Parameter Estimation of Transfer Function of Pilot Behavior Model from Measured Data

Transcription

1 Parameter Estimation of Transfer Function of Pilot Behavior Model from Measured Data JAN BORIL, RUDOLF JALOVECKY Department of Aerospace Electrical Systems University of Defence Kounicova 65, Brno CZECH REPUBLIC Abstract: - This paper describes calculations and results of time constants of mathematical model of a pilot s behavior. Pilot was tested to a sudden altitude change whilst he controlled an aircraft. For calculations were used two different methods of measured data processing. Firstly the method using System Identification Toolbox from programming environment MATLAB was applied. The second method used the identification algorithm to identify parameters of a transfer function of dynamic system which has been created by authors few years ago. The analytical model of human behavior from the basic element of an automated regulation was created. Experimental measurements were made on the Cessna 152 cockpit simulator at the University of Hertfordshire, Hatfield. The tested pilots were pilot students with several tens of flight hours in real planes. The pilot s response to a sudden aircraft altitude change was measured. The achieved results will be analyzed at other stages of research activity in order to reach maximum plausibility of human behavior model. Key-Words: - MATLAB, System Identification Toolbox, Pilot Behavior Model, Pilot Model, Data Identification, X-Plane Software, Flight Simulator, Pilot Response, Identification Algorithm 1 Introduction The complexity of human behavior is not possible to describe by simple mathematical models of behavior. The variable human characteristics do not allow creating a one universal human behavior model which would fully describes the dynamic characteristics in the different activities. This makes it creating the mathematical model of a human (pilot) behavior when flying an aircraft more complicated. To determine the optimal mathematical model of a pilot s behavior when flying an aircraft is, from an automated control point of view, a very difficult and complex task. The reason is that the parameters and time constants of the pilot (as a human) are time variables and are influenced by many unpredictable factors such as the pilot s experience, tiredness, stress, surrounding noise etc. To determine a human s behavior, within a control loop, in a given flight mode is possible only after obtaining a correct pilot response in a given mode in the correct time. Authors of this paper longer time analyze a human behavior in order to compile the most plausible human behavior model. The basic information about human behavior represents time characteristics of transfer functions that are based on knowledge of automated regulation elements. 2 Mathematical Model of Pilot Behavior The human model is based on the dynamics of its behavior. One possible model of human behavior dynamics is shown in the block diagram in Fig 1. There are 3 mutually interfering blocks. The input sensors are the pilot s sensory organs, from where the detected information goes into the central nervous system. The average speed of emotion transmission is in the range of 5 to 125 ms-1. In an automated control system this transmission feature can be represented by a transport delay. Fig. 1. One of the possible pilot behavior models in the machine The response time mainly depends on the level of the pilot s internal stress, the actual pilot s condition and perhaps also on some other factors. After processing the received signal a command to hand or leg muscles is sent to adjust the elevator, aileron and rudder deflections. Figure 2 presents the key ISBN:

2 Human body model Pilot experience & skill Biomechanical model Atmospheric Disturbances Inceptor Aeroelastic Aircraft & Actuation System Pilot Control Action Neuro-muscular system Flight Control Systems Proprioceptive Thresholds & Dynamics Flying control system Fig. 2. Block diagram representing the pilot-vehicle system under manual control [9] components involved in the manual control mode of aircraft with objectives from the pilot s mind. For maintaining the requested flight parameters the pilot uses three different types of regulators [1, 2]: Predictive regulator, keeping the required flight mode based on the pilot s received visual and sensory perception of the flight. Feedback regulator, created by correct visual and sensory perception of the required flight mode. Precognitive regulator, recalling the learnt maneuver from memory, i.e. a clear sequence of elevator, aileron and rudder deflections making the required aircraft movement. Creating mathematical models of human behavior is based on long-term experiments and also from the information obtained in the literature. For modeling human behavior a linear model is often being used (which is not quite correct for example regarding output value limitations) with a transfer delay defined by a transfer function as follows [1, 2, 3, 4]: ( s) ( T3s + 1) ( T s + 1)( T s + 1) Y( s) τ s F( s) = = K e (1), X where: Objective High level processing Control theoretic model 1 2 Non-Visual Thresholds & Dynamics Visual Thresholds & Dynamics Human sensory model K T 1 T 2 T 3 τ Out-thewindow cues Primary Flight Display Scenario Aircraft Sensor Suite Pilot Gain representing the pilot s ability to respond to an error in the magnitude of a controlled variable. Lag Time Constant describes the ease with which the pilot generates the required input. Neuromuscular Lag Time Constant represents the time constant associated with contraction of the muscles through which the control input is applied by the pilot. Lead Time Constant reflecting the pilot s ability to predict a control input. Represents a pure time delay describing the period between the decision to change a control input and the change starting to occur. 3 Experimental Workplace and the Measuring Methods For subsequent analysis of human behavior whilst flying an aircraft is necessary to obtain the data of real response pilot and aircraft. For the Identification Algorithm purpose and for the System ISBN:

3 Fig. 3. Cessna 152 Cockpit Simulator, University of Hertfordshire, Hatfield Identification Toolbox purpose the measurements of input and output information were providing. Measurements were carried out on the flight simulator Cessna 152 Cockpit Simulator at threemonth research fellowship within ERASMUS program at the University of Hertfordshire, Hatfield. The university has a laboratory with flight simulators used for pilot training as well as for research purposes. The lab is under the auspices of a specialist in automated aircraft control Dr. Rashid Ali. The flight simulator Cessna 152 consists of a Cessna 152 aircraft fuselage with two seats for crew. This fuselage is anchored to a static base fixed to the floor. The flight simulation was done by three projectors, projecting images onto a parabolic wall. Based on the research needs software X-Plane 9 from Laminar Research Company was used. The main advantage of this software is its precise and detailed simulation of flight physics for all individual aircrafts. The simulator as a whole is controlled by a PC - also called an Instructor Station. An instructor sitting at this station can change any flight parameters during the flight simulation. All control elements, flight instruments and control stick inside the cockpit are connected to the instructor station. The pilot can fully focus on flying the plane while the instructor can see all the real time parameters on his monitor. The tested pilots were around the age of 23 and all holding Commercial Pilot Licenses (CPL). They all had several hours of flight experience on the Cessna 152 and Cessna 172 aircrafts. After an initial induction and simulator training the pilot was explained the test procedure. The pilot s task was to take the plane into a straight horizontal flight. The instructor suddenly changed the aircraft altitude by 100 feet. The pilot s task was to put the aircraft back to the original altitude as fast as possible and stay there. He could do this by using only the aircraft elevator controls. Input and output data was recorded and stored in the instructor station. 4 The Obtained Parameters of Transfer Functions The tested subjects were four pilots. Each of them had to deal with the series of sudden altitude changes. From the beginning the pilots reacted to sudden step changes of altitude by rapid control yoke movement in order to get the aircraft back to the previous flight level as soon as possible. Thereby the course occurred to a greater number of overshoots with larger amplitude. With series of test on the flight simulator the pilots obtained experiences and make return to the previous flight level more efficient and thus the time required for maneuver was shorter. For demonstration purposes of two methods of obtaining the transfer functions from measured data the only one attempt was selected from the amount of data. It was the last pilot attempt. Value of altitude was suddenly decreased by 100 feet. For the defined conditions and limitations, this maneuver seems to be best performed. For the parameters calculation of the transfer function of human behavior the programming environment MATLAB was used and especially the System Identification Toolbox which constructs mathematical models of dynamic systems from measured input-output data. Input data were the measured value of altitude change according to the control yoke deflection. Output data were measured values of control yoke deflection in longitudinal direction. The value is dimensionless with maximum in value 1 and minimum in value -1. Another way of calculating the parameters of the ISBN:

4 Fig. 4. Identification of Transfer Function Coefficients (Identification Algorithm) Fig. 5. Measured and simulated model input and output (Identification Toolbox ) transfer function was the use of previously created algorithm. These algorithm authors of this paper have used in the past for purposes of parameter identification of the pilot behavior model. In this case, the authors were focused on the verification of algorithm plausibility with subsequent implementation of the measured data into the algorithm. Input and output data for identification algorithm were entirely the same as for System Identification Toolbox. Figure 4 shows the input, output waveforms and the obtained curve, which was calculated after 1201 iterations by the identification algorithm. The algorithm is able to a certain extent, based on the input and output data, calculates the transfer function of a dynamic system. For this purpose the algorithm uses function fminsearch from MATLAB library. The curve which showing the altitude change function of time is depicted by full black line. The values and scale of graph is 100 times smaller due to computing operations and for illustrative purpose. In two seconds, the instructor suddenly decreased altitude by 100 feet and the pilot responded as quickly as possible and tried to climb back to previous flight level precisely. It is possible to notice that the pilot acted similarly like a PID controller with one overshoot. In the phase opposition of altitude is a curve illustrating the control yoke movement in the longitudinal direction and it is depicted by dash-dot line. After few milliseconds the pilot will realize that sudden altitude change was performed. Then the pilot pulled the control yoke to the maximum and the aircraft ascends back to the previous flight level. The pilot will stop the maneuver quite late and due to aircraft inertia the one overshoot will become. Afterwards the pilot is able to stabilize the aircraft to a previous flight level. Immediately without any calculation method can be determine the time constant of pilot - time delay. Time delay is time between step change of altitude and beginning of control yoke movement to the maximum. All the conducted tests show fairly higher time delays than assumed in theory [1]. That is caused by a wide range of factors affecting both the method of testing and assessment. There are two main reasons for these higher delays. Firstly, the tested pilots only sensed the altitude change visually by watching the altimeter in the cockpit and by expecting a sudden change. Secondly, the pilots were not informed when the altitude would suddenly drop or increase by the 100ft and thus taking longer to analyze the situation and react appropriately. In other cases e. g. for oscillation damping by pilot this high value of time delay ISBN:

