The Design And Realization Of The Controller Based On Wavelet Multiresolution Analysis

In engineering practice,the system often has multiresolution characteristics,such as the existence of high-frequency signal noise,multi-rate of the system input and output.So there is often some limitations on the use of traditional time-domain methods to control the system.The wavelet transform in the field of signal analysis has good timefrequency characteristics.Therefore,wavelet transform can be applied to system analysis and system control.Moreover,in the field of real-time system control,the systems require the controller to have high computational performance,and the computational complexity of wavelet transform is smaller than Fourier transform.Therefore the main research of this paper is to apply wavelet multiresolution analysis to traditional time domain control algorithm to improve the ability of denoising and reduces the complexity of the control algorithm.In this paper,the wavelet multiresolution analysis is applied to the single-input singleoutput(SISO)system and the multi-input multi-output(MIMO)system.According to the structures of classical PID control algorithm and model predictive control algorithm,multiresolution PID controller and multi-scale model predictive controller are designed respectively.In order to meet the requirements of the miniaturization and high real-time performance of the controller,this paper uses FPGA to implement the multiresolution PID control.In order to verify the effectiveness of the controller,a practicality experiment for motor speed tracking problem is proposed.Specifically,this paper mainly includes the following aspects:1.Firstly,wavelet multiresolution analysis is applied to SISO contorl system.According to the classical PID control algorithm,a SISO multi-resolution controller which is called multi-resolution PID controller is designed,which can decompose the input signal to get the signal-noise separation,and then weight the original input signal at different resolution(frequency)separately to achieve the filtering control.Aiming at the factors that need to be considered in the process of the design of multiresolution PID controller,this paper makes a detailed analysis and finally completes the design of the controller.In order to verify the effectiveness of the controller,the paper applies the controller to the brushless DC motor low-speed control which is sensitive to the noise,and the MATLAB off-line simulation results show that the multiresolution PID controller has better denoising effect than traditional PID controller.2.For the MIMO system control,this paper applies the wavelet resolution analysis to the classical model predictive control algorithm.First,a multi-scale model of the system is established by discrete wavelet transform.Compared with the traditional time domain model,a scale(frequency)information is added.The parallel characteristics of the multi-scale model can be found by the use of binary tree structure.Then,by using the discrete wavelet transform,the classical MPC algorithm can be transformed from time domain to time-scale domain.Through the structural characteristics of the binary tree,the scale calculation method of multi-scale predictive control is proposed,which can obtain the appropriate horizon length of multi-scale predictive control and then reduce the computational complexity of the algorithm effectively.In order to verify the effectiveness of the control algorithm,the experimental results from MATLAB show that the multi-scale MPC control algorithm has a smaller computational cost than classical MPC algorithm,and it will be more flexible in a controller design for the reason that multi-scale MPC control algorithm contains more information of the system.3.A multi-resolution PID control algorithm is taken as an example to illustrate the steps of the implementation of the control algorithm based on FPGA.Firstly,the parallel structure of the multi-resolution PID control algorithm is analyzed,and then use the C/C++ code to describe the algorithm.After the fixed-point processing of the algorithm,the Xilinx high level synthesis tool(Vivado HLS)is used to turn the C/C++ code of control algorithm into the hardware language code.In order to verify the validity and realtime performance of the hardware multi-resolution PID controller based on FPGA,this paper uses Model Sim to simulate the hardware code.Through the simulation results,we can get that the latency of multi-resolution PID is only 0.015 ms,which verifies that the controller has high computational performance;Finally,this paper applies the hardware controller to the real motor speed tracking control?Through the construction of the appropriate interface circuit,this paper completes the motor speed control experiment,the experimental results also proved that the controller has a very good performance.