15 thoughts on “Blue Origin”

  3. Are Blue Origin and Space-X using different control algorithms for the tail-first rocket booster landing?

    The Space-X vehicle looks to come “straight-in” whereas the New Shepard appears to overcorrect more before touchdown?

    1. Also seems like New Shepard starts the landing burn much later (suicide burn indeed!) but maybe that’s just because it’s smaller?

    2. Can you clarify what you mean by “overcorrect”? In the last two launches/landings, the New Shepard boosted finished right-side-up on the pad, so as a layperson, it seems like it’s doing just the right amount of correction. New Shepard can perform those corrections because BE-3 is deeply throttleable. Merlin 1/F9R 1st stage can’t go T/W < 1, so they pick spot and hoverslam onto it. Although in the news update (https://www.blueorigin.com/news) Jeff Bezos said they've removed the function to hover to the exact center of the pad, rather they target the center and then land in a "position of convenience". Apparently it's more robust to wind disturbances. Dr. Lars Blackmore does a lot of the control work at SpaceX. He's on Twitter (https://twitter.com/larsblackmore).

      1. IANACSTIJRMAOTAFGA (I am not a control system theorist I just represented myself as one to a Federal Granting agency).

        OK, I took multiple semesters of Optimal Control Theory in graduate school and I spent the last two years studying literature on the subject. The balancing-a-broomstick problem is something they (i.e. my colleagues who actually work with this stuff) say you can solve with a classical PID (proportional-integral-differential) feedback controller you learn about in your required undergrad course for Electrical/Chemical Engineering.

        Optimal Control is typically an advanced subject and an engineering specialization. The optimal control was of particular interest in the early Space Race days for just such things such as reentry trajectories and lunar landers, and a (simplified) lunar lander is offered as an example of an optimal control subject to a terminal constraint (i.e., not crumping the landing) in almost every Optimal Control textbook.

        That said, both New Shepard as well as the Space-X first stage have each on at least one occasion satisfied their terminal constraint (i.e., not crumped — I would call the last Space-X “event” a crumping because they didn’t crash but the nevertheless wrecked the vehicle — they crumped it).

        On the other hand, Space-X seems to come “straight in” whereas New Shepard appears to wobble back and forth lining up for their landing contact. They bring to mind Neil Armstrong’s “cross country flight” with the Eagle lunar lander, searching for a smooth landing spot and giving Houston Mission Control heart palpitations.

        So that is what I mean by “overshoot.” New Shepard is not overshooting the landing point (the terminal constraint) or at least not by much (they are only a little off the bull’s eye whereas Space-X appears to be dead on, whether they crump the landing or not). But New Shepard appears to be wobbling before they “stick” their landing.

        Maybe instead of appealing to control theory, I should refer to figure skating jumping. They both landed their “triple Axle” at least once, but one of them is “wrapping their free leg”, which may be a “points deduction” for certified skating judges.

        2. The vertical landing rocket problem is what’s called a non-minimum phase problem: in layman’s terms, the response to the controls “goes the wrong way” initially. For the rocket, you want to tilt the rocket so that there is a horizontal thrust component in the direction you want to translate the rocket (the magnitude is T sin(theta), where T is the thrust magnitude and theta is the angle from the vertical). But in order to pitch the rocket over by that angle theta, you tilt the rocket nozzle in the opposite direction to generate a pitching moment, and that makes the horizontal thrust component momentarily point in the wrong direction, so the initial position response is opposite of the command. Non-minimum phase systems have inherent limits on the control bandwidth, which in this case exacerbates the issue of controlling an unstable system. I’m not too surprised that the pitch response looks a little underdamped.

          But I also suspect that they don’t have a lot of control authority from their aero controls, so the amount of position error they can null out prior to engine relight is not that big. Hence when they relight, they may have a substantial position error and hence get a relatively large maneuver.

          FWIW, if I were doing this control law, it would be a more-or-less classical multi-loop design looking like: proportional feedback on position error and position error rate to generate a horizontal acceleration vector command; feed that into a command resolver to turn it into an attitude command; proportional plus integral on attitude error with attitude rate feedback to generate an attitude acceleration command; turn that into a gimbal angle command using the current throttle setting to determine thrust. I’d let the vertical closure loop set the thrust based on getting to a hover at a predetermined altitude (a big advantage of the deep throttling engine).

          1. What you describe is almost exactly what was used on blue ball…

            position error->proportional-> velocity (with max limit)
            velocity ->pid ->acceleration
            acceleration ->proportional to attitude…
            attitude ->pid ->actuators…

            altitude error-> vertical rate
            vertical rate >pid ->throttle actuator.

        3. I might take a perhaps simpler approach if I had horizontal thrusters at the top of the stage.

          Assuming you’re in a very vertical descent like Blue Origin, maintain a purely vertical orientation for the stage and calculate the horizontal error distance and its radial direction. Noting the time till landing given the desired descent profile, the rocket needs to traverse horizontal distance s in time t with a linear horizontal acceleration ramp, a period at constant horizontal speed, and then a linear horizontal decel, your classic slope sided mesa shape used in countless machine motions.

          So you make a rule that the main engine will gimbal to produce a proportion of the desired horizontal thrust component while the upper thruster’s component keeps the stage vertical throughout the maneuvers. That ratio might shift a bit as the center of mass lowers due to fuel consumption, but even a first pass might be good enough because the upper thrusters could be slaved to a gyro to maintain the vertical orientation. A suggested corollary is that the upper horizontal thrusters can match the torque of any main engine gimbal angle and you no longer have to care about the pogo problem at all. A similar constant-vertical approach was used on the lunar lander to simplify the controls physics.

          The main engine is then throttled to provide the desired vertical thrust profile given the engine’s gimbal angle to meet the horizontal thrust profile. Leave some throttle margin and the vertical control system only needs to know the horizontal control systems desired thrust to solve for an engine gimbal angle and thrust level.

          During the descent recalculate the vertical and horizontal error at a few points to catch any wind drift, which would also recalculate the horizontal course angle correction which lets landing remain a 2-D problem broken down into two perpendicular components, vertical and horizontal.

          I don’t think the solution needs to be optimal because if you only have enough fuel for the optimal solution, you don’t have enough fuel for a safe landing, and any fuel you save is going to boil off anyway after you touch down.

          You could probably implement this method with some cams for the desired profile and some op-amps. Landing can’t be that hard or kittens couldn’t nail it every time! ^_^

    3. One possibility is that the grid fins SpaceX uses are more effective at control than what BO uses. In their December landing, the rocket was aimed to hit offshore if there was a problem. The system corrected the trajectory once it confirmed everything was working properly. Perhaps the drag fins on New Shepherd aren’t steerable or are not as effective. If that’s the case, the rocket would have to make a larger correction once the engine is running.

  4. Am I the only one bemused that two companies are launching or will launch reusable rockets just miles from a border that the government to which they pay taxes refuses to control?

    1. Yes, you are.

      Until now, that is.

      The paramount argument made against border enforcement is that nothing (repeat nothing) will keep the Mexicans out. So I say we should do the following: In the name of humanity colonizing space, we should put signs up all along the border advertising high-paying unskilled jobs, free education, and free health care on the Moon. Since nothing can keep the Mexicans out of the United States, nothing could keep them off of the Moon. It just stands to reason.

      There. Problems solved.

  5. You don’t need to be a scientist or mathematician to be a nerd but the comments above are why I like to use the term Alpha Nerd, which implies a certain professional competency in an intellectually complex field.

  6. Aviation Week published an interesting article on BO. It included some info relevant to our discussion here that I have not seen elsewhere:

    Commenting on the test, Blue Origin founder Jeff Bezos says the biggest difference between the first and second mission was a software change to the logic in the guidance, navigation and control system. “Rather than the vehicle translating to land at the exact center of the pad, it now initially targets the center, but then sets down at a position of convenience on the pad, prioritizing vehicle attitude ahead of precise lateral positioning,” he says.

    The slight change to the landing software was evident in the behavior of the vehicle as it dropped to the desert pad. Unlike the first successful landing, in which the gimbaling thrust vectoring system could be seen working dynamically to perfectly center the vehicle for touchdown, the second flight showed a more direct final descent.

    “It’s like a pilot lining up a plane with the centerline of the runway,” says Bezos. “If the plane is a few feet off center as you get close, you don’t swerve at the last minute to ensure hitting the exact mid-point. You just land a few feet left or right of the centerline. Our Monte Carlo sims of New Shepard landings show this new strategy increases margins, improving the vehicle’s ability to reject disturbances created by low-altitude winds.”

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