Research of Visual H∞ Control of Inverted Pendulum With Time-varying Computational Time and Computational Error
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摘要: 针对基于视觉传感的倒立摆实时控制系统中，通过每帧图像计算小车位移和摆杆偏角产生的时变计算时间和计算误差直接影响控制系统性能甚至导致系统失稳问题，不同于目前不考虑计算时间和计算误差或将计算时间视为定时滞进行研究倒立摆视觉实时控制方法，本文首先创新设计了新型的倒立摆视觉伺服控制实验平台，然后设计了一种基于事件触发机制的工业图像采集策略，提出了考虑小车和摆杆特征的小车位移和摆杆偏角计算方法，并统计分析了图像处理计算时间和计算误差特性；进一步建立了融合计算时间和计算误差的闭环控制系统模型，理论证明系统的稳定性并建立了反映计算时间与系统稳定性能之间关系，给出了系统对计算误差的H∞扰动抑制水平γ和控制器设计方法.最后，仿真和实时控制实验验证了所提方法可行且有效.Abstract: In visual-feedback-based real-time control of an inverted pendulum on a cart, some new challenges are as follows. On the one hand to get the values of cart position and pendulum angle from images needs more computation time. On the other hand, the values obtained have bigger errors than those in the traditional sensor approach. These will affect the system performance and even lead the system to instability. In this paper, we present an analytical study and experiments on:1) a novel platform; 2) event-triggered sampling and signal processing of the values from images, and statistical analysis of time-varying computational time and error; 3) modelling of a visual-based feedback closed-loop system; 4) conditions for system stability in terms of the statistics as described before; and 5) H∞ norm based controller design. At the end simulation and experiment are conducted to validate the design method.
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Key words:
- Inverted pendulum /
- visual servoing /
- image processing /
- computational time /
- computational error
1) 本文责任编委 侯增广 -
图 1 倒立摆视觉伺服控制实验平台结构
Fig. 1 Scheme of inverted pendulum visual servoing control platform
图 2 倒立摆视觉伺服控制系统控制框图
Fig. 2 Control block diagram of inverted pendulum visual servoing control system
图 16 在控制律${K_1}$下的小车位移和摆杆偏角(仿真)
Fig. 16 Cart position and pendulum angle in controller ${K_1}$ (simulation)
图 17 在控制律${K_2}$下的小车位移和摆杆偏角(仿真)
Fig. 17 Cart position and pendulum angle in controller ${K_2}$ (simulation)
图 18 在控制律${K_1}$下的小车位移和摆杆偏角(实时控制)
Fig. 18 Cart position and pendulum angle in controller ${K_1}$ (real-time control)
图 19 不同图像处理计算时间上界$\bar d$的小车位移
Fig. 19 Cart position in different upper bound of image processing computational time $\bar d$
图 20 不同图像处理计算时间上界$\bar d$的摆杆偏角
Fig. 20 Pendulum angle in different upper bound of image processing computational time $\bar d$
表 1 相机内部参数
Table 1 Intrinsic parameters of camera
参数 取值 $f$ 909.5 pixels $d$ 0.9263 m ${\alpha _u}$ $1.6241\times 106 $ pixels/m ${\alpha _v}$ $1.6241\times106 $ pixels/m $s$ 0 ${u_0}$ 334.85 pixels ${v_0}$ 267.46 pixels 
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