The Computing DBT Design, Build, Test

Transcription

1 The Computing DBT Design, Build, Test Lab Organizer Prof David Murray dwm/courses/1p5 Hilary / 33

2 Lecture 4: The end of the DBT What is the 2nd part of the DBT about Why is landing different from launching Controller and Vehicle Simulator: more detail 2 / 33

3 What is the 2nd part of the DBT about? 3 / 33

4 The 2nd part of the DBT The second part of the Computing Design Build Test is more open-ended, and you will have to make your own design decisions and then implement them. You will be concerned with controlling the thrust from a vehicle s rocket motor, so that it touches down smoothly on some planet, or can hover above it... 4 / 33

5 The 2nd part of the DBT You will design and build two software components A controller which repeatedly inputs the vehicle s height, velocity and mass and outputs a sensible thrust to be generated by the rocket motor at that moment; and A simulator of the vehicle dynamics, which inputs that thrust, along with current height, velocity and mass of the vehicle, and works out how the vehicle state changes over the next short time interval. 5 / 33

6 What is the difference between the launcher and lander? 6 / 33

7 The launcher again...? The problem shares much with the rocket launcher problem. There your top level script used Euler s method like this: % Initialize everything first, then for t=0 : dt : tend Rocket.a = getacceleration(t, Rocket,...) Rocket.h = Rocket.h + Rocket.v * dt; Rocket.v = Rocket.v + Rocket.a * dt; % store telemetry etc end You assumed that the thrust varied v simply with time so, using t and Rocket you could find the current mass and thrust, work out the drag, and work out and return the acceleration. 7 / 33

8 But to slow to a hover before landing the thrust must vary over time in a more complicated way. If everything was known ahead of time, you could write a differential equation and solve it in advance. BUT! there are always uncertainties due to unmodelled and unpredictable disturbances eg, a sudden down draught in the atmosphere example. Conclusion: You need to be able to recompute the required thrust from moment to moment. This is where automatic control comes in 8 / 33

9 Control Desired Outputs Error Controller Thrust Demand Rocket Vehicle (Simulator) Actual Outputs position velocity acceleration fuel The controller is told the desired outputs from the system. It examines the current outputs, and adjusts the inputs into the plant to achieve them. The outputs from the plant are measured using sensors altimeters, radars, star fixes, etc. 9 / 33

10 Control Desired Outputs Error Controller Thrust Demand Rocket Vehicle (Simulator) Actual Outputs position velocity acceleration fuel In a real system, the controller is likely to be a piece of software running on a computer indeed microcontrollers are microcomputers purpose-built for the task. but the controlled plant (the rocket vehicle) will be the physical mechanism itself. Here you have to simulate the plant too. 10 / 33

11 Controller and Vehicle Simulator 1. Data Structures 11 / 33

12 Getting started You have learnt about structures in Matlab. Structures helps keep the number of parameters passed to functions to a minimum... myfunc(rmass,rv,rh,rfuel,rthis,rthat,rtheother); % is replaced by... myfunc(r); They also help us think about the important data entities or objects with which one must interact in software. Here three or four stand out, and it seems good practice to initialize them at the top of your top-level script or function. 12 / 33

13 Three or four structures... 1 The Vehicle structure 2 The Simulator structure 3 The Controller structure / 33

14 Vehicle Structure The Vehicle structure contains some fixed attributes, but others that change over time. For example, % Initialize Vehicle structure Vehicle.fixedmass = 500; % kg Vehicle.fuelrateperN = 0.001; % kg/s/n Vehicle.drag_k = 0.33; % (Not Cd)... etc... % These are initial values for those that change Vehicle.fuelmass = 1500; % kg Vehicle.a = 0; % m/s/s Vehicle.v = -300; % m/s Vehicle.h = 3000; % m Vehicle.thrust = 0; % N... etc... In a real system, the fixed ones might be found by tests during manufacture, and the ones that change would be returned by sensors. 14 / 33

15 Simulator Structure This structure holds quantities more related to the simulation and (perhaps) the simulation environment. For example... % Initialize Simulator structure Simulator.t = 0.0; Simulator.dt = 0.1; Simulator.g = 9.81; % m/sˆ2 You could shove these into the Vehicle structure but now imagine that the Vehicle is replaced by the real mechanism. Quantity dt has no meaning for the real vehicle, so you might argue that it doesn t belong in the Vehicle structure. 15 / 33

16 Simulator Structure Again you might argue you should have another structure Planet to hold g and, say, information about the atmosphere, and so on. You could define corresponding information in structures called Earth and Mars, then have statements like Planet = Mars; to run the simulator for martian conditions rather than earth conditions. Perhaps a bit too fancy for now... but up to you! 16 / 33

17 The Controller Structure The controller is sure to require some parameters in its code. Later you will see that one controller suggested has just two. Perhaps we will need different control models? Anyway, for the simple one % Initialize Controller structure Controller.vdesired = 0; % m/s downwards Controller.gain = 1; % Er, I m guessing! 17 / 33

18 Controller and Vehicle Simulator 2. The Simulation Loop 18 / 33

19 The Simulation Loop Having initialized the various structures, you now wish to start a loop that involves advancing time. Something like for t = 0 : dt : tend Do interesting stuff end But you do not know how long the landing will take! Instead, run the loop for as long as it takes... %% Keep simulating while above the ground while (Vehicle.h > 0) Do interesting stuff end 19 / 33

20 The Simulation Loop /ctd The body of the loop should follow the feedback loop. Desired Outputs Error Controller Thrust Demand Rocket Vehicle (Simulator) Actual Outputs position velocity acceleration fuel while (Vehicle.h > 0) % ask the controller what would be a good thrust... thrust=getthrustfromcontroller(vehicle,controller,simulator); % imagine that time dt has passed with that thrust Simulator.t = Simulator.t + Simulator.dt; % Update the Vehicle s state using the suggested thrust Vehicle = updatevehicle(thrust,vehicle,simulator); end 20 / 33

21 Something else for the loop: telemetry Telemetry.t = [Simulator.t]; Telemetry.h = [Vehicle.h]; Telemetry.v = [Vehicle.v]; Telemetry.thrust = [Vehicle.thrust];... etc... while (Vehicle.h > 0) thrust = getthrustfromcontroller(vehicle,cont,sim); Simulator.t = Simulator.t + Simulator.tstep; Vehicle = updatevehicle(thrust,vehicle,simulator); % Grow telemetry vectors... Telemetry.t = [Telemetry.t, Simulator.t]; Telemetry.h = [Telemetry.h, Vehicle.h];...etc... end % Finally, plot the telemetry PlotTelemetry(Telemetry); 21 / 33

22 Controller and Vehicle Simulator 3. Updating the Vehicle State 22 / 33

23 Updating the Vehicle state function newv = updatevehicle(thrust,v,sim) %% Step 1: work out actual V.thrust if ( V.fuelmass <= 0 ) %% empty :-( V.thrust = 0; else %% can do :-) V.thrust = thrust; end %% Step 2: work out acceleration V.a = getacceleration(v,sim); %% Step 3: update everything that needs updating V.h = V.h + V.v * Sim.dt;... etc and don t forget you have used fuel V.fuelmass =... %% Step 4: Return the new updated V structure newv = V; 23 / 33

24 getacceleration() I think we can do this now... function accel = getacceleration(v,sim) % find the total force... totalforce = % find the total mass... totalmass = % work out the acceleration... accel = 24 / 33

25 Some details Fuel mass consumption rate per unit thrust Recall we had this as a member of the Vehicle structure Vehicle.fuelrateperN = 0.001; % kg/s/n This C is the consumption of fuel mass per second per Newton. So in time t at thrust F (t), m fuel = C F (t) t. 25 / 33

26 Some details The drag force is F d = 1 2 AC dρv 2. Now the vehicle is initialized with mass m = 2000 kg, velocity v = 300 ms 1 at height h = 3000 m above the earth, where density ρ Air = 0.7kg m 3. If we assume this is a terminal velocity, mg = = 1 2 AC d AC d = 0.31N s 2 m 2 If the lander has a diameter of 2 m, A = π, so that C d 0.2. This C d seems a bit low eg a car is 0.3 to 0.4, and recall the Phoenix piccy but let s use this figure nonetheless. 26 / 33

27 Controller and Vehicle Simulator 4. The Controller 27 / 33

28 The Controller Suppose you want the vehicle to descend at some desired velocity v d and the velocity now is v. Why not set the thrust proportional to the error v d v... Big error Big corrective thrust Small error Small corrective thrust F(t) = k [ v d v(t) ] where k is a suitably chosen gain constant to be found by experiment. Watch out! When the velocity is correct the engine generates no thrust, so the vehicle is still accelerating under gravity! Simple remedy: offset the vehicle s instantaneous weight F(t) = k[v d v(t)] + m(t) g. 28 / 33

29 function getthrustfromcontroller() function thrust=getthrustfromcontroller(v,controller,sim) % What is the error error = Controller.vdesired - V.v; % find the demanded thrust thrust = Controller.gain*error + V.m*Sim.g; 29 / 33

30 Example of a BAD result Height (m) Vel (ms 1 ) Acc (ms 2 ) Mass (kg) Thrust (kn) Exercise VI Time to landing s Max acceleration g Time 30 / 33

31 Example of a GOODish result Height (m) Vel (ms 1 ) Acc (ms 2 ) Mass (kg) Thrust (kn) Exercise VI Time to landing s Max acceleration 8.19 g Time 31 / 33

32 The Final Curtain 32 / 33

33 DBT Assessment The launcher and the lander code should be in good shape. From 2pm through your last session (some in H, others in T) you will be assessed on these essentials the neatness of your filestore, how well designed your code is, how clearly the code is written, how well your code works, how clearly you can talk about your d, b & t. In addition, demonstrators will also look out for ingenuity, invention, and the unexpected. 33 / 33

34 Remember this? Aims... To begin to equip you with computing competencies... that will be used throughout your four years at Oxford for project work, and so on that will be useful as an aide to learning when bashing out work for tutorials that are central to the professional engineer s working life nomatter which speciality you eventually pursue. The demonstrators and I hope the aims have been met, at least in part that the labs have been enjoyable that you keep learning see item 1 above! 34 / 33