5 would have been unacceptable [5]. Critical parameter of the human pilot time delay destabilizing closed loop automatic flight control system is 0.9 sec [8]. In particular case pilot losing the control over the aircraft and may generate so called pilot induced oscillation (PIO) which can be dangerous for flight safety. In worst case the PIO can lead to damage of the airframe. The results respectively the calculated curve is shown in Fig. 4 by dashed line. It is obvious that the algorithm is able to keep the trend of curve until the pilot sharply pulls and holds the control yoke in maximum. At this moment the limitation of rudder deflection occurs, which means the creation of nonlinearities. Computational algorithm is not able to deal with nonlinearities and then the program (algorithm) is unable to return and copy the trend of curve. The algorithm ensures at least the partial copying the trend of curve of control yoke movement. The obtained parameters of transfer function are given in Tab. 1 Figure 5, inter alia shows the calculated curve which was obtained from the input and output data and for parameter estimation the System Identification Toolbox was used. The trend of the calculated curve is almost identical with the identification algorithm method. But even here the nonlinearity in the area of sudden movement changes when the control yoke achieved the maximum value is evident. Also the System Identification Toolbox is not able to handle nonlinearities properly. The obtained parameters of transfer function using System Identification Toolbox are given in second row in Tab. 1 Table 1. Parameters of the identified transfer functions Figure K τ T 3 T 1 T 2 T 1 +T Conclusion Using the identification algorithm, whether the algorithm created by authors or the System Identification Toolbox, for determine the parameters of the proposed pilot model behavior whilst flying an aircraft shows what possibilities are provided by modern computer technology and especially programming environment MATLAB. Relatively decent consensus of theoretic and calculated time constants indicates that an even simulation is possible to approach to the real pilot behavior model. The authors are preparing to set up the experimental laboratory with an aircraft simulator in which testing and data assessment would continue to be improved. The algorithm for experimental identification will be refined so that the algorithm clearly separates the important pilot time constants needed for determining its limits. Acknowledgments: The paper was written within development organization project UO - K206 titled "Complex Electronic System for UAS" and supported by the association UDeMAG (University of Defence MATLAB Group). References: [1] Havlikova, M.: Diagnostic of Systems with a Human Operator, Doctoral Thesis (in Czech), Brno University of Technology (2008) [2] Jalovecky, R., Janu, P.: Human Pilot s Features During Aircraft Flight Control from Automatic Regulation Viewpoint. In: 4th International Symposium on Measurement, Analysis and Modeling of Human Functions, pp Czech Republic: Czech Technical University in Prague, Prague (2010) [3] Jalovecky, R.: Man in the Aircraft s Flight Control System, In: Advance in Military Technology Journal of Science, Vol.4, No.1, pp (2009) [4] Cameron, N., Thomson, D.G., Murray-Smith, D. J.: Pilot Modelling and Inverse Simulation for Initial Handling Qualities Assessment, In: The Aeronautical Journal, Vol. 107, No. 1744, pp (2003) [5] Boril, J., Jalovecky, R.: Simulation of Mechatronic System Pilot - Aircraft - Oscillation Damper. In: ICMT 11 - International Conference on Military Technologies, pp University of Defence, Brno (2011) [6] Boril, J., Jalovecky, R.: Response of the Mechatronic System, Pilot - Aircraft on Incurred Step Disturbance. In: 53rd International Symposium ELMAR-2011, pp ITG, Zagreb (2011) [7] McRuer, D.T., Krendel, E.S.: Mathematical Models of Human Pilot Behavior, AGARD- AG-188, (1974) [8] Szabolcsi, R.: Pilot-in-the-Loop Problem and its Solution, Review of the Air Force Academy, No1, 2009, pp , Brasov, Romania [9] Lone M. M., Cooke A. K.: Development of a pilot model suitable for the simulation of large aircraft, 27th International Congress of Aeronautical Sciences 2010, September 2010, Paper ICAS , Nice, France ISBN: