An adaptive model predictive controller for turbofan engines

Transcription

1 American Journal o Engineering Research (AJER) e-issn: p-issn : Volume-4, Issue-12, pp Research Paper Open Access An adaptive model predictive controller or turboan engines Xian Du*, Yingqing Guo, Hao Sun Northwestern Polytechnical University, Xi an , PR China ABSRAC: An adaptive model predictive controller o turboan engines that can transer working states within a certain light envelope was proposed. Due to a very wide range o light and operation conditions or turboan engines, a series o model predictive controllers should be well established and arranged. First, constrained linear model predictive control algorithm is investigated and a number o model predictive controllers were designed based on linear models at dierent nominal points. hen, control domain in the light envelope was divided according to the inlet parameters o aero-engines, and the nominal points were determined in all subsections. Finally, an adaptive predictive controller was achieved using a multilayer parameters scheduling scheme, which possesses the ability to realize the regulation o engines under dierent light and working conditions. Simulation results show that the proposed adaptive predictive control system displays good perormances in the control domain, which provides an eective approach or the design o the whole envelope controller. Keywords - urboan engine, transition state, adaptive model predictive control, light envelope, parameters scheduling I. INRODUCION In the process o aero-engine control, input and output variables are subject to all kinds o physical and operational limits [1-3]. For example, a uel low metering valve, as one o the actuators, cannot deal with too ast o a uel low rate luctuation arbitrarily due to mechanical or hydraulic limit; and the controlled output rotor speeds or exhaust temperature cannot exceed their limits or security reasons. In addition, a variety o sensors are also limited due to their measuring range, thereore, an unconstrained control system cannot exist. Not only limit management, but also good dynamic response is a critical element in the aero-engine control [4]. With the increasing complexity and improved perormance o aero-engines, commercial and military aircrat put orward higher requirements on the control o the propulsion system, where advanced control method is the main way to ace this challenge [5]. Model predictive control (MPC) is a kind o advanced closed-loop optimization strategy, which has the ability to process all kinds o constraints directly and conveniently [6-7], and be more powerul than traditional PID control method [8]. In general, predictive controller could adapt to a wide range o disturbances and achieve good control perormance, even in the case o a model mismatch [9]. For aero-engines, which are nonlinear complex systems, it is diicult to ensure that a predictive controller can achieve satisactory dynamic response in the ull light envelope. Speciically, taking a predictive controller based on a ixed linear engine model as an example, a series o simulations are conducted in the entire light envelope at step inputs. he results showed that the system is stable with no steady-state error in any sections and is able to meet the control requirements. While in some parts, there exist large overshoot, requent oscillations, and even instability during the transitions, which is beyond the scope o perormance requirements [10]. In this paper, a multilayer parameter scheduling scheme is proposed to design an adaptive model predictive controller or a commercial turboan engine. he rest o the paper is organized as ollows. Section II introduces the mathematical models o the turboan engine and the design o model predictive controllers at nominal points. he regional divisions about the control domain in the envelope are established in Section III. Section IV investigates the multilayer parameters scheduling scheme to construct an adaptive model predictive controller. Section V discusses the model predictive controller design or acceleration/deceleration transition state and analyzes the simulation results. he conclusions are summarized in Section VI. w w w. a j e r. o r g Page 170

2 II. MODEL PREDICIVE CONROLLER DESIGN A NOMINAL POINS For a certain type o high bypass commercial turboan engine, the literature [11] realizes the usage o a packaged component level nonlinear dynamic model in Matlab/Simulink platorm via dynamic link library technology, which was originally constructed and tested perectly in the Gasurb sotware. o design model predictive controllers at nominal points, linear engine models are obtained using the itting method at given light conditions and working states. Note that the inal adaptive model predictive controller based on multilayer parameters scheduling scheme is tested in the nonlinear component level engine model, although a series o linearized models are prepared or model predictive control designs. he purpose o an aero-engines control system is to provide required thrust by changing uel low according to throttle positions [1]. However, in practice, thrust cannot be sensed and thereore cannot be controlled directly. Generally, speeds or engine pressure (EPR) is used as the indicator o thrust. In this paper, the control objective is to track an speed setpoints while considering input and output constraints. hereore, discrete single-input state space based linear models o the engine can be expressed as: where x N N, c x ( k 1) A x ( k ) B u ( k ) y ( k ) C x ( k ) D u ( k ) u W, y [ N sm H P C ].he control variable is the deviations o uel low (W ) in kg/s rom the steady state, state variables are the deviations o an speed N and core speed N c in r/min. hree output variables are considered here, where an speed is used or tracking and the other two output variables (high pressure compressor outlet temperature in o R and high pressure compressor stall margin sm H PC in %) are regarded as limited outputs. he values o matrices A, B, C and D are dierent corresponding to dierent light conditions (e.g. light altitude H and Mach number Ma) and working states (expressed as a percentage o the max cruise speed or an speed N ). Model predictive control algorithm consists o three parts [9]: predictive model, receding horizon optimization and eedback emendation. Eq.(1) is utilized as the predictive model. he cost unction o the optimization section is deined as ollows: where e ( k i) r ( k i) y ( k i). r ( k i ) i n y n u 1 i1 i 0 outputs and inputs in the uture i time steps respectively. input constraints. Y m in, Y m ax J e ( k i ) e ( k i ) u ( k i ) u ( k i ) s. t. U m in u ( k i ) U m a x i 0,1.. n 1 Y m in y ( k i ) Y m a x i 1,... n is the reerence value. y ( k i) and u ( k i) are the predicted U m ax, U m in indicate the output constraints. n and n u y y u (1) (2) represent the maximum and minimum are control horizon and prediction horizon respectively. 0, is the control variable weight. As or eedback emendation, a simple method that correct the reerence values according to the errors between the actual N output and the predicted N output at every sampling time is used, which can be deined as: ( k 1) q ( N Nˆ ) (3) where q is the correction actor, which can be adjusted by trial-and-try. Conveniently, graphical user interace (GUI) design toolbox in MALAB/Simulink can be used to design model predictive controllers at nominal points. Key parameters mentioned above are included in the Graphical design interace. According to the inluences o each parameter on the system, appropriate values can be inally tuned based on simulation results at nominal points or these model predictive controllers. III. DIVISIONS OF HE CONROL DOMAIN AND HE SELECION OF NOMINAL POINS It is supposed that the control domain, part o the entire light envelope, considered in this paper is shown in Fig.1. Fig.1 Control domain w w w. a j e r. o r g Page 171

3 Although MPC has good robustness, simulation results show that one predictive controller alone cannot satisy the requirements o dynamic perormance or the turboan engine in the entire control domain, as shown in Fig.2, where the nominal point is H=11km, Ma=0.8, and power=100%. Fig. 2 N response at non-nominal points Fig. 2(a) shows that the response speed is too slow when Ma is ar rom its nominal point; Fig. 2(b) represents that the overshoot is too large when H is o its nominal point; and bad dynamic response appears when working state is o its nominal point, as shown in Fig. 2(c). Ater all, model predictive controllers are designed based on small deviation linear dynamic models, which are only applicable to small areas around nominal points or better dynamic response. In order to obtain better control eects, the control domain should be divided into subsections and a reasonable nominal point is to be picked out or each subsection. In this way, a series o model predictive controllers can be designed or subsections, ensuring the perormance requirements in the whole control domain. In this paper, the control domain is divided according to the relative variation o aero-engine inlet parameters [12]. For the given uel low supply and the ixed nozzle area, the an speed and the turbine expansion ratio, as well as other engine outputs are a unction o only the light altitude H and Mach number Ma. Furthermore, i the inlet o the turboan engine is determined, the total temperature 1 and total pressure P1 o inlet are a unction o H and Ma, as presented in Eqs.(4) and (5). hereore, it can be concluded that the small deviation linear state space models are closely related to parameters P1 and 1. When H 11km, there exists: When H>11km, there exists 1 ( H ) (1 0.2 M a ) H P (1 ) (1 0.2 M a ) (1 0.2 M a ) H ( ) P e (1 0.2 M a ) I the sensed parameters 1 and P1 change within a certain small range, it is assumed that a model predictive controller can be used to regulate this subsection. So the selection rules J or subsection divisions can be deined as: J P 1 P x 0 2 x 0 2 ( ) ( ) (6) P where P 1 0, 1 0 are the inlet total pressure and temperature at nominal points respectively, P 1 x, 1 x are the inlet total pressure and temperature at a given place in this control domain, and is the acceptable range rom nominal points. Simulation results show that when 0.2, good dynamic and static perormance can be achieved within the subsection by one controller that was designed based on nominal points. Here, is selected as 0.2 and nominal points should be chosen so that their subsections can cover the entire control domain. hrough continuous attempts, three nominal points in the control domain are inally selected as (H=11km, Ma=0.8), (H=11.7km, Ma=0.65) and (H=9.5km, Ma=0.75), as pointed out by * in Fig.3. Dierent colors in Fig.3 represent dierent subsections. It can be seen that the predictive controller designed at these three nominal points can cover the entire control domain. (4) (5) w w w. a j e r. o r g Page 172

