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PID Control of Multisources Complex Excitations Active Vibration Isolation System: An Improved Particle Swarm Optimization Algorithm

Song Chunsheng, Jiang Youliang, Zhang Jinguang
Published: 21 November 2016

Abstract: Active vibration isolation technology is the key technique to solve the vibration isolation problems related to the multisources complex excitations vibration isolation system. The electromagnetic actuators-based multisources complex excitations active vibration isolation system is built. Additionally, in view of the complex structure and strong coupling of the system, the least-squares method to identify and obtain the mathematical model of the vibration isolation system is adopted. Furthermore, this paper also sets up the acceleration feedback-based PID control model for multisources complex excitations active vibration isolation system, proposes an improved particle swarm optimization (PSO) algorithm of dynamic inertia weight factors used to optimize parameters of the built PID control model, and conducts simulation analysis. The simulation results show that, compared with the passive system before the control, the multisources complex excitations active vibration isolation system under the PID control has the far less peak-to-peak amplitude of acceleration which is transmitted to the foundation and has the much better vibration isolation effect. Finally, the paper conducts experimental verification, which demonstrates that active vibration control effect is identical to the simulation results and the vibration control effect is significantly improved.1. IntroductionAlong with the development of ships, the mechanical structure inside the ships becomes more and more complex, and so do the excitation mode and the components of excitation signals. Due to the limited load capacity and inner space of the ships, a majority of power devices are installed together rigidly or flexibly to form the isolation object with multiple excitation sources. As the vibration excitations generated by each equipment are different in amplitude, phase, frequency, and direction, those excitation signals are mixed and overlapped, resulting in complicated and variable frequency and phase of excitation signals which happen on the entire vibration isolation object [1–4]. The energy generated from mechanical vibration of the ships is mainly delivered via the supporting base. Vibration isolation technology can effectively isolate the mechanical vibration transfer. The vibration isolation technology can be divided into passive and active ones. Despite the simple structure and reliable operation, passive vibration isolation technology has inherent defect of poor vibration isolation performance in low frequency and resonance regions. It is difficult to purely rely on passive vibration isolation technology to further improve vibration isolation performance of multisources complex excitations vibration isolation system. Active vibration isolation technology can overcome the defect of the passive vibration isolation technology, which is the poor vibration isolation performance in low frequency and resonance regions. Thus, studies on theories, methods, and technologies of active vibration isolation technology under multiple complex excitation sources are critical to achieve vibration isolation of machinery equipment of ships in terms of whole frequency domain.Active vibration isolation technology can be carried out from three aspects: structural optimization of the active vibration isolation system, control of active vibration isolation system, and active vibration isolator (actuator) [5]. The active noise and vibration control (ANVC) system was developed by the USA, which used marine high-speed network technology and was applied to full boat equipment for active vibration isolation below 100 Hz [6]. Four solenoid actuators were applied into single excitation active vibration isolation system, which effectively solved the control issue around the flexible plate with modal frequencies and obtained good vibration isolation performance [7]. A “smart spring” mounting system that ordinary springs and electric magnetic actuators were connected in parallel to was proposed. This system solved the response peak of traditional isolators and was applied to single excitation source active vibration isolation system [8, 9]. A kind of vibration isolation structure was introduced, where the electrorheological fluid damper was used to change the damping force and adjust the system rigidity. This structure was applied to single excitation source active vibration isolation system and certain control algorithms were used, enabling the system rigidity to be adjustable within a certain range [10]. Active vibration isolation and system modeling of double-layer isolation system for ship engine or auxiliary engine with single excitation source was studied [11]. The literature [12] targeted the application of unidirectional excitation double-layer isolation system of electrorheological fluid damper to design a semiactive static output feedback fuzzy sliding mode controller. The simulation results showed that the vibration isolation performance was superior to that of the optimal passive damping system. The magnetic suspension technique was applied into microvibration platform with single excitation source and the theories of magnetic suspension vibration isolation under slight excitation were studied. Good vibration isolation effect was obtained [13]. Authorized by the US Navy, magnetic suspension vibration isolators were applied to floating raft isolation system, and active theories and control simulation experiments were studied, with good active vibration isolation effect [14, 15]. Theoretical electromagnetic force model of the magnetic suspension vibration isolator with single excitation source according to measured data was modified [16].Among the abovementioned research papers related to active vibration isolation, a majority focus on single-layer and double-layer active vibration isolation system with single excitation source, studying dynamics model and control strategy and algorithm, while some propose active control policies and guidelines of multifreedom degree vibration isolation system. However, there have yet been no deep and comprehensive studies about whether resultant effect can be achieved by jointly using multiple active vibration isolators. Multisources complex excitations active vibration isolation system is the system which achieves vibration isolation by giving play to combined effect of active and passive vibration isolation components. It is the typical mechatronic system. Due to the complicated and changeable excitation, strong nonlinear relationship, and interconnection among different excitation sources and different isolators via structure, the system is very complicated. Thus, it is difficult to build a mathematical model which meets the requirements with the analysis method. Experimental data include all information of the model and the use of model identification method in the experimental data is an effective way to solve such issues [16, 17]. The least-squares method is the method which determines the parameter of system model by minimizing square and function of the generalized error. It is applicable to both linear and nonlinear systems. Thus, this paper adopts this method to complete model identification of multisources complex excitations active vibration isolation system. The control is the core link of the active vibration isolation system and the feedback control is especially suitable for complex systems and systems with uncertain parameters [17]. With simple structure, good stability, reliable operation, and strong robustness, PID feedback controller is mainly subject to three parameters, namely, P, I, and D. Determination of control parameters is the core of control system design. As taking of PID control parameters by hands not only is time-consuming, but also fails to ensure optimal performance, intelligent control algorithm-based PID controller obtained the PID parameters by combining with modern intelligent algorithms such as genetic algorithm, ant colony optimization algorithms, and particle swarm optimization (PSO) algorithm [18–27]. The PSO algorithm is a kind of swarm optimization algorithm in the field of smart computing which is obtained by referring to preying of birds. Compared with the genetic algorithm, ant colony optimization algorithms, and other smart computing methods, the PSO algorithm has simple structure, few parameters, fast convergence speed, easiness to implement, and low time complexity and space complexity. It is demonstrated to obtain the good optimal solution at a low computational cost, and thus it is widely studied and applied in PID parameter optimization field [19–27].The response amplitude of the acceleration delivered to the foundation or the attenuation ratio in the course of acceleration passing is an important indicator to measure the vibration isolation effect of mechanical equipment. Therefore, taking the strong coupling, nonlinear characteristics of complex multisources excitation active vibration isolation system, and the difficulty in establishing an accurate model using traditional kinetic methods into account, the least-squares model identification method is adopted to establish the active vibration isolation system model under the multiple complex excitation sources and build the intelligent PID control model which is based on acceleration feedback. In addition, this paper proposes the improved PSO algorithm of dynamic inertia weight factor, optimizes the built PID control parameters, and conducts simulation analysis and finally experimental verification.2. Model of Multisources Complex Excitations Active Vibration Isolation SystemThe model of multisources complex excitation active vibration isolation system is shown in Figure 1. Two vibration motors 1-1 and 1-2 are connected rigidly with plate 2. By modulating the frequency via a convertor, the rational speed of two vibration motors can be adjusted and the amplitude and frequency of excitation signals can be changed and adjusted u
Keywords: vibration / power amplifier / Nonlinear Systems / PID / Springs / inertia weight / particle swarm optimization / Feedback Output

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