Tool for Turbine Engine Closed-Loop Transient Analysis (TTECTrA) Users' Guide

To link the TTECTrA MATLAB code with the full Simulink engine model, the user must: 1. Set the MATLAB workspace up for simulation of their model (with a given command or set of commands) in the “Model-specific workspace setup” section of simFromTTECTrA.m .

2. Write the required Simulink outputs to TTECTrA by modifying the “Model execution setup” section of simFromTTECTrA.m .

The following sections contain instructions for making these modifications, using an example application of TTECTrA with a piecewise-linear engine model.

2.3.4.1 Model-Specific Workspace Setup The model-specific workspace setup section of the simFromTTECTrA.m file should contain all the code necessary to setup the MATLAB workspace for simulation; as such, this section of the code requires the most user modification for TTECTrA to run successfully.

The user-provided code should perform the following functions: 1. Unpack the flight condition from the . in field of inputs ( inputs.in ) (shown in Table 3). The flight condition is defined by three scalar values: altitude ( alt ), Mach number ( MN ), and deviation of ambient temperature from standard-day temperature ( dTamb ).

TABLE 3.—FIELDS OF THE inputs STRUCTURE VARIABLE ARGUMENT TO simFromTTECTrA.m Field Field Name Description in t_vec Time (vector) Alt Altitude (scalar) MN Mach number (scalar) dTamb Temperature deviation from standard day condition (scalar) simTime Length time for simulation to run simFileName File name of user’s engine model loop Controller switch (1=control variable, 2=solver for thrust, 3=open loop) FT_dmd Thrust demand (vector or scalar (if constant thrust)); required only for in.loop = 1 or in.loop = 2 wf_vec Fuel flow demand (vector or scalar (if constant fuel flow)); required only for in.loop = 3 Fdbk_flag Flag for feedback filter (= 1) SPcalc wf_rng Fuel flow range for engine model ([wfmin wfmax]) idle Idle thrust takeoff max takeoff thrust bkpt breakpoints controller FdbkFilterBw Bandwidth for feedback filter if >0, else no filter used PreFilterBW Bandwidth for prefilter (filters the thrust command or setpoint) actuator wf_bw Bandwidth for first-order filter modeling fuel actuator dynamics SMLimit Accel Desired minimum surge margin during an acceleration Decel Desired minimum surge margin during a deceleration gains Kp Proportional controller gain (vector, scheduled by control variable) Ki Integral controller gain (vector, scheduled by control variable) Fdbk Control variable breakpoints (vector, for gain scheduling) SP FT_bkpt Thrust breakpoints (vector) SP Control variable setpoints (vector, scheduled by thrust) Limiter NcR25_sched Corrected core speed at station 25 (vector, for acceleration schedule) Ncdot_sched Core acceleration limit (vector, scheduled by corrected core speed) LPC_Limiter Wf/Ps3 limit (scalar) NASA/TM—2014-216663 6 If, for example, the workspace is setup using a function that requires a structure containing these environmental variables, the following code may be used to unpack those values: % setup vectors defining altitude, Mach number, dTamb (and time) in.t_vec = inputs.in.t_vec; in.alt = inputs.in.alt; in.MN = inputs.in.MN; in.dTamb = inputs.in.dTamb; (Additional formatting may be necessary if, for instance, these conditions should be provided to the setup function as vectors instead of scalars.)

2. Assign the default simulation name to the inputs.in.simFileName variable to ensure that the simulation executes: if ~isfield(inputs,'in') || ~isfield(inputs.in,'simFileName') ...

|| isempty(inputs.in.simFileName) inputs.in.simFileName = ’ filename.ext '; % modify this end 3. Add any additional MATLAB code required to setup the workspace and trim the model to the initial conditions. This code may be included directly in the file, or may be contained in external function created to execute any of the following steps: a. Adding folders containing functions or data files needed during the simulation to the current MATLAB path b. Loading data, or creating variables, needed by the engine model (e.g. compressor maps, lookup table data, sampling time) c. Trimming the model to the initial fuel flow or thrust demand in order to define the initial condition of the simulation For a model that places all data needed for a simulation into a single workspace variable and uses a lookup table for trimming the model, this can be done by the following code: % trim model to initial thrust demand, if closed-loop simulation if isfield(inputs.in,'FT_dmd'); wf_0 = trim_model(inputs.in.FT_dmd(1),9); else wf_0 = inputs.in.wf_vec(1); end % add paths, find initial conditions, create MWS MWS=setup_workspace(in.t_vec,wf_0); Here, trim_model performs the table lookup for the initial fuel flow and setup_workspace performs the remaining setup tasks from the above list. (A more complex model may use a steady-state solver in place of a lookup table to trim the model.)

NASA/TM—2014-216663 7 4. Assign the model sampling time, initial fuel flow, and initial core speed to the in field of the DWS structured variable, along with the initial conditions for pressure and temperature at station 2: DWS.in.Ts_cont = MWS.Ts; % model sampling time DWS.in.Wf_zro = MWS.IC.Wf_0; % initial fuel flow DWS.in.Nc_zro = MWS.IC.Nc_0; % initial core speed DWS.in.P2 = MWS.IC.P2_0; % initial P2, used for correction DWS.in.T2 = MWS.IC.T2_0; % initial T2, used for correction 2.3.4.2 Model Execution Setup The model execution setup section of the simFromTTECTrA.m file contains the MATLAB commands that run the model simulation and place the results in the outputs variable, which contains the fields listed in Table 4. The model is simulated using the function sim , called with the output argument y (to which simulation outputs are returned); each individual output can be accessed using the get command and specifying the variable name as it appears in the Simulink model.

For example, if pressure at station 2 is written to the workspace variable P2 , the field ‘P2’ of outputs would be assigned using: outputs.P2 = y.get('P2'); This may be done for each field of outputs listed in Table 4, which are required for use during the control design process.

Because get accepts a single argument (the variable name), additional manipulation of the output variables must be done external to retrieval of results. This may be exemplified by the assignment of the field for corrected thrust, ‘Fnet,’ in the case that uncorrected thrust is written to the workspace from the model. Assuming uncorrected thrust is written to the workspace variable Fnet by the model, the following code cannot be used: outputs.Fnet = y.get('Fnet./P2')/14.696; % this doesn’t work TABLE 4.—FIELDS OF THE OUTPUTS STRUCTURE VARIABLE RETURNED BY simFromTTECTrA.m Field Name Description t Time vector P2 Inlet pressure Fnet Corrected net thrust Wf_vec Fuel flow input T25 Temperature at station 25 Nc Core (or high spool) speed NcR25 Corrected core (or high spool) speed (used for acceleration schedule) Nc_dot Core acceleration (used for acceleration schedule) HPC_SM High pressure compressor surge margin (used for acceleration schedule) LPC_SM Low pressure compressor surge margin (used for Wf/Ps3 limiter) CV_fdbk Controlled variable output CV_dmd Control variable setpoint or demand FT_dmd Thrust setpoint or demand Wf_dmd Fuel flow input or demand Ps3 High pressure compressor static pressure (used for Wf/Ps3 limiter) NASA/TM—2014-216663 8 Instead, it is necessary to retrieve the arrays Fnet and P2 separately and do the calculation using: outputs.Fnet = y.get('Fnet')./(outputs.P2/14.696); The variables necessary for TTECTrA to function are indicated in the simFromTTECTrA.m file, and listed in Table 4: 10 output fields assigned from outputs of the engine model and four from outputs of the TTECTrA Simulink block . Additional outputs, such as Ps3 , may also be returned by retrieving the workspace variable and storing it in a corresponding field of outputs .

2.3.4.3 TTECTrA Simulink Block Setup Prior to running the simulation, the simFromTTECTrA.m file calls the function setup_TTECTrA_block.m to create the DWS variable (used by the TTECTrA Simulink block) from data in the inputs variable. The fields contained in DWS are shown in Table 5. The user should not have to modify this function, as it pertains to the controller designed using TTECTrA and not to a specific engine model.

TABLE 5.—THE DWS VARIABLE STRUCTURE Field Field Names Description in loop Control/Feedback indicator t_vec Time vector wf_vec Fuel flow input (default values unless loop=3) FT_dmd Thrust demand (default values unless loop=1 or loop=2) Fdbk_Flag Flag to enable/disable filter in feedback loop Ts_cont Simulation sample time (from user’s model) Wf_zro Initial fuel flow (from user’s model) Nc_zro Initial core speed (from user’s model) TTECTrA_controller Fdbk_num_Z Discrete feedback filter numerator Fdbk_den_Z Discrete feedback filter denominator PreFilterBW Bandwidth of prefilter on thrust command (Hz) Fdbk Feedback breakpoints (for controller gain lookup tables) P_gain Proportional gains (lookup table data) I_gain Integral gains (lookup table data) IWUP Integral Wind-up Protection gain TTECTrA_Wf bandwidth Bandwidth of first-order filter modeling fuel flow dynamics TTECTrA_Limiter Nc_sched Corrected core speed breakpoints (for acceleration schedule lookup table) Ncdot_sched Core acceleration limits (lookup table data) WfPs3Limit Deceleration protection limit on Wf/Ps3 Kp_accel Proportional gain for the acceleration limiter Ki_accel Integral gain for the acceleration limiter IWUP_accel Integral Wind-up Protection for the acceleration limiter accel_num Acceleration filter numerator decel_num Acceleration filter denominator TTECTrA_setpoints FT_bkpt Thrust feedback breakpoints (for setpoint lookup table) SP Controlled variable setpoints (lookup table data)

3.0 TTECTrA Operation

This section focuses on setting up and operating the Tool for Turbine Engine Closed-loop Transient Analysis, which can be done once it has been integrated with the user’s nonlinear engine model as described in Section 2.0. An example application based off of the Commercial Modular Aero- Propulsion System Simulation 40,000 (C-MAPSS40k) (Ref. 4) has been included with TTECTrA ( TTECTrA_example.mdl ). As the tool is discussed, it may be helpful to follow along using this example, which is a piecewise-linear version of the C-MAPSS40k engine model. In addition, a set of linear models developed at sea-level static conditions (0 ft and 0 Mach number) are included in the file LM_PWL.mat NASA/TM—2014-216663 9 for use in developing a controller; a pre-design controller can be found in the file TTECTrA_example_design.mat . Before running TTECTrA with this model, the make_file.m file (found in example_model/MEX/C_code) must be run to create the supporting code for the simulation.

A typical control design using TTECTrA involves three main steps: calculating the setpoint map, finding the controller gain schedules, and calculating the acceleration and deceleration limiters. After TTECTrA has been started, the steady-state mapping between corrected thrust and the control variable setpoint is calculated. This relationship is dependent on the engine model and requires that the user connects the appropriate feedback signal to the Fdbk input of the TTECTrA Simulink block in the Simulink model before performing the calculation. Next, the tool calculates the controller gains for each model composing the provided piecewise-linear model of the engine; these controller gains will be scheduled (based on control variable) for implementation in the setpoint controller. The final set of calculations addresses the need for implementing transient limiters to protect the engine from surge; acceleration and deceleration schedules can be found to ensure the user-specified minimum surge margins for the high- and low-pressure compressors (HPC and LPC) are not violated during periods of high engine demand. The TTECTrA controller only considers these two limiters, but it is possible to expand the limit logic to include additional constraints, such as core speed or Ps3 .

After the controller has been designed, two simulations will be run to test the functionality of the controller: a simulation with small changes in thrust demand (to test the setpoint controller) and a simulation with large changes in thrust demand (to test the limiters). The results for the control design and verification for the example model will be presented here along with discussion of each step of the design process using TTECTrA.

3.1 Getting Started Before operating TTECTrA, the user has the option to specify default values and preferences for the parameters listed in Table 6 in the file TTECTrA_Inputs.m . The values in this file are loaded by TTECTrA and recalled when the GUI is started, but may be changed during the design process if necessary.

TABLE 6.—USER DEFAULT INPUTS FROM TTECTrA_Inputs.m FILE, WHICH ARE LOADED INTO THE GUI SubField Field Name Description in alt Altitude (scalar) MN Mach number (scalar) dTamb Ambient temperature deviation from standard day (scalar) simTime Length of the simulation (scalar) simFileName File name (and extension) of the user’s Simulink engine model with the TTECTrA Simulink Block controller SPcalc wf_rng Fuel flow range ([min max]) idle Idle corrected thrust takeoff Takeoff corrected thrust bkpt If scalar, specifies the number of linearly spaced thrust values from idle to takeoff for calculating setpoints If vector, defines specific thrust breakpoints for calculating setpoints controller LMFileName Name of .mat file which contains linear model lmVar Name of variable containing the linear model data FdbkFilterBW Feedback filter bandwidth if > 0, otherwise no filter is used PreFilterBW Prefilter bandwidth CVoutput Element of the linear model output vector ( y ) corresponding to the controlled variable i Wfinput Element of the linear model input vector ( u ) corresponding to fuel flow i bandwidth Default bandwidth for tuning the controller phasemargin Default phase margin for tuning the controller actuator wf_bw Bandwidth of filter modeling fuel flow dynamics SMlimit Accel Minimum allowed surge margin during acceleration (for limiter design) Decel Minimum allowed surge margin during deceleration (for limiter design) NASA/TM—2014-216663 10 3.2 GUI Operation To begin the control design using TTECTrA, run the TTECTrA.m file. The dialog box shown in Figure 4 will appear, asking if a previously-saved controller should be loaded. To load a previously- designed controller (with the option of full or partial redesign of the loaded controller), select “yes” and proceed as follows when the Load Controller Data GUI of Figure 5 appears. Otherwise, select “no” to bring up the Setpoint Calculator GUI (Go to “Setpoint Calculator” section).

1. Press the “Choose File to Load” button to browse to and select the appropriate file. If the file is not on the current MATLAB path, the location of the file will be added to the path to ensure it can be loaded successfully. (The file TTECTrA_example_design.mat , located in the example_model folder, contains data for a controller designed for the example model.)

2. Verify that the correct file name appears in the text box, and then press the “Load Data” button to load the controller. MATLAB will issue a warning if any required fields are missing from the data; these fields may be assigned later by TTECTrA. An error will be encountered if there is a problem loading the appropriate data from the file (e.g. the file name is incorrect, or the file does not contain a variable named inputs ).

3. The Controller Redesign GUI in Figure 6 will appear, asking which parts of the controller the user would like to redesign, if any; check the appropriate boxes then click Continue. If the loaded controller is missing any of the three parts required by TTECTrA, the corresponding check boxes will be marked as shown in Figure 6, forcing the controller design to complete before simulation.

4. If no part of the controller is to be redesigned, the model will be simulated immediately after the controller data is loaded (Go to the “Verify and Execute Simulation” section). Otherwise, TTECTrA will proceed with the specified controller design steps.

Figure 4.—Dialog box asking if the user would like to load previously designed controller data.

Figure 5.—Load Controller Data GUI.

NASA/TM—2014-216663 11 Figure 6.—Redesign Controller GUI.

Figure 7.—The Setpoint Calculator GUI.

3.2.1 Setpoint Calculator The Setpoint Calculator GUI, shown in Figure 7, allows the user to define the flight condition and parameters for the simulations through which the relationship between corrected thrust and the control variable will be defined. The GUI is divided into four sections: Environmental Inputs, Simulation Inputs, Fuel Flow, and Corrected Thrust Inputs.

3.2.1.1 Calculate the Control Variable Setpoints 1. Enter the environmental condition (altitude, Mach number, and dTamb ) in the “Environmental Inputs” section. The values specified in the input file will be loaded by default, but may be changed in the GUI.

2. Select the setpoint control type to indicate how the relationship between the corrected thrust and the control variable should be derived. The choices are: NASA/TM—2014-216663 12 a. Thrust setpoint—constant corrected thrust is provided to the model; the setpoint relationship is defined by the steady-state control variable for each corrected thrust b. Constant Fuel Flow—constant fuel flow is provided to the engine; steady-state corrected thrust and control variable values at each fuel flow are used to define the relationship 3. Specify how long the simulation should run to allow the engine to establish a steady-state condition for the given input (“simulation time”).

4. Select the file containing the nonlinear engine model integrated with the TTECTrA Simulink block ; if the file is not on the MATLAB path, the location of the model will be added to the path definition.

5. Enter the information necessary to calculate the setpoints, as required by the control type selection made in Step 2.

If “thrust setpoint” control type is selected: The “Corrected Thrust Inputs” section is enabled and the following information should be entered: a. Idle thrust b. Maximum takeoff (or corrected) thrust c. The number of thrust breakpoints or a vector containing the specific thrust breakpoints for which control variable setpoints are to be calculated If “constant fuel flow” control type is selected: The “Fuel Flow” section is enabled and the following information should be entered: a. Minimum fuel flow b. Maximum fuel flow c. The number of breakpoints at which the relationship between control variable and corrected thrust is to be determined In both cases, the breakpoint vector will include the specified minimum and maximum values; if a vector of thrust breakpoints is specified, TTECTrA will check whether the minimum and maximum values are included and add them if they are not.

6. Press the “Calculate Setpoints” button to begin the process of determining the relationship between the corrected thrust and controlled variable. Once the lookup table has been defined, a plot of the setpoint relationship will appear, like that shown in Figure 8.

7. Close the figure window, or click the “Continue” button in the GUI, to accept the calculated setpoint relationship and continue with the control design process. Otherwise, the figure window should be left open and new inputs (such as different breakpoint locations) may be entered and the setpoints recalculated by pressing the “Recalculate Setpoints” button (previously the “Calculate Setpoints” button).

NASA/TM—2014-216663 13 Close figure to accept setpoints Leave figure open and use GUI to recalculate Control Variable 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Corrected Thrust x 10 Figure 8.—Example setpoint relationship between the corrected thrust and control variable using TTECTrA.

3.2.2 Control Design Setup The TTECTrA setpoint controller contains a simple proportional integral (PI) controller with integral wind-up protection, where the PI gains are scheduled as functions of the control variable. The PI gains are found using the MATLAB functions pidtune and pidtuneOptions , which are included in the Control System Toolbox . The pidtune function produces a controller which meets the specifications provided through input arguments to the function and options set using pidtuneOptions. In this case, the bandwidth and phase margin of the loop gain (product of the controller and engine model transfer functions) are specified when calling pidtune . Prior to designing the gains for the PI controller, TTECTrA allows the user to identify the file containing the linear models used to calculate the gains, and to provide the default tuning parameters, through the Control Design Setup GUI shown in Figure 9. This GUI has two sections: Linear Model Setup and Controller Tuning Setup.

3.2.2.1 Linear Model Setup To specify the linear model data for control design, the user should specify: 1. The file containing linear model data, which will be shown under the text “Model Selected.” If the correct file is not shown, select the “Load Linear Model” button to open a popup box and browse to and select the correct data (. mat ) file; if the file is not on the MATLAB path, its location will be added to the path definition. The required format of the linear models in this file is detailed in Appendix B.

2. The index, i , of the element in the linear model output vector corresponding to the control th variable (i.e. the control variable is the i element of the output vector y , y ).

i NASA/TM—2014-216663 14 Figure 9.—The TTECTrA Control Design Setup GUI.

3.2.2.2 Controller Tuning Setup To define the initial parameters for tuning the PI controller gains for each linear model, the user should specify: 1. The desired bandwidth of the loop gain (Hz), which is the product of the controller and plant transfer functions.

2. The desired phase margin (degrees).

3. The bandwidth (Hz) of the feedback filter in Figure 1, which filters the control variable error (difference between setpoint and feedback). The feedback filter will not be used if no value, or a negative value, is provided. If EPR is the control variable, then it is recommended to specify a feedback filter bandwidth of 10 Hz, especially if the engine model is zero-dimensional (does not contain volume dynamics).

4. The bandwidth (Hz) of the prefilter in Figure 1, which filters the thrust command and does not affect the stability of the system.

Once all the data is entered, the user can press the “Start” button to begin control design.

3.2.3 TTECTrA Controller AutoTune At each thrust point for which a linear model was provided, a PI controller is designed using the design parameters specified in the Controller Tuning Setup section of the Control Design Setup GUI. The window shown in Figure 10 will appear, displaying metrics for the controller designed for a specific linear model. Bode plots of the open loop plant (engine only) and the loop gain (engine and controller) are shown in the leftmost column; the top plot shows the magnitude response and the bottom plot shows the phase response. The top right plot shows the root loci of the plant and loop gain and the bottom right plot shows the step response of the closed-loop linear model with and without a prefilter on the input (labeled “Pre-Filter” and “LM,” respectively). This latter information is useful in determining whether modification of the prefilter bandwidth is warranted. The Controller AutoTune GUI, shown in Figure 11, also appears, indicating the thrust point of the model for which the controller is being designed and displaying the rise time and settling time of the step response of the linear model response with a prefilter, along with the bandwidth, phase margin, and proportional ( Kp ) and integral ( Ki ) gains of the PI NASA/TM—2014-216663 15 controller, in the Current Controller Design section. If the response is not satisfactory, the controller can be retuned (for a specific thrust point) by specifying a different bandwidth and/or phase margin in the Controller Design Inputs section of the GUI. Enter a bandwidth greater than the current bandwidth as the “Bandwidth” input to design a more aggressive controller. Enter a phase margin larger than the current phase margin as the “Phase Margin” input to reduce overshoot in the step response.

Bode Diagram Root Locus 150 20 ) -1 -10 Magnitude (dB) Imaginary Axis (seconds -20 -20 0 20 40 60 -1 Real Axis (seconds ) -50 1.5 Plant Loop Gain -45 -90 Phase (deg) 0.5 -135 Control Variable LM Pre-Filter -180 0 1 2 3 4 5 Time, s Frequency (rad/s) Figure 10.—The controller auto tune output showing the Bode plot, root locus, and linear model response of the current controller.

Figure 11.—The Controller AutoTune GUI.

NASA/TM—2014-216663 16 1. Press the “Execute” button to recompute the controller and update the performance metrics (Figure 10).

2. Once the performance is satisfactory (for a given thrust point), press the “Finish” button to design the controller for the next thrust breakpoint.

This process gets repeated for each thrust breakpoint, tuning the controller gains for each breakpoint in the linear model. Once the current breakpoint finishes, the Figure 10 plot will appear for the next point using the bandwidth and phase margin specified in the Controller Tuning Setup step.

3.2.4 Transient Limiter Design Transient limiters are designed to protect against engine surge during acceleration and deceleration.

The Transient Limiter Setup GUI opens after the setpoint controller has been designed, and contains sections for designing the acceleration and deceleration limiters, as shown in Figure 12.

3.2.4.1 Design the Acceleration Limiter 1. Enter the minimum HPC surge margin that is acceptable during an acceleration 2. Press the “Design Accel Limiter” button to begin calculation of the acceleration schedule 3. Once the acceleration schedule is designed, the “Show Accel Schedule” button will be enabled; pressing this button will display the acceleration schedule, as shown in Figure 13. (A default schedule will be displayed if this button is pressed prior to step 2.)

4. To redesign the schedule (for a different minimum surge margin), go back to step 1.

3.2.4.2 Design the Deceleration Limiter 1. Enter the minimum LPC surge margin that is acceptable during a deceleration.

2. Press the “Design Decel Limiter” button to begin calculation of the deceleration limiter.

3. Once the limiter has been designed, the value will be shown under the “Designed Wf/Ps3 Limiter” heading. If the desired minimum surge margin is too low, “NaN” will be shown under “Designed Wf/Ps3 Limiter.” The limiter will show 0, as in Figure 12, if the deceleration limiter has not yet been designed.

After designing both the acceleration and deceleration limiters, the “Continue” button will be enabled; pressing this button will continue running TTECTrA.

Figure 12.—Transient Limiter Setup GUI.

NASA/TM—2014-216663 17 Core acceleration limit 7000 8000 9000 10000 11000 12000 Corrected core speed Figure 13.—Example acceleration schedule.

x 10 actual command R net F 0 10 20 30 40 50 60 70 80 Time (sec) Control variable 0 10 20 30 40 50 60 70 80 Time (sec) Figure 14.—Thrust and control variable commands and outputs for small thrust transients to test the setpoint controller.

3.2.5 Verification/Simulation Before running verification simulations, TTECTrA will execute the function TTECTrA_integration.m to calculate the integral wind-up protection (IWP) gain for the setpoint controller. This is done automatically and requires no user interaction. The process involves running multiple closed-loop simulations of the model and adjusting the IWP gain to reduce the maximum overshoot below a specified threshold.

The full controller is tested by simulating the model with two different thrust transients, constructed from the control variable setpoints from Figure 7. The first is a series of four small, equally-spaced transients from minimum (idle) to maximum (takeoff) thrust, which tests the setpoint calculator and controller. Figure 14 shows a comparison of actual to demanded thrust and control variable for simulation of the example model with the included controller (top and bottom plots, respectively). The plots show that both the control variable and thrust are driven to the commanded values, even though the controller has no knowledge of the actual thrust produced by the engine.

NASA/TM—2014-216663 18 x 10 actual 4 command R net F 0 10 20 30 40 50 60 Time (sec) Control Variable 0 10 20 30 40 50 60 Time (sec) Figure 15.—Actual and commanded thrust and control variable for large thrust transient to test the transient limiters.

actual limit HPC surge margin (%) 0 10 20 30 40 50 60 time (sec) c,dot -1000 -2000 core acceleration, N 7000 8000 9000 10000 11000 12000 corrected core speed, N R c 25 Figure 16.—The HPC surge margin and acceleration schedule for the large thrust transient.

The second transient profile is a large throttle transient, from the largest of 14% of the takeoff thrust and the minimum thrust to the maximum thrust (specified in the control variable setup). The actual and commanded thrust and control variable for the example application are compared in Figure 15. The verification simulations can be changed by modifying the data assigned to the fields ttectra_in.in.t_vec and ttectra_in.in.FT_dmd under the Test Controller Design section of TTECTrA.m .

Although the controller is able to drive the engine to both the takeoff and idle thrust values, the presence of the limiters slows this response significantly, as can be seen in Figure 15. When the engine begins to accelerate at low core speeds, it is operating at or near the acceleration schedule limit and the controller restricts the fuel flow to the engine to protect from surge, increasing the time it takes for the engine to reach takeoff thrust from idle thrust. This is reinforced by the top plot of Figure 16, where the HPC surge margin can be seen to approach the limiting value on the same time range in which the responses in Figure 15 are slowed during acceleration. Similar results are seen in Figure 17 during deceleration, where the limit on NASA/TM—2014-216663 19 Wf/Ps3 is reached, but not exceeded, protecting the engine from violating the LPC surge margin. Like the HPC surge margin, the LPC surge margin remains above the minimum limit (the top plots in Figure 16 and Figure 17), approaching it only at the time in which the limit on Wf/Ps3 is reached. These results demonstrate that the limiters are working as intended for the controller designed for the example model.

3.2.6 Save Controller Data Once simulation of the closed-loop model has completed, the dialog box in Figure 18 will appear, asking the user if they would like to save the controller data.

To save the controller data, select “yes” to bring up the Save Data GUI in Figure 19 and enter the name of the .mat file in which to save the data, then press “Save Data.” A confirmation message will print to the MATLAB window stating that the file has been saved. Select “no” to skip saving the controller.

The tool will finish running once the controller has been saved (or the user has selected “no” and the window has closed).

actual 40 limit LPC surge margin (%) -10 0 10 20 30 40 50 60 time (sec) -3 x 10 s3 5 /P f W -5 -10 0 10 20 30 40 50 60 time (sec) Figure 17.—The LPC surge margin and Wf/Ps3 limit for the large thrust transient.

Figure 18.—Save controller popup box. Figure 19.—Save Controller Data GUI.

NASA/TM—2014-216663 20

Appendix A.—Nomenclature

A.1 Variables accel Acceleration alt Altitude* decel Deceleration dTamb Free-stream static temperature minus standard atmosphere temperature* DWS Dynamic systems analysis workspace (WS) variable Fdbk Feedback signal Fnet (Uncorrected) thrust* i Index for input or output vectors of linear models ( u and y ) inputs Variable containing inputs for configuring simulation of engine model with TTECTrA Kp Controller proportional gains Ki Controller integral gains MN Mach number Nc (Uncorrected) core speed* Ncdot Core speed acceleration* NcR25 Core speed corrected at station 25* Nf (Uncorrected) fan speed* outputs Variable containing outputs from simulation of engine model with TTECTrA P2 Pressure at station 2* Ps3 High-pressure compressor static pressure* u Input vector for linear models Wf/Ps3 Ratio of fuel flow to static high-pressure compressor static pressure y Output vector for linear models * Units of these variables are model-specific A.2 Acronyms EPR Engine Pressure Ratio GUI Graphical User Interface HPC High-Pressure Compressor IWP Integral Wind-up Protection LM Linear Model LPC Low-Pressure Compressor PI Proportional Integral controller TTECTrA Tool for Turbine Engine Closed-loop Transient Analysis NASA/TM—2014-216663 21

Appendix B.—Linear Model Input Requirements

The Tool for Turbine Engine Closed-loop Transient Analysis requires a “good” state space linear model at a minimum of two thrust points. Here, “good” implies that the linear model converges at a given thrust breakpoint so that the four state-space matrices can be found. The linear models should be saved to a structure array that has a length equal to the number of thrust breakpoints for which a steady-state model has been obtained. The structure should contain the following fields:  A – state matrix of state space model (A)  B – input matrix of state space model (B)  C – output matrix of state space model (C)  D – feed-through matrix of state space model (D)  IC – Initial conditions or trim values at the linearization point  Fn – thrust breakpoint at which the model has been constructed If an automated script is used to determine the linear models, it is possible that some models will not converge; in this case, the matrices and initial conditions (or trim values) can be entered as empty inputs.

The controller code will print a warning to the command window and continue with the linear model of the engine at the next thrust point when it encounters an “empty” model.

NASA/TM—2014-216663 23

Appendix C.—Controller Elements to be Verified Against Another Model

The TTECTrA Simulink Block has been designed and tested on an in-house engine model and includes the following control elements in addition to those designed by TTECTrA:  A gain correction on the setpoint controller based on P2 , primarily to decrease the gain of the controller at higher altitudes.

 IWP gain in the setpoint controller, calculated by running simulations of the closed-loop model to find the gain that reduces overshoot during acceleration and deceleration below a specified threshold  PI gains in the thrust setpoint controller, designed using linear models of the in-house model, and further adjusted to improve the model response  PI and IWP gains in the acceleration schedule, designed (using the in-house model) to depend on the ambient pressure (altitude) at which the model is being simulated Although necessary to obtain acceptable results from simulations of the in-house model, these modifications may not be required when the controller is implemented with other engine models. A piecewise-linear version of this in-house model has been developed and tested successfully with the tool, but it is necessary to test the controller block with other engine models (independent from the in-house model) to verify the necessity of these additional elements.

References

1. Jaw, L., and Mattingly, J.D., Aircraft Engine Controls: Design, Systems Analysis, and Health Monitoring , American Institute of Aeronautics and Astronautics, Inc., Virginia, 2009.

2. Mattingly, J.D., Heiser, W.H., and Pratt, D.T., Aircraft Engine Design , American Institute of nd Aeronautics, Inc., 2 Edition, Virginia 2002.

3. Csank, J., May, R.D., Litt, J.S., and Guo, T.-H., “Control Design for a Generic Commercial Aircraft th Engine,” AIAA-2010-6629, 46 AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Nashville, TN, July 25-28, 2010.

4. May, R.D., Csank, J., Lavelle, T.M., Litt, J.S., and Guo, T.-H., “A High-Fidelity Simulation of a th Generic Commercial Aircraft Engine and Controller,” 46 AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Nashville, TN, July 25-28, 2010.

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