4 Fig. 3 Nominal points and subsections In addition, i the control domain is extended to the whole light envelope, the method or regional divisions and nominal point selections is the same, but a ew more nominal points must be chosen to cover the ull envelope, which increases the workload. In this paper, we just take a part o the whole envelope, known as control domain, or example. IV. MULILAYER PARAMEERS SCHEDULING SCHEME In this paper, an adaptive predictive controller is designed to realize the control o the turboan engine that work rom 80% to105% speed changes in the entire control domain (H, Ma) o Fig.1. ake three speed nominal points 85%, 93% and 100% or example, covering the 80%-105% working states. Considering the act that there are three light nominal points in the control domain in Fig.3, a total o nominal points need to be included under dierent working states and light conditions, as listed in able 1. able.1 Dierent Nominal Points (NP) NP Power Speed H Ma (r/min) (km) 1 85% % % % % % % % % A multilayer parameters scheduling scheme is proposed to design the adaptive predictive controller, as shown in Fig. 4. he Outermost layer Adaptive MPC controller Internal structure he third layer Working states N scheduling he second layer 85% 93% 100% he irst layer 1 H Ma 2 H Ma H Ma 8 9 Fig. 4 he principle diagram o the multilayer structure w w w. a j e r. o r g Page 173

5 In the irst layer, the 9 predictive controllers are designed based on 9 dierent working states and light conditions, where numbers 1 to 9 correspond to the 9 dierent nominal points in able 1. As mentioned in Section II, each MPC controller in this layer can only control the working states and light conditions around the nominal speeds and nominal light points. here are three MPC controllers in the second layer, each o which can achieve the management o the entire control domain around a certain nominal speed state. Every MPC controller in the second layer dispatches the three corresponding controllers in the irst layer according to the light altitude H and Mach number Ma, which has been discussed in Section III. he MPC controller in the third layer owns the ability to realize the objective that the turboan engine can operate randomly during 80%-105% working states in the entire control domain. he an speed N is used as the scheduling variable to regulate the MPC controllers in the second layer (detailed descriptions will be ollowed later). hereore, the MPC controller in the third layer can govern all the 9 controllers in the irst layer. In this multilayer ormat, the design o an adaptive model predictive controller is accomplished, being able to realize the scheduling process based on the working states being expressed as N, and the light conditions expressed as H and Ma at that point in time. he outermost layer is the external structure o the third layer, which has the purpose o making the adaptive predictive controller intuitive and clear. he inputs o the outermost layer is composed o an speed N, the driver's instruction (the percentage o the speed), the light attitude H, as well as the Mach number Ma, and the output is the main uel low W. Now we turn our attention to the principle o the third layer as it relates to how the an speed N is utilized as the scheduling parameter variable. A set o linear MPC controllers are obtained based on dierent speed nominal points, and the switching problem between two adjacent MPC controllers at speed nominal points need to be studied to ensure the smooth transitions. From able 1, it is obvious that working states (expressed as a percentage o the max cruise speed) correspond to a ixed physical speed at steady state. hereore, the an speed N can be chosen as the scheduling variable. For any working state between k and k+1, two nominal points, the output value o the adaptive predictive controller (uel low) is obtained by interpolation o the output values o the MPC controllers based on the k and k+1 nominal points. In other words, N is used to describe the current an speed, whereas N k and N (k+1) indicate the steady-state speed corresponding to the k and k+1 nominal points. Control variables W k and W (k+1) are the control values corresponding to the k and k+1 nominal points. Suppose that the inequalities N N N hold, then the inal output value k ( k 1) u o the adaptive c m d predictive controller can be deined as: N N k u W ( W W ) cm d k ( k 1 ) k N N ( k 1 ) k Next, simulations are studied to veriy the eectiveness o the proposed adaptive model predictive controller. he controller is connected with the packaged nonlinear component level engine model in the Matlab/Simulink platorm. he control objective here is to maintain the working states, regardless o the changes in the light conditions. In this example, the desired working state is 90% (N equals 00r/min), and the light conditions (H, Ma) changes requently with time, as shown in Fig. 5. In this situation, the changes o light conditions can also be regarded as disturbances applied to the system. he input and output dynamic responses are then displayed in Fig.5. (7) Fig. 5 Input and output response with light conditions changes w w w. a j e r. o r g Page 174

6 In Fig.5, it is observed that when light conditions change, the regulated output N can be restored to the original setpoint in a very short time with minor deviations, which indicates that the MPC controller can deal with light disturbances in an eective manner during the steady state. Similarly, or other desired N constant values, it can be validated that the control eects under small disturbances are consistent with good disturbance rejection. V. DESIGN FOR ACCELERAION AND DECELERAION RANSIION SAE he controller design o transition state accounts or a large part o aero-engine control system. During the transition state, a variety o limits should be considered to ensure the sae operation o aero-engines, such as speeds limits, temperature limits, compressor stall margin limits and both acceleration and deceleration limits. In this paper, only the acceleration and deceleration design or transition state is considered, which is based on schedule scheme [1]. his method involves the acceleration and deceleration schedule. In other words, the idea o an acceleration schedule is to limit the maximum change rate o uel low WFM. On the contrary, the deceleration schedule control is to limit the minimum change rate o uel low WFM. Unlike traditional transition controls (e.g. PID controller) where anti-windup (IWU) must be taken into account, MPC is well-known as a good way to deal with input constraints directly within the process o optimizations. However, such constraints are not included in the conventional control algorithms, which cannot produce a control input that breaks away rom constraints to overcome the IWU phenomenon. hereore, or the adaptive MPC controller, there is no need to consider the IWU problem during the transition state. Suppose the maximum limit o the W change rate is 0.35kg/s or the acceleration schedule and the minimum limit is -0.25kg/s or deceleration schedule based on the equilibrium values at steady state. In addition, output limits, 600K and smhpc 20% are also taken into account during the transition state. hese constraints are then added to the adaptive MPC controller designed in Section IV. he acceleration and deceleration simulations o transition state are then carried out to realize the working states transers or a large range rom 80% to 105% (N, 4200r/min-5200r/min), as shown in Fig.6. Fig. 6 Response during transition state As seen in Fig.6, acceleration and deceleration schedules play an important role in the process o transition state changes, where the maximum increments are limited to 0.35kg/s and the minimum increments are limited to -0.25kg/s compared with equilibrium values at steady state. It is shown that N can track the setpoints with good dynamic perormance. In addition, the steady-state adaptive MPC controller operates in the irst 0s-5s, then the acceleration schedule works during 5s-7s, ollowed by the steady-state controller working during 7s-20s, and then the deceleration schedule takes over to work in 20s-21s, with the steady-state controller working again at the end. It is also observed that the change values o limited outputs, and smhpc, are within their limits during the transition state. he simulation results show that the designed adaptive MPC controller meets the perormance requirements o both the steady state and the transition state processes. hereore, it is easible or the adaptive MPC controller to be applied into turboan engines. w w w. a j e r. o r g Page 175

7 VI. CONCLUSIONS An adaptive model predictive controller based on multilayer scheduling scheme was designed and tested with nonlinear component level turboan engine model, which can drive the engine to operate randomly under the working states rom 80% to 105% in the entire control domain. Acceleration and deceleration schedules are realized by adding input constraints to the control system. In addition, the output constraints can also be considered in the adaptive MPC controller. Although the control domain considered in this paper is just a section o the ull light envelope, the method to divide the entire envelope is the same, and so it is easy to extend the controller to realize the control in the whole light envelope. For the similar reason, wider working states can also be achieved using the multilayer parameters scheduling scheme. hereore, the method proposed in this paper gives instructions or the controller design involving the whole working states and the entire light envelope. REFERENCES [1] L. C.Jaw, J. D.Mattingly, Aircrat Engine Controls Design, System Analysis and Health Monitoring. Reston: AIAA, 2009: [2] J. Csank, R. D. May, J. S. Litt, and. H. Guo: Control design or a generic commercial aircrat engine, AIAA [3] H. Richter: Advanced control o turboan engines. Springer New York, 2012, pp [4] hompson, J. Hacker, C. Cao. Adaptive engine control in the presence o output limits, AIAA [5] G. Nathan. Intelligent engine systems Adaptive Control. NASA/CR [6] H.X. Qiao, S. Q. Fan, L. Yang. Constrained predictive control based on state space model o aero-engine. Journal o Propulsion technology, 26(6), 2005, [7] X. Du, Y.Q. Guo, X.L. Chen. Multivariable constrained predictive control and its application to a commercial turboan engine. Advanced Materials Research, Vol.909, 2014, [8] X. Du, Y.Q. Guo, X.L. Chen. MPC based active ault tolerant control o a commercial turboan engine. Journal o Propulsion echnology, 36(8), 2015, [9] J. X. Qian, J. Zhao, Z. H. Xu. Predictive Control. Beijing: Chemical Industry Press, [10] H. X. Qiao, S. Q. Fan. Predictive control o aero-engine with model mismatching. Journal o Propulsion technology, 27 (5), 2006, 5-8. [11] S. G. Zhang, Y.Q. Guo, J. Lu. Component level model o Aero-engine based on Gasurb / MALAB and its Implementation. Journal o Aerospace Power, 35(2), 2014, [12] H.Q Wang, Y.Q. Guo. Design o Full Flight Envelop Controller or Aero-Engine. Measurement and control technology, 28(5), 2009, w w w. a j e r. o r g Page 176