Control Of Non-Gaussian Systems:Methods And Applications

The fact that most industrial processes are subjected to random noises makes modeling,control and application of stochastic system an attractive research area in control theory.Many control algorithms have been proposed under the assumption that the controlled system is characterized to be Gaussian,such as self-turning control,minimum variance control,Markov jumping parameter control and linear quadratic Gaussian control.These control algorithms are based on the expectation and variance of system variables which can fully reflect the dynamic characteristics only under Gaussian circumstances.However,in actual industrial processes the system model is often nonlinear and the disturbances does not always follow Gaussian distribution,which commonly makes the controlled system non-Gaussian.Therefore,these expectation and variance based methods may not achieve satisfactory control effect.On the other hand,with the rapid development of precision instruments,communication networks,image processing and data processing technology,we can easily get the distribution of system random variables which contains all the probability information of random variables.In this paper,some new ideas and methods for the control of non-Gaussian stochastic systems are proposed based on probability density function.The main work are shown as follows:1)For a class of non-Gaussian stochastic systems that can be represented by controlled auto-regressive integrated moving average(CARIMA)models,an MPCPID control method based on minimum entropy criterion is proposed.For a stochastic system subject to non-Gaussian disturbance,the predicted outputs are obtained through a certain model,thus the estimated survival information potential of the system output can be calculated,then the optimal parameters of the PID controller can be obtained by minimizing a performance criterion which mainly consists of the survival information potential.Compared with traditional entropies,the survival information potential has stronger robustness and simpler calculation.The method is tested in the waste heat recovery system based on organic Rankine cycle.The simulation results show that the method has good control performance.2)A data-driven control method based on minimum entropy is proposed for the organic Rankine cycle superheating control system.The moment generating function is used to calculate the tracking error entropy of the superheat control system,and the optimal control law is obtained by minimizing the tracking error entropy.Furthermore,the model of the organic Rankine cycle system is established to analyze the stability of the controlled system.Simulation results show that the proposed method has better control performance than traditional PID control under non-Gaussian circumstances.3)For the frequency modulation of power systems considering aggregated inverter air conditioners to be a regulation resource,a control method based on minimum entropy is proposed.The moment generating function is used to calculate the entropy of system frequency deviation,and the optimal control law is then obtained by minimizing the entropy of system frequency deviation.The influence of energy consumption and control input constrains are considered.Meanwhile,the stability of the system is analyzed.The effectiveness of this control method is tested by power system primary frequency modulation simulation experiment.4)A minimum entropy control method based on moment generating function is proposed for multivariable non-Gaussian stochastic systems.The probability density function of each output is obtained from the system model,and the moment generating function is obtained according to the output probability density function,and then the performance criterion is constructed.The optimal control law is determined by minimizing the performance criterion.The effectiveness of this method is verified in a nonlinear non-Gaussian two-input two-output system.5)A moment-generating function based molecular weight distribution shaping control is proposed for the polymerization process.Motivated by the PDF shaping control,the output molecular weight distribution is approximated by B-spline neural network,and then the dynamic weight model of the system is identified by subspace identification method.Based on the moment generating function,a performance criterion representing the difference between the output and the target molecular weight distribution is constructed.By minimizing the performance criterion,the output molecular weight distribution is regulated towards the target molecular weight distribution.The effectiveness of this method is verified by a simulation of polystyrene polymerization process.