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The advanced nonlinear sliding mode control method of DGEN380 aero engine is presented in this paper. This aero engine is a small high bypass ratio turbofan engine by which the nonlinear control approach of the aero engine is invested. And this paper focuses on the power management function of the aero engine control system which includes steady control and transient control. The mathematical model of DGEN380 aero engine is built by a set of nonlinear dynamic equation that is validated by experimental data. The single controller based on sliding mode approach is designed that can keep some certain thrust levels during steady state and maintain repeatable performance during transient operation from one requested thrust level to another. The single controller can offset the impact of the signal noise and harmonic disturbance at a certain power point. And the dynamic performance of the single controller is satisfactory at the transient process. The experiment is conducted by aero engine test bench for the single control.

A new configuration of the small aero engine, DGEN380 aero engine, is presented in this research. The DGEN380 aero engine which is a turbofan engine has been designed to motorize private flight aircraft. The DGEN380 aero engine constitutes the core of the family of high bypass ratio engines with a thrust ranging from 2.5 kN to 4 kN. The DGEN380 aero engine is also modern and innovative in its geared architecture, even more so in its “all-electric” design for all the equipment around the engine, all the pumps of DGEN380 being not mechanically but electrically driven. Meanwhile, this aero engine can be used for the investment of the control approach. The advanced control approach of the aero engine is analyzed by the DGEN380 real engine test bench. And the advanced control approach may be embodied in the control of aero engine to the engine. So, the DGEN380 aero engine is regarded as a control object. Nonlinear control approach is concerned by DGEN380 real engine test bench.

There are two essential functions in the control system of the aero engine which are power management and limitation protection. And power management includes steady state control and transition state control [

Some nonlinear control methods have been used to overcome the disadvantages of robustness and a limited operating domain such as fuzzy sliding mode control, adaptive neural network, and integral sliding mode control [

The purpose of this research is then to propose that a nonlinear control approach for DGEN380 aero engine is to implement the power management of the aero engine. The main achievements are the nonlinear model of DGEN380 aero engine and the advanced nonlinear controller which both can be used for steady control and transient control [

In this paper, the mathematical model of DGEN380 aero engine is built, and the control scheme based on the nonlinear model is designed by the sliding mode control method. In Section

The structure of DGEN380 aero engine is generally similar to a general turbofan engine. There are two (or three) shafts in the aero engine. And they are low pressure rotor and high pressure rotor. Figure

Schematic configuration of DGEN380 aero engine.

Since this research intends to design a controller based on aero engine model which can be competent in doing power management of an aero engine at the steady state and the transition state, the aero engine model should be able to capture the dynamic characteristic and steady characteristic of the aero engine in a broad flight envelope.

The differential equation is a useful way to establish the mapping relation between state variables and input variables. If the differential term equals zero, the steady state characteristic can be obtained. Nevertheless, if the differential term does not equal zero, the dynamic process is described. So, the two-shaft differential equations which simulate among the rotation processes of high pressure rotor and low pressure rotor and the one volume dynamic equation which concludes aerodynamic parameters variation and simultaneous equations are both developed in engine modeling [

The model neglects not only the ignition process but also the starting process and numerous physical features of the aero engine, such as reaction, diffusion, and fluid-structure interactions; all of them are ignored. But the adiabatic exponent is constant. This research ignores the heat exchange between high temperature gases and components.

The shaft dynamic equation, derived by Newton’s second law, is proposed to describe the motion process of high pressure and low pressure shafts. Equation (

The volume dynamic equation can draw the aerodynamic parameters’ (pressure and temperature variation) change at both the inlet and outlet of chambers, which is then used for combustor chamber modeling. Equation (

The continuity equation can be expressed as

The volume dynamic equation can be simplified by the continuity equation, which is written as

The DGEN380 engine model is built by low pressure rotor and high pressure rotor and a volume dynamic equation. The DGEN380 engine model can be written as a nonlinear system affine with respect to the engine input vector:

The vector

The consumed work or produced work can be obtained by system identification method. The relation equation identified by experimental data is written as follows:

DGEN380 aero engine test bench.

