立点位置并使速度为零.为了获得最优摆起控制序列,采用混合遗传算法进行优化计算,通过编码操作解决控制力矩受限问题.仿真实验证明,该策略是有效和可行的,并为其他非线性多变量系统的控制提供了有效方法.     

A new approach to inversion-based feedforward control design for nonlinear systems

The finite-time transition between stationary setpoints of nonlinear SISO systems is considered as a scenario for the presentation of a new design approach for inversion-based feedforward control. Design techniques which are based on a stable system inversion result in input trajectories with pre- and/or post-actuation intervals. The presented approach treats the considered transition task as a two-point boundary value problem (BVP) and yields causal feedforward trajectories, which are constant outside the transition interval. The main idea of this approach is to provide free parameters in the desired output trajectory to solve the BVP of the internal dynamics. Thereby, a standard MATLAB function can be used for the numerical solution of the BVP. Feedforward control design techniques are illustrated by simulation results for a simple example.     

二级倒立摆摆起控制的研究

通过对二级倒立摆系统的理论分析，研究二级摆从自然悬垂位置摆到倒立点位置的摆起控制问题，提出了基于动态设计变量优化算法的复杂非线性系统控制策略．仿真实验证明，该策略可成功地实现圆轨和直轨两种二级倒立摆的摆起控制，并且算法具有较快的收敛速度和较高的计算精度．     

Complementary compound set-point control by combining muscular internal force feedforward control and sensory feedback control including a time delay

This paper proposes a new set-point control method for a musculoskeletal arm by combining muscular internal force feedforward control with feedback control including a large time delay. The proposed method accomplishes robust and rapid positioning with a relatively small muscular force. In the positioning by the muscular internal force feedforward controller, a large muscular force is required to achieve good performance. On the other hand, in the positioning by the feedback controller including the large time delay, the system can easily fall into an unstable state. A simple linear combination of these two controllers makes it possible to improve the control performance and to overcome the drawbacks of each controller in a complementary manner. First, a two-link six-muscle arm model is considered as a musculoskeletal system in this study. Second, the new set-point control method, which consists of the feedforward control signal and the feedback control signal including the time delay, is designed. Third, the stability of the proposed method is investigated using the Lyapunov–Razumikhin method. Finally, the results of numerical simulations and experiments are presented to demonstrate the advantages of the proposed method.     

Quantized feedback control for nonlinear feedforward systems with unknown output functions and unknown control coefficients

This paper investigates the quantized feedback control for nonlinear feedforward systems with unknown output functions and unknown control coefficients. The unknown output function is Lipschitz continuous but may not be derivable, and the unknown control coefficients are assumed to be bounded. To deal with this challenging quantized control problem, a time‐varying low‐gain observer is designed and a delicate time‐varying scaling transformation is introduced, which can avoid using the derivative information of the output function. Then, based on the well‐known backstepping method and the sector bound approach, a time‐varying quantized feedback controller is designed using the quantized output, which can achieve the boundedness of the closed‐loop system states and the convergence of the original system states. Moreover, a guideline is provided for choosing the parameters of the input and output quantizers such that the closed‐loop system is stable. Finally, two simulation examples are given to show the effectiveness of the control scheme.     

Output feedback control of a class of feedforward nonlinear systems in the presence of sensor noise

We propose an output feedback controller for a class of feedforward nonlinear systems under sensor noise. The sensor noise is any signal whose DC component is finite, which covers not only deterministic signals but also random signals including many practical noises. We introduce a notion of virtual state, then propose a measurement output feedback controller that utilizes a gain scaling factor. The gain scaling factor is commonly employed by the observer and controller. Through analysis, we show that all system states and output remain to be bounded in the presence of sensor noise, and the bound of states except output can be made arbitrarily small. Moreover, if the DC component of sensor noise is zero, the ultimate bound of the states and output can be made arbitrarily small by increasing the gain scaling factor in the presence of sensor noise. Copyright © 2013 John Wiley & Sons, Ltd.     

三级倒立摆的自动摆起与稳定控制

采用非线性逆系统轨迹控制实现三级倒立摆的自动摆起,并设计了变增益LQR控制器将其稳定在竖直倒立位置.首先,三级倒立摆从静止下垂状态摆起到竖直倒立位置的过程,从数学角度看是一个两点边值问题,通过求解该两点边值问题获得摆起的标称轨迹,利用逆系统方法设计前馈控制,同时结合增益调度反馈控制使摆起过程稳定;其次,在稳定控制阶段,...     

Analysis of the energy‐based swing‐up control for the double pendulum on a cart

Designing and analyzing controllers for mechanical systems with underactuation degree (difference between the number of degrees of freedom and that of inputs) greater than one is a challenging problem. In this paper, for the double pendulum on a cart, which has three degrees of freedom and only one control input, we study an unsolved problem of analyzing the energy‐based swing‐up control which aims at controlling the total mechanical energy of the cart‐double‐pendulum system, the velocity and displacement of the cart. Under the energy‐based controller, we show that for all initial states of the cart‐double‐pendulum system, the velocity and displacement of the cart converge to their desired values. Then, by using a property of the mechanical parameters of the double pendulum, we show that if the convergent value of the total mechanical energy is not equal to the potential energy at the up–up equilibrium point, where two links are in the upright position, then the system remains at the up–down, down–up, and down–down equilibrium points, where two links are in the upright–down, down–upright, and down–down positions, respectively. Moreover, we show that each of these three equilibrium points is strictly unstable in the closed‐loop system by showing that the Jacobian matrix valued at each equilibrium point has at least one eigenvalue in the open right half plane. This shows that for all initial states with the exception of a set of Lebesgue measure zero, the total mechanical energy converges to the potential energy at the up–up equilibrium point. This paper provides insight into the energy‐based control approach to mechanical systems with underactuation degree greater than one. Copyright © 2010 John Wiley & Sons, Ltd.     

一类非线性时滞广义系统的状态反馈控制

利用线性矩阵不等式(LMI),讨论了一类非线性时滞广义系统的状态反馈控制问题.通过对非线性映射Frechet导数的逆矩阵的估计,给出了系统渐近稳定的充分条件.这一条件与时滞相关,可归结为一个线性矩阵不等式的可解性.在LMI有解的条件下,可得到系统状态反馈控制器的参数表示.数值实例表明该方法是有效的.     

Internal model based robust inversion feedforward and feedback 2DOF control for LPV system with disturbance

To reduce the adverse effects on the control performance and disturbance rejection caused by system uncertainty, a novel internal model based robust inversion feedforward and feedback 2DOF control approach was proposed for LPV system with disturbance. The proposed control approach combines the internal model control and robust inversion based 2DOF control, it utilizes internal model based control to reject external disturbance, utilizes robust inversion 2DOF control to enhance the control resolution and guarantee the system control performance. At first, a LMI synthesis approach for LPV system model identification and a disturbance compensator optimization design method which could minimize H_∞ norm of output error caused by disturbance are presented. Then, combined with internal loop for disturbance compensation, a robust inversion feedforward controller is designed by robust inversion approach and the feedback controller which could render the requirements of reference signal tracking performance and robustness satisfied is obtained by the H_∞ mixed sensitivity synthesis approach. Finally, atomic force microscopy (AFM) vertical positioning simulation experiments are conducted and the experiment results showed that the proposed control approach could achieve better output performance and disturbance rejection compared with conventional internal model based control and robust inversion based 2DOF control approach.     

双轮共轴移动式倒立摆动力学建模与状态反馈控制

应用第一类拉格朗日方法对系统进行力学分析,建立了以电机转矩为输入且轮在轴向无滑移的非完整约束下系统的数学模型.双轮共轴移动式倒立摆的运动控制目标是移动式倒立摆在二维平面内按指定的方向和速度运动,同时保持摆杆平衡.利用状态反馈,构造闭环系统的状态方程,通过极点配置求得控制量.仿真结果验证了系统状态方程的正确性和控制方法的合理性.     

LMI-based LSVF control of a class of nonlinear systems with parametric uncertainty: an application to an inverted pendulum system

This work centres around the stabilisation of a nonlinear system containing parametric uncertainty using a new Control Lyapunov Function (using Lie derivatives) which comes up with a linear matrix inequality-based design. The paper has three major contributions. The first one is an extension of a theorem proposed to find the convex-concave bounds of nonlinear function towards robustness. With some restrictions in the structure of the uncertainty, the theory developed here may be applied to find out the bounds of any nonlinear function with uncertainty. The next one is the main contribution of this paper in which the form of the control law obtained is linear and has several advantages from a practical point of view over almost all other nonlinear control techniques. The third one is the expansion of the proposed control scheme towards underactuated systems. To show the effectiveness of the proposed theory the controller design is attempted for both the traditional cart inverted pendulum and the more complex mobile wheeled inverted pendulum model.     

Universal adaptive control of nonlinear systems with unknown growth rate by output feedback

This paper investigates the problem of global stabilization by output feedback, for a family of uncertain nonlinear systems without zero dynamics. These nonlinear systems are dominated by a triangular system satisfying linear growth condition. In contrast to the previous work in the literature, the growth rate here is a positive constant but not known a priori, and therefore the problem becomes more involved and difficult. Using the idea of universal control combined with the output feedback design method developed in Qian and Lin (2002, 2003), we explicitly construct a universal-type adaptive output feedback controller which globally regulates all the states of the uncertain systems without knowing the growth rate.     

一类受扰旋转单摆系统的建模与跟踪控制设计

本文考虑一类受扰旋转单摆系统的建模与跟踪控制问题. 首先, 利用动静法和相对运动原理建立受扰情形下空间旋转摆系统的动力学模型. 然后, 分别以实际跟踪和渐近跟踪为控制目标, 给出相应的控制设计方法. 具体地,利用向量式的反推控制设计方法与不确定性动态补偿机制, 给出自适应实际跟踪控制器, 保证闭环系统所有状态都有界且在有限时间内系统输出到达并保持在参考信号给定的邻域内. 利用反推设计方法, 并结合扰动的学习、切换补偿机制设计自适应切换渐近跟踪控制器, 通过在线调节控制器参数, 保证闭环系统所有状态都有界且系统输出渐近跟踪到给定的参考信号. 最后, 仿真实验验证所提理论结果的有效性. 值得指出的是, 与相关文献相比, 本文所给出的控制设计方法允许系统同时含有未知参数和扰动, 并且扰动不必有已知上界, 因而具有更强的抑制不确定性的能力.     

Output feedback pole placement for linear time-varying systems with application to the control of nonlinear systems

The output feedback pole placement problem is solved in an input-output algebraic formalism for linear time-varying (LTV) systems. The recent extensions of the notions of transfer matrices and poles of the system to the case of LTV systems are exploited here to provide constructive solutions based, as in the linear time-invariant (LTI) case, on the solutions of diophantine equations. Also, differences with the results known in the LTI case are pointed out, especially concerning the possibilities to assign specific dynamics to the closed-loop system and the conditions for tracking and disturbance rejection. This approach is applied to the control of nonlinear systems by linearization around a given trajectory. Several examples are treated in detail to show the computation and implementation issues.     

Output feedback strict passivity of discrete-time nonlinear systems and adaptive control system design with a PFC

In this paper, a passivity-based adaptive output feedback control for discrete-time nonlinear systems is considered. Output Feedback Strictly Passive (OFSP) conditions in order to design a stable adaptive output control system will be established. Further, a design scheme of a parallel feedforward compensator (PFC), which is introduced in order to realize an OFSP controlled system, will be provided and an adaptive output feedback control system design scheme with a PFC will be proposed.     

Decentralised robust sliding mode control for a class of nonlinear interconnected systems by static output feedback

In this paper, a class of nonlinear interconnected systems with nonlinear nominal subsystems is considered. Matched and mismatched uncertainties are both dealt with. Based on sliding mode techniques, a decentralised robust control scheme, using only output information, is presented to stabilise the system locally, but under certain circumstances, global results can be obtained. The approach allows a more general structure for the interconnections and uncertainty bounds than other literature in this area. The conservatism in the results is reduced by fully using system output information and the uncertainty bounds. A numerical example is used to demonstrate the efficacy of the method.     

一类非线性时滞互联系统模糊分散输出反馈控制

对于一类状态不可测非线性互联时滞系统,给出一种基于观测器的模糊分散输出反馈控制方法.首先采用模糊T-S模型对非线性互联时滞系统进行模糊建模,在此基础上给出了模糊分散观测器和基于观测器的模糊分散输出控制器的设计.应用李亚普诺夫函数法和线性矩阵不等式方法给出了模糊分散控制系统稳定的充分条件.仿真结果进一步验证了所提出的模糊分散控制方法的有效性.     

A note on stability, robustness and performance of output feedback nonlinear model predictive control

In recent years, nonlinear model predictive control (NMPC) schemes have been derived that guarantee stability of the closed loop under the assumption of full state information. However, only limited advances have been made with respect to output feedback in the framework of nonlinear predictive control. This paper combines stabilizing instantaneous state feedback NMPC schemes with high-gain observers to achieve output feedback stabilization. For a uniformly observable MIMO system class it is shown that the resulting closed loop is asymptotically stable. Furthermore, the output feedback NMPC scheme recovers the performance of the state feedback in the sense that the region of attraction and the trajectories of the state feedback scheme can be recovered to any degree of accuracy for large enough observer gains, thus leading to semi-regional results. Additionally, it is shown that the output feedback controller is robust with respect to static sector bounded nonlinear input uncertainties.