Research On The Control Of Under-actuated Nonlinear Systems

Under-actuated systems refer to a kind of systems whose dimension of driving is fewer than its dimension of freedom,which is different from fully-actuated systems.In control theory,these two are both very important classifications of control systems.Under-actuated system has many advantages such as saving energy,reducing cost and improving degrees of freedom.Besides,sometimes certain mechanical devices working in some specific environment or performing specific function may require the use of under-actuated structure.And under-actuated system can also be a back-up system for fully-actuated ones.Therefore,under-actuated systems are applied more and more widely and gaining more and more research results.However,the control problems of under-actuated systems remain to be difficult.In the process,while keeping the under-actuated elements balance,the controller also have to be able to control the actuated elements,which makes the whole problem even more difficult.Therefore,there have been a great deal of attention and research in this field.In order to extend the research results of under-actuated systems and develop more control methods for controlling it,this paper is aimd to studie under-actuated systems and two control methods are proposed.The first method is single neuron PID feedback compensation control.This method belongs to the range of intelligent control.In this structure,single neuron PID controller is the main controller,along with a single neuron PID identifier.The single neuron PID identifier aperforms online learning and transport the parameters to the single neuron PID controller so that it can apply them to the internal algorithm.As a result,the advantages of intelligent control are guaranteed,and offline learning can be avoided at the same time.In addition,a traditional PID controller is added to the whole control structure.The single neuron PID structure needs time for learning.Therefore,its parameters are not suitable for the system at the beginning.Adding a PID controller can effectively avoid the disturbance before the learning process of artificial neural network control is finished.Besides,when the system is disturbed,the structure can also increase the overall resistance of the system and increase robustness.Then MATLAB's Simulink module is used to simulate the control of an under-actuated system using this method.The results are compared with those of other control methods.The second method is the direct parametric feedback linearization method.Feedback linearization method uses the output signal to offset the nonlinear components of the original system,which makes the nonlinear system linear,reducing the difficulty of control.Second-order dynamic system is a common system structure and is often used in various mechanical systems.The method of this paper aim to control a class of under-actuated second-order nonlinear systems using the direct parametric method,which operates directly on the original system parameter matrices,in order to reduce the amount of computation and increase numerical stability.