The results of the identification of mapping relation between the rotary. (a) The corresponding relation between the consumed work by fan and low rotor speed (spot-component test data, line-identification curve). (b) The corresponding relation between the produced work by LPT and low rotor speed (spot-component test data, line-identification curve). (c) The corresponding relation between the consumed work by HPC and high rotor speed (spot-component test data, line-identification curve). (d) The corresponding relation between the produced work by HPT and high rotor speed (spot-component test data, line-identification curve).

Equations (

Transient simulations and steady state simulations are implemented in the MATLAB commercial software that establishes a simulation environment. A variable-step implicit solver was designed to solve stiff problems, “ode15s,” which was chosen as the time-stepping algorithm.

Table

Steady simulation results.

Manual value | Simulation result | Error (%) | Manual value | Simulation result | Error (%) | Manual value | Simulation result | Error (%) | |
---|---|---|---|---|---|---|---|---|---|

Idle | 0.4701 | 0.47006 | 0.5676 | 0.56761 | 0.6516 | 0.65154 | |||

Cruise | 0.925 | 0.9251 | 0.9559 | 0.95594 | 0.939 | 0.93902 | |||

Climb | 1 | 1.00043 | 1 | 1.00026 | 1 | 1.00034 |

Simulation curves of steady state.

The approach presented in this paper can meet the target value. Comparing to that of traditional method, this approach has simpler formulations, more rapid convergence (as shown in Figure

The transition simulation describes the acceleration process and the deceleration process, that is, the acceleration (or deceleration) process starts from one set point to another, which combines a fuel schedule between them. The DGEN380 engine test is implemented to validate the dynamic characteristic of DGEN380 aero engine model. And the test results can provide accurate test data comparison with transient simulation computation results by the variable-step implicit solver. The acceleration/deceleration process of the test is the same with the process of simulation which includes two increasing procedures of shaft speed from the idle power to the climb power, a decreasing process from the climb power to the idle power, a decreasing process from the climb power to the cruise power, and a decreasing process from the cruise power to the idle power. The test results are displayed as the

The results of transition state simulation. (a) Variation curve of

A systems-level engine model, DGEN380 aero engine model, which form is simple to obtain is presented here. By solving a set of nonlinear dynamic equation, the solutions of steady state and transient state are obtained which are compared to get the manual data and test data. The results show that the DGEN380 engine model on steady state is accurate as well as on transition state simulation. The DGEN380 aero engine model built by dynamic equations can simulate steady state and transient state of the engine, which will be applied to design the DGEN380 aero engine controller that implements steady control and transient control function.

The control system of the DGEN380 aero engine has to ensure optimal production of thrust (power) of the aero engine. The optimal amount of thrust production relies on certain flight conditions that consist of consistent thrust and smooth variation of thrust [

All say, in essence, the steady state control and the transition state control are the same. The steady state control process keeps the aero engine in maintaining a certain speed of steady state point. Meanwhile, the process of transition state control starts from one steady state point speed to another steady state point speed. They can be expressed as follows:

So, it is significant to control the low pressure rotor speed of the aero engine, to optimize the aero engine thrust, i.e., control

Control scheme of power management of DGEN380 aero engine.

Section

The core of sliding mode control method is to force the system trajectories to converge to a sliding surface and to be maintained on it in spite of perturbations and uncertainties, thanks to a discontinuous control input. The main features of this class of control are as follows: (1) the input variable is based on the sliding variable which is determined in the control objectives, from the sliding mode, the variable defined the sliding mode surface; (2) the input variable has to force the system trajectories to reach the sliding mode surface, in a finite time and spite of the uncertainties and disturbance; and (3) when the sliding mode surface is reached, the trajectories are evolving on it. By this way, the control objectives are fulfilled in spite of uncertainties and disturbance.

The control strategy design is used into the DGEN380 aero engine described in Section

The output vector can be defined as follows:

The control objective is to force

From the definition of output vector,

Then, from DGEN380 aero engine model, one gets

Each parameter can be written as the equation that a nominal part plus an uncertain one equals the parameters. And both

The uncertain terms

Considering the following control law

It is obvious that the

The objective

To evaluate the performance of the single controller of DGEN380 aero engine, the control system of DGEN380 aero engine simulations have to been performed. The power management function of the proposed approach control strategy can be used to maintain table thrust levels (steady state control) and maintain repeatable performance (transition state control). So, the simulations include steady state simulation and transition state simulation.

