欠驱动非线性桥式吊车自动控制系统研究
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摘要
欠驱动系统是指控制量的数目少于系统自由度的一类系统。由于省去部分驱动器可以减小系统设计的复杂程度,并且能够有效地节约成本或者降低系统自身的重量,因而实际应用中许多系统都被设计成为了欠驱动系统,如航天器、直升飞机、水下航行器、卫星、柔性机器人等;此外当一些全驱动系统的某个驱动失效的时候,它也会成为一个欠驱动系统。欠驱动特性虽然在系统设计、制造上带来很大方便,但是它也使得系统的内部动力学特性更加复杂,而且通常伴有非完整约束条件,因此为系统控制带来了极大的挑战,近年来针对这类系统的研究逐步发展成为控制理论界的一个研究热点。
桥式吊车是一种典型的非线性、强耦合、欠驱动系统,它具有负载能力强、操作灵活、节能显著等优点,已经被广泛应用到工业生产、港口运输等多个领域。为了提高吊车系统的运送效率与安全性能,当前迫切需要设计出合理的控制策略来实现其自动操作。具体而言,对于桥式吊车运送控制的目标可以总结为以下两点:一方面是使台车快速准确地到达目标位置,以完成对负载的高效运送;另一方面要求负载在运行过程中的摆动尽可能地小,以避免与周围的货物或人员发生意外碰撞。然而,由于桥式吊车系统的非线性欠驱动特性,以及系统内部存在的摩擦力等多种不确定性因素,如何同时满足这两方面的性能要求是一个非常困难的问题。多年来,控制领域的学者对桥式吊车进行了广泛研究,分别采用输入整形、最优控制、人工智能技术等多种方法来设计桥式吊车控制系统,但是这些方法都还存在着一些不足之处,尚不能完全解决实际吊车系统的自动控制问题。
本论文针对具有不确定特性的非线性欠驱动桥式吊车系统进行了深入研究。具体而言,论文针对吊车运送过程,分别采用基于能量分析的方法和基于台车运动规划的方法设计了两种新颖的自适应控制策略。针对紧急制动情况,论文提出了一种基于切换逻辑的吊车制动控制策略。论文通过李雅普诺夫方法(Lyapunov's Method)、芭芭拉特引理(Barbalat's Lemma),并结合拉塞尔不变性原理(LaSalle's Invariant Theorem)对于这些吊车控制方法的性能进行了理论分析。同时,为了进一步验证吊车控制系统的性能,论文设计并实现了桥式吊车系统的仿真与实验平台,并对所设计的吊车自动控制系统进行了仿真与实验测试。具体而言,本论文的工作主要分为以下几个部分:
(1)桥式吊车动力学建模。论文利用拉格朗日方程建立了三维桥式吊车系统的动力学模型。模型中充分考虑了系统摩擦力(包括了库仑摩擦力,粘滞摩擦力和Stribeck效应)、空气阻力等干扰因素对于系统状态的影响,因而能够非常准确地描述实际吊车系统的动态特性。桥式吊车动态模型是设计与实现仿真平台的依据,同时也是后续章节中各种基于模型的控制方法设计与分析的基础。
(2)仿真与实验平台设计及实现。仿真与实验是目前科学研究中常用的手段。本文以所建立的动力学模型为基础,设计并开发了三维桥式吊车仿真平台。该平台不仅能准确地反映吊车系统的状态变化,同时也非常方便进行各种控制器的测试,以及仿真结果的观察与分析。在该仿真平台中,论文提出了一种基于掩膜方法的状态量选定方法,因此可以非常方便地对系统特定的状态量进行选定。根据实际吊车系统的工作原理和组成结构,论文进一步设计并搭建了三维桥式吊车实验平台。利用实验平台与仿真平台的对比测试,有效地验证了仿真平台的可靠性,以及所建立的动力学模型的正确性。此外,由于仿真和实验平台均采用基于Matlab/Simulink的控制结构,所以它们可以实现无缝连接,随后所设计的各种控制器可以非常方便地在两个平台上相互移植。
(3)基于能量分析的自适应控制器设计。在运送过程中为了实现台车的快速准确定位与负载防摆,本文通过对吊车系统的能量进行分析,设计了一种性能优越的自适应控制器,它可以对负载重量、吊绳长度等未知参数进行在线估计,从而提高了控制器对这些参数变化的适应能力。此外,通过引入关于摆角的动态增益,论文构造了一种改进的自适应控制器,它能够更好地抑制负载摆动。对于闭环系统中的台车位置误差与负载摆角,本文利用李雅普诺夫理论与拉塞尔不变性原理证明了它们均能渐近收敛到零。进一步,通过仿真和实验平台得到的实际测试结果也验证了上述自适应控制器的良好性能。
(4)基于台车运动规划的桥式吊车自适应控制策略。为了提高吊车控制器设计的灵活度,本文设计了一种基于台车运动规划的自适应控制策略,它通过两步控制策略来实现台车精确定位与负载防摆控制:第一步规划出一条抗摆的台车运动轨迹;第二步设计了一种自适应跟踪控制器,利用李雅普诺夫理论与芭芭拉特引理可以证明:在该控制器的作用下,台车位置与速度均能够渐近跟踪上所规划的轨迹,并且负载摆角以及摆角速度也会渐近收敛到原点。论文中所设计的控制器不仅能对系统参数进行在线估计,而且对于摩擦力等干扰因素中的系数变化也具有良好的适应性。仿真与实验结果验证了这种基于运动规划的自适应控制策略在台车定位与负载防摆两方面都具有优良的性能,并且特别适用于长距离运输。
(5)负载紧急制动控制。紧急制动是桥式吊车自动控制系统中保障系统安全性的重要一环。本文根据桥式吊车欠驱动的特性,提出了一种基于切换逻辑的控制策略,它首先通过一个制动控制器使负载在最短时间内实现制动的目标;然后利用一个阻尼控制器来加速整个系统能量的快速衰减。论文在理论上对控制器的切换条件进行了深入分析,并证明了在阻尼控制阶段,负载不会因为摆动而引起二次碰撞。此外,文中还提出了负载制动时间与制动距离的一个上界。仿真与实验结果有力地证明了本文所提出的紧急制动策略的有效性。
Underactuated systems are systems that have fewer independent control inputs than degrees of freedom to be controlled. Because fewer actuators are utilized, the mechanical design and manufacture of underactuated systems become more simplified than that of the full-actuated systems. Moreover, the cost as well as the system weight could be reduced. Thanks to these benefits, a lot of practical systems are designed to be underactuated, such as aircrafts, underwater vehicles, satellites, flexible robots and so on. Besides, a full-actuated system would become underactuated due to actuator failure. Although the underactuated nature brings much convenience to system design and manufacture, it creates a great challenge for the control of these systems. For these reasons, underactuated systems have become a research focus in the field of control theory and technology.
An overhead crane is a typical nonlinear underactuated system with strong states coupling. Due to such merits as high flexibility and less energy consumption, it is widely used for industrial production, port transportation, and so on. To improve the efficiency and the safety of the crane system, there is a great need for an effective control approach. Specifically, two control objectives should be achieved in the transportation task: on one hand, the trolley is required to arrive at the desired position within a short time to increase transferring efficiency; on the other hand, the payload swing should be suppressed within a given domain for safety concern. Unfortunately, the overhead crane is an underactuated system and there exist some uncertain disturbances such as frictions, thus it is usually difficult, if not completely impossible, to reach the aforementioned two control objectives simultaneously. For years, some researchers have made great efforts to address the control problem of the overhead crane system. Although many novel control methods have been proposed, for instance, input shaping, optimal control, intelligent control, and so on, there are some deficiencies hindering them in applications.
This dissertation makes a further study on the control techniques of the overhead crane systems. Specifically, two energy-based adaptive strategies are proposed for the transportation, and a switching-based braking control method is employed to ensure the safety of the transportation in case of an unexpected emergency. With the aid of some stability analysis tools including Lyapunov's Method, Barbalat's Lemma and LaSalle's Invariant Theorem, it proves that the stability of the closed-loop system can be ensured by the proposed control methods. Besides, a simulation testbed and a prototype testbed are constructed to demonstrate the superior performance of the proposed control techniques. In general, the work in this dissertation can be summarized as follows:
(1) Modeling of a 3D overhead crane system. The dynamic model of a 3D overhead crane system is established with utilizing Lagrange's equation. Because the model pays much attention on such nonlinear disturbances existing in the environment as mechanical frictions (including coulomb friction, linear friction and Stribeck effect) and air resistance, it can describe the dynamics of the practical system well and accurately. This dynamic model is a precondition for the construction of the simulation testbed, and it is also a foundation for system analysis and model-based controllers design which will be discussed in the following parts.
(2) Design and construction of the simulation and prototype testbed. Simulations and experiments are important means for performance evaluation in engineering science. Based on the dynamic model of a 3D overhead crane system, a simulation testbed is designed and developed using Matlab/Simulink, which can simulate the variations of the system states accurately. Furthermore, it can be easily used to test various control algorithms, as well as observe and analyze the simulation results. In the simulation testbed, a mask matrix is utilized to keep some states constant. According to the working principle and the components of a commercial overhead crane, a prototype testbed of a 3D overhead crane is constructed. Using the simulation testbed and the prototype testbed, various tests are carried out in a comparison way, and the test results show the correctness of the dynamic model and the validity of the simulation platform. Furthermore, the controller modules of the two testbeds are both developed via Matlab/Simulink, hence a control algorithm can be transported from one testbed to the other freely.
(3) Energy-based adaptive controller design. To position the trolley rapidly and suppress the payload swing in the transportation, an energy-based adaptive controller is designed for the overhead crane system. The controller can estimate the unknown parameters including the mass of the payload and the length of the rope on line. In addition, an improved adaptive controller is proposed and it can reduce the swing of the payload effectively. Utilizing Lyapunov's Theory and LaSalle's Theorem, it is proved that both the position error of the trolley and the swing angle of the payload converge to zero asymptotically. Simulation and experiment results show that the designed adaptive controllers achieve a superior performance for the overhead crane system.
(4) An adaptive control strategy based on motion planning of the trolley. To increase the flexibility of the controller design for an overhead crane, a novel two-step control approach is presented for the positioning of the trolley and the reduction of the payload swing. In the first step, this dissertation proposes a desired anti-swing trajectory for the trolley, and in the second step, an adaptive control law is designed to make the trolley track the planned trajectory. As shown by Lyapunov Theory, the proposed adaptive controller guarantees asymptotic tracking even in the presence of uncertainties including system parameters and various disturbances. Simulation and experiment results demonstrate that the motion planning based control strategy has a superior performance for the underactuated cranes, and it is especially suitable for long-distance transportation.
(5) Emergency braking control for the payload. Emergency braking plays an important role in the safety of overhead crane systems. According to the underactuated nature, this dissertation proposes a switching logic based control strategy. At the first stage, a braking controller is exerted on the trolley to prevent the payload from moving forward as soon as possible. At the second stage, an energy-based damping controller is adopted to stabilize the whole system rapidly. The switching time for the two controllers is selected carefully to ensure that the payload swing will not lead to another collision during the stage of the damping control. Furthermore, a pair of upper bounds are calculated for the braking time and distance of the payload. Both simulation and experiment results are provided to demonstrate the effectiveness of the proposed braking control method.
桥式吊车是一种典型的非线性、强耦合、欠驱动系统,它具有负载能力强、操作灵活、节能显著等优点,已经被广泛应用到工业生产、港口运输等多个领域。为了提高吊车系统的运送效率与安全性能,当前迫切需要设计出合理的控制策略来实现其自动操作。具体而言,对于桥式吊车运送控制的目标可以总结为以下两点:一方面是使台车快速准确地到达目标位置,以完成对负载的高效运送;另一方面要求负载在运行过程中的摆动尽可能地小,以避免与周围的货物或人员发生意外碰撞。然而,由于桥式吊车系统的非线性欠驱动特性,以及系统内部存在的摩擦力等多种不确定性因素,如何同时满足这两方面的性能要求是一个非常困难的问题。多年来,控制领域的学者对桥式吊车进行了广泛研究,分别采用输入整形、最优控制、人工智能技术等多种方法来设计桥式吊车控制系统,但是这些方法都还存在着一些不足之处,尚不能完全解决实际吊车系统的自动控制问题。
本论文针对具有不确定特性的非线性欠驱动桥式吊车系统进行了深入研究。具体而言,论文针对吊车运送过程,分别采用基于能量分析的方法和基于台车运动规划的方法设计了两种新颖的自适应控制策略。针对紧急制动情况,论文提出了一种基于切换逻辑的吊车制动控制策略。论文通过李雅普诺夫方法(Lyapunov's Method)、芭芭拉特引理(Barbalat's Lemma),并结合拉塞尔不变性原理(LaSalle's Invariant Theorem)对于这些吊车控制方法的性能进行了理论分析。同时,为了进一步验证吊车控制系统的性能,论文设计并实现了桥式吊车系统的仿真与实验平台,并对所设计的吊车自动控制系统进行了仿真与实验测试。具体而言,本论文的工作主要分为以下几个部分:
(1)桥式吊车动力学建模。论文利用拉格朗日方程建立了三维桥式吊车系统的动力学模型。模型中充分考虑了系统摩擦力(包括了库仑摩擦力,粘滞摩擦力和Stribeck效应)、空气阻力等干扰因素对于系统状态的影响,因而能够非常准确地描述实际吊车系统的动态特性。桥式吊车动态模型是设计与实现仿真平台的依据,同时也是后续章节中各种基于模型的控制方法设计与分析的基础。
(2)仿真与实验平台设计及实现。仿真与实验是目前科学研究中常用的手段。本文以所建立的动力学模型为基础,设计并开发了三维桥式吊车仿真平台。该平台不仅能准确地反映吊车系统的状态变化,同时也非常方便进行各种控制器的测试,以及仿真结果的观察与分析。在该仿真平台中,论文提出了一种基于掩膜方法的状态量选定方法,因此可以非常方便地对系统特定的状态量进行选定。根据实际吊车系统的工作原理和组成结构,论文进一步设计并搭建了三维桥式吊车实验平台。利用实验平台与仿真平台的对比测试,有效地验证了仿真平台的可靠性,以及所建立的动力学模型的正确性。此外,由于仿真和实验平台均采用基于Matlab/Simulink的控制结构,所以它们可以实现无缝连接,随后所设计的各种控制器可以非常方便地在两个平台上相互移植。
(3)基于能量分析的自适应控制器设计。在运送过程中为了实现台车的快速准确定位与负载防摆,本文通过对吊车系统的能量进行分析,设计了一种性能优越的自适应控制器,它可以对负载重量、吊绳长度等未知参数进行在线估计,从而提高了控制器对这些参数变化的适应能力。此外,通过引入关于摆角的动态增益,论文构造了一种改进的自适应控制器,它能够更好地抑制负载摆动。对于闭环系统中的台车位置误差与负载摆角,本文利用李雅普诺夫理论与拉塞尔不变性原理证明了它们均能渐近收敛到零。进一步,通过仿真和实验平台得到的实际测试结果也验证了上述自适应控制器的良好性能。
(4)基于台车运动规划的桥式吊车自适应控制策略。为了提高吊车控制器设计的灵活度,本文设计了一种基于台车运动规划的自适应控制策略,它通过两步控制策略来实现台车精确定位与负载防摆控制:第一步规划出一条抗摆的台车运动轨迹;第二步设计了一种自适应跟踪控制器,利用李雅普诺夫理论与芭芭拉特引理可以证明:在该控制器的作用下,台车位置与速度均能够渐近跟踪上所规划的轨迹,并且负载摆角以及摆角速度也会渐近收敛到原点。论文中所设计的控制器不仅能对系统参数进行在线估计,而且对于摩擦力等干扰因素中的系数变化也具有良好的适应性。仿真与实验结果验证了这种基于运动规划的自适应控制策略在台车定位与负载防摆两方面都具有优良的性能,并且特别适用于长距离运输。
(5)负载紧急制动控制。紧急制动是桥式吊车自动控制系统中保障系统安全性的重要一环。本文根据桥式吊车欠驱动的特性,提出了一种基于切换逻辑的控制策略,它首先通过一个制动控制器使负载在最短时间内实现制动的目标;然后利用一个阻尼控制器来加速整个系统能量的快速衰减。论文在理论上对控制器的切换条件进行了深入分析,并证明了在阻尼控制阶段,负载不会因为摆动而引起二次碰撞。此外,文中还提出了负载制动时间与制动距离的一个上界。仿真与实验结果有力地证明了本文所提出的紧急制动策略的有效性。
Underactuated systems are systems that have fewer independent control inputs than degrees of freedom to be controlled. Because fewer actuators are utilized, the mechanical design and manufacture of underactuated systems become more simplified than that of the full-actuated systems. Moreover, the cost as well as the system weight could be reduced. Thanks to these benefits, a lot of practical systems are designed to be underactuated, such as aircrafts, underwater vehicles, satellites, flexible robots and so on. Besides, a full-actuated system would become underactuated due to actuator failure. Although the underactuated nature brings much convenience to system design and manufacture, it creates a great challenge for the control of these systems. For these reasons, underactuated systems have become a research focus in the field of control theory and technology.
An overhead crane is a typical nonlinear underactuated system with strong states coupling. Due to such merits as high flexibility and less energy consumption, it is widely used for industrial production, port transportation, and so on. To improve the efficiency and the safety of the crane system, there is a great need for an effective control approach. Specifically, two control objectives should be achieved in the transportation task: on one hand, the trolley is required to arrive at the desired position within a short time to increase transferring efficiency; on the other hand, the payload swing should be suppressed within a given domain for safety concern. Unfortunately, the overhead crane is an underactuated system and there exist some uncertain disturbances such as frictions, thus it is usually difficult, if not completely impossible, to reach the aforementioned two control objectives simultaneously. For years, some researchers have made great efforts to address the control problem of the overhead crane system. Although many novel control methods have been proposed, for instance, input shaping, optimal control, intelligent control, and so on, there are some deficiencies hindering them in applications.
This dissertation makes a further study on the control techniques of the overhead crane systems. Specifically, two energy-based adaptive strategies are proposed for the transportation, and a switching-based braking control method is employed to ensure the safety of the transportation in case of an unexpected emergency. With the aid of some stability analysis tools including Lyapunov's Method, Barbalat's Lemma and LaSalle's Invariant Theorem, it proves that the stability of the closed-loop system can be ensured by the proposed control methods. Besides, a simulation testbed and a prototype testbed are constructed to demonstrate the superior performance of the proposed control techniques. In general, the work in this dissertation can be summarized as follows:
(1) Modeling of a 3D overhead crane system. The dynamic model of a 3D overhead crane system is established with utilizing Lagrange's equation. Because the model pays much attention on such nonlinear disturbances existing in the environment as mechanical frictions (including coulomb friction, linear friction and Stribeck effect) and air resistance, it can describe the dynamics of the practical system well and accurately. This dynamic model is a precondition for the construction of the simulation testbed, and it is also a foundation for system analysis and model-based controllers design which will be discussed in the following parts.
(2) Design and construction of the simulation and prototype testbed. Simulations and experiments are important means for performance evaluation in engineering science. Based on the dynamic model of a 3D overhead crane system, a simulation testbed is designed and developed using Matlab/Simulink, which can simulate the variations of the system states accurately. Furthermore, it can be easily used to test various control algorithms, as well as observe and analyze the simulation results. In the simulation testbed, a mask matrix is utilized to keep some states constant. According to the working principle and the components of a commercial overhead crane, a prototype testbed of a 3D overhead crane is constructed. Using the simulation testbed and the prototype testbed, various tests are carried out in a comparison way, and the test results show the correctness of the dynamic model and the validity of the simulation platform. Furthermore, the controller modules of the two testbeds are both developed via Matlab/Simulink, hence a control algorithm can be transported from one testbed to the other freely.
(3) Energy-based adaptive controller design. To position the trolley rapidly and suppress the payload swing in the transportation, an energy-based adaptive controller is designed for the overhead crane system. The controller can estimate the unknown parameters including the mass of the payload and the length of the rope on line. In addition, an improved adaptive controller is proposed and it can reduce the swing of the payload effectively. Utilizing Lyapunov's Theory and LaSalle's Theorem, it is proved that both the position error of the trolley and the swing angle of the payload converge to zero asymptotically. Simulation and experiment results show that the designed adaptive controllers achieve a superior performance for the overhead crane system.
(4) An adaptive control strategy based on motion planning of the trolley. To increase the flexibility of the controller design for an overhead crane, a novel two-step control approach is presented for the positioning of the trolley and the reduction of the payload swing. In the first step, this dissertation proposes a desired anti-swing trajectory for the trolley, and in the second step, an adaptive control law is designed to make the trolley track the planned trajectory. As shown by Lyapunov Theory, the proposed adaptive controller guarantees asymptotic tracking even in the presence of uncertainties including system parameters and various disturbances. Simulation and experiment results demonstrate that the motion planning based control strategy has a superior performance for the underactuated cranes, and it is especially suitable for long-distance transportation.
(5) Emergency braking control for the payload. Emergency braking plays an important role in the safety of overhead crane systems. According to the underactuated nature, this dissertation proposes a switching logic based control strategy. At the first stage, a braking controller is exerted on the trolley to prevent the payload from moving forward as soon as possible. At the second stage, an energy-based damping controller is adopted to stabilize the whole system rapidly. The switching time for the two controllers is selected carefully to ensure that the payload swing will not lead to another collision during the stage of the damping control. Furthermore, a pair of upper bounds are calculated for the braking time and distance of the payload. Both simulation and experiment results are provided to demonstrate the effectiveness of the proposed braking control method.
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