Research On The Optimal Control Problem Of Aero-engine Based On Linear Variable Parameter Systems

Aero engines are the power units of aircraft,and the system models are usually highly nonlinear and complex,which are difficult to be accurately described by simple linear systems,which brings great challenges to the design of controllers for optimal control purposes.Linear Parameter Varying(LPV)systems are often seen as a bridge between linear and nonlinear systems,on the one hand it can capture more nonlinear features of the engine system,and on the other hand,it is also possible to apply the mature linear system theory for research.The description of aero-engine dynamic processes using LPV system can show the nonlinear and time-varying properties of the system through the introduction of scheduling parameters.In this paper,the optimal control problem based on LPV system is studied in the context of optimal control of aero-engine around the control requirements,and the main contents are summarized as follows.1.Based on the Equilibrium Manifold Expansion(EME)model,an improved LPV model is refined and the corresponding optimal control problem is considered.The scheduling parameters of the improved LPV system are no longer pre-defined parameters,but are adjusted according to the output values of the system at the sampling points.The exact form and order of each subsystem is unknown until the control strategy is given,and the permissible set of switching subsystems is infinite-dimensional.Through the standard control parameterization method,we transform the optimal control problem into an optimal parameter selection problem,and we derive the gradient information of the objective function with respect to the control parameters by the variational method,and based on the gradient descent method,we give the corresponding algorithm for solving the numerical solution.We demonstrate the uniqueness of the proposed LPV system by studying the example containing two subsystems,and finally we show the effectiveness of our algorithm through the example of any finite number of subsystems.2.In addition to the goal of high thrust and low fuel consumption during engine operation,other constraints(e.g.size,mass,etc.)must also be taken into account.During the actual acceleration of an aero-engine,on the one hand,it is necessary to reach the fast state from the idle state in the shortest possible time for safety reasons,and on the other hand,it is necessary to keep the temperature in front of the turbine within the maximum temperature it can withstand.Based on the classical LPV system,a nonlinear term is added to compensate for modeling errors.By the same modeling approach,the pre-turbine temperature is also an LPV system with a nonlinear term and shares the same scheduling parameters with the power system,the values of which depend on the output of the power system.We consider the time-optimal control problem based on the LPV system with temperature constraints,and we transform the time-optimal control problem into a finite-dimensional optimization problem using the control parameterization.In order to obtain the global optimal solution and avoid solving complex gradient information,we choose the Particle Swarm Optimization(PSO)algorithm to solve the transformed problem,and the corresponding numerical example is given.3.For aero-engines,the time required to accelerate from the slow state speed to the maximum operating speed is an important indicator of the engine acceleration performance.According to the actual engine operation process,we add inequality constraints to the control and state variables of the LPV system on the basis of engine operation safety and effectiveness,and introduce new constraint functions by converting the constraints and giving the gradient information of the constraint functions with respect to the control parameters after smoothing.Considering the actual engine operation process,we improve the particle position update formula based on the classical particle swarm optimization algorithm by adding the control value of the previous moment to the position update formula with certain weight,and combine the gradient descent method and the improved particle swarm optimization algorithm to propose an optimization algorithm for the LPV system based on the tracking control problem with state inequality constraints.The numerical example shows that the improved algorithm obtains a smooth transition control strategy for the system with guaranteed computational efficiency.4.In recent years,multi-objective control has gradually become an important research area in aero-engine control as the requirements for control quality are increasing.Therefore,we consider a class of multi-objective optimal control problems based on the LPV system in which the aero-engine high pressure turbine speed and low pressure turbine speed both reach the set target value within a given time.The multi-objective optimal control problem is transformed into a multi-objective planning problem using a control parameterization method,and then a fast genetic algorithm with elite strategy for non-dominated ranking is used to compute the problem,retaining the best individuals in the population and reducing the complexity of computing the non-dominated order by the fast non-dominated ranking method,introducing the elite strategy to improve the accuracy of the optimization results,and using the crowding and crowding comparison operators to maintain the ability to retain the ability to retain population diversity using crowding and crowding comparison operators.In the mean time,the fast genetic algorithm of non-dominated ranking with elite strategy is improved by using the special structure based on LPV system itself,and the numerical results are obtained from Pareto frontier,which can provide some theoretical reference for the final decision.