Steady state simulation focusses on a certain steady state point which concludes fuel step response simulation and harmonic disturbance simulation. The idle power point is selected in the simulation.

The proposed control strategy is comparing with a general PI controller which is applied in aero engine steady state control now, by evaluating different performances such as oscillations and harmonic disturbance of the rotor speed and outlet temperature. The performance of the two controllers can be checked. Meanwhile, the robustness of the two controllers can also be tested.

The PI controller of the idle power point is defined by a general method [

Table

PI controller parameters of the idle power point.

Controlled variable | Proportional gain | Integral gain |
---|---|---|

Speed | 29.77 | 5.20 |

Temperature | 33.09 | 6.55 |

The harmonic disturbance can be written as

A white noise is considered on the main measured variables of control system sensor, such as low pressure rotor speed

Noise characteristics.

Measured variable | Noise magnitude (%) |
---|---|

Rotor speed | 5 |

Turbine outlet temperature |
4 |

Figure

The simulation results of step response of steady state power management. (a) Low pressure rotor speed

According to Figure

Figure

The simulation results of harmonic disturbance of steady state power management. (a) Low pressure rotor speed

According to the results of the steady state simulations, the single controller is designed by this research which possesses the expected property of steady state control. That is to say, the single controller of DGEN380 aero engine can maintain table thrust levels at a certain steady state point. When the system (control objective) achieves sliding mode surface, sliding function

Now considering the transient process: the state of aero engine changes from one requested thrust level to another, the controller should maintain repeatable performance during this transient operation. Then, the idle power state, cruise power state, and climb power state are selected for simulation. The following scenario is assumed: DGEN380 aero engine implements acceleration from the idle power point to the climb power point; then, it decelerated back to cruise power point. And low pressure speed is selected as the output variable.

The proposed approach control strategy is compared with a gain scheduling approach based on a multi-PI controller that is applied in aero engine transient control now. PI controller only calculates the steady state performance of the aero engine. However, the transient control focuses on at least two steady state points. The gain scheduling approach is applied in actual aero engine control now which switches the corresponding PI controller based on aero engine performance. Table

PI speed controller parameters.

Power point | Proportional gain | Integral gain |
---|---|---|

Idle power | 29.77 | 5.20 |

Cruise power | 33.52 | 5.58 |

Climb power | 34.90 | 6.86 |

In concluding that the single controller can compensate for the influence of signal noise, the harmonic disturbance is obtained in Section

Figure

The simulation results of transition state power management. (a) Low pressure rotor speed

According to the results of the transition state simulations, the single controller designed by this research possesses the anticipate behavior of transition state control. That is to say, the sliding mode controller of DGEN380 aero engine can maintain repeatable performance during the transient process. The nonlinear controller, single controller, can realize the transient control function. Meanwhile, the specific fuel consumption of this control approach is lower than that of the traditional approach which gains scheduling when the system state changes from one state to another.

The performance of the single controller can be obtained by simulation in Section

The single controller will be tested in DGEN380 aero engine test bench (Figure

The test bench aero engine is run at a cruise condition of 10,000 ft and Mach 0.33. The single controller is conducted. To ensure that the single controller as applied to the real aero engine meets the control system requirement, a PLA command at the 0.6-second mark from 43% PLA power (idle power) to 47% PLA power (climb power) is shown in Figure

The test of single controller.

A new configuration of the small aero engine, DGEN380 aero engine, has been presented in this research. A nonlinear dynamic model of DGEN380 aero engine has been built by rotor dynamic equations and volume dynamic equations. Meanwhile, the sliding mode control method has been developed, which is an advanced nonlinear control approach. A single controller based on sliding mode control method has been designed with the objective to keep table thrust levels during steady state and maintain repeatable performance during transient operation from one requested thrust level to another. The proposed control scheme is compared to a general PI controller or multi-PI controllers (gain scheduling approach). Because of the robustness of the single controller designed by this paper, the controller can offset the impact of the signal noise and harmonic disturbance at a certain power point. And the dynamic performance of the single controller is satisfactory at the transient process. Meanwhile, the single controller calculates fewer fuel flow. These performances are explained by computer simulation. The single controller has been examined in the aero engine test bench. The experimental results depicted good performance.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest.