Many system concepts and ideas for fully reusable space transportation systems have been proposed, and technology maturation studies are actively underway. A rocket SSTO (Single Stage To Orbit) should be a final goal of rocket engineers, and it is believed that it has become possible by applying the latest technologies such as engine performance augmentation by external expansion and light-weight materials and structure. Among these system configurations, a vertical lander is one of the attractive systems. There are typically two system configurations from the return flight point of view: horizontal landers and vertical landers. A horizontal lander returns to an air-strip like the Space Shuttle orbiter, which has a wing for landing and after landing it has to be converted to a vertical position for the next launch. On the other hand a vertical lander must have a certain amount of fuel for the landing delta-V, however the wing can be eliminated. For volume and structural efficiency, a vertical lander would be advantageous if properly designed, because it could employ a fatter shape than horizontal landers. This will lead to light-weight construction which is a major concern in designing an SSTO vehicle. From the ground operation point of view, what is needed for such a future vehicle is quick turnaround capability for good reusability like conventional aircraft. To eliminate huge ground support facilities and laborious ground operations for converting its position from horizontal to vertical would be beneficial for good reusability. But it is still controversial which approach is better in these respects, since no real operational vehicle has ever existed.

Taking a vertical landing vehicle into consideration, it should have a wide range of engine throttling capability for the powered landing maneuver. In some engine and nozzle arrangements such as an external expansion mechanism like an aero-spike engine1, it would not be possible to use engine gimballing because of the fixed engine / nozzle layout. When the primary propulsion is used for attitude control as is done in conventional rocket vehicles by gimballing, the possibility of using differential throttling of these engines for the attitude control moment generator will arise. Even for horizontal landers when they employ such an engine layout, these requests could be common for the high performance future reusable vehicles. For example X-33; a rocket SSTO demonstrator, employs the linear aero-spike engine layout. Particularly for vertical landers, aerodynamic control surfaces cannot be used at landing, because its air-speed is very low. Therefore, it is important to know the feasibility of differential throttling from the viewpoint of both static and dynamic engine responses for these reasons.

Figure 1 shows a small vertical landing reusable rocket vehicle proposed for demonstrating good operability and reusability2. It is designed so as to return to the launch site after a ballistic flight, and to be used as a test bed for technology demonstration for SSTO such as light-weight construction and high performance propulsion. Another goal of the vehicle is first to achieve a reusable vehicle with enhanced operability, to demonstrate the benefits of reusability. At the same time, the rocket vehicle is used as a multi-purpose sounding rocket. Enhancing the flight operability and low cost operation of the vehicle will give a good opportunity, which means the frequent use of the vehicle is expected. This is the background idea for the present vehicle.

As for the performance of the vehicle, it has a ballistic flight capability to an altitude of up to 300 km, and returns safely to the launch site. Finally it lands vertically and offers safe return of the payload. Its propulsion system is composed of four liquid hydrogen / liquid oxygen engines, and it lifts off vertically as a conventional rocket, ascending up to the maximum altitude. After falling back to the atmosphere, it is aerodynamically decelerated and lands vertically at the same place from which it was launched. It uses all four engines for ascent, but it uses two in symmetrically opposite positions for landing by throttling down to about 30% of full thrust level. In the case of one-engine failure, it has the ability to abort and come back to the launch site in the same way as in normal operation. At any time during powered flight, it is able to change to the abort mode in which all engines are cut, and after coasting flight it lands by use of a pair of sound engines in the symmetric position. In that way it has a full-time abort capability and savability in that failure mode. In addition, due to the benefit of deep throttling capabilities of each engine, it has flexible maneuverability in flight; e.g. hovering at constant altitude, low-speed powered flight, and so on.

A major objective of the present study is to identify to what extent the concept of differential throttling is feasible. Therefore for a case study, taking into account the attitude motion in atmospheric flight of the demonstrator vehicle presented above, the necessary restoring moment is evaluated for both powered ascent and landing. Then this is converted to the throttling requirement for each engine both in terms of static and dynamic characteristics. A rocket firing test was then carried out. Engine throttling was done by controlling the hot turbine working fluid with electric motor driven valve. An attempt to augment the frequency response by giving a combustion pressure signal feedback to the throttling device was made. After showing the results and comparing them with the dynamic model-derived responses, a discussion on further improvement for better dynamic response is made in the following sections.

The vehicle presented above has three phases of powered flight, powered ascent, powered descent before landing, and vertical landing. Differential throttling is done as shown in Figure 2, which summarizes the flight environment and necessary vehicle parameters for the following evaluation both for powered ascent at its maximum dynamic pressure, and for the descent flight transient starting from aerodynamically equilibrium descent to hovering at a certain altitude2. At the final landing the attitude motion would be primarily governed by the soft-landing guidance requirement, not by aerodynamic forces, because the air-speed is very small at landing. In the following part of this section, a simple evaluation is made to give a preliminary requirement for the engine throttling.

The necessary range of the engine throttling is derived from the dynamic balance between control moment and aerodynamic torque at maximum dynamic pressure. The dominant disturbance in the atmospheric powered flight is taken into account. Table 1 indicates the required magnitude of throttling as a percentage of the nominal thrust, which is evaluated for the maximum dynamic pressure expected during the powered ascent phase as shown in Figure 2. In the table, the vehicle is assumed to be aerodynamically unstable and the throttling amplitude for three different negative static margins are evaluated. The maximum allowable angle of attack, having a significant influence on the level of disturbance, is also treated as an important design parameter. As maximum angle of attack encountered in this specific flight condition, two cases are taken into account.

The table clearly shows the importance of aerodynamic design of the vehicle, indicating that control design should proceed in conjunction with it. One example of practical requirements for the throttling range may be 20 % for a vehicle having static margin of -5 %. The angle of attack at maximum dynamic pressure is also strictly required to be below 3 degrees. This can deteriorate by inevitable wind profile dispersion, but the level is considered within a scope of expectation. It should, however, be recognized that a 3 degree angle of attack is equivalent to a deviation of as little as 18 m/s, which is 26 % of the nominal wind velocity at the altitude considered here.

On the other hand, the required frequency characteristics of the engine throttling can be determined by the tolerable level of delay in the actuating system as evaluated at the rigid mode frequency. At the maximum dynamic pressure, the rigid mode frequency is estimated at 3.6 rad/sec. Allowing a phase delay of 30 degrees, equivalent to 145 msec. delay in time, the bandwidth requirement of the engine throttling control results in approximately 2 Hz, as measured when the phase delay reaches 90 degrees. It must be emphasized here that the delay may not be as short as it should be, although the level is expected to be improved by appropriate control architecture.

The powered descent phase takes place at an altitude below 2 km, where the aerodynamic forces due to crosswind would be dominant. In this region, the required throttling magnitude can be given as follows

where Vw means the cross wind speed. Dispersion of the surface wind velocity can be assumed to be below 15 m/sec based on statistical data of normal rocket launch, thus 15 % of the throttling range is required for the descent phase. It should be noted that the requirement for the descent mode is less than that for the powered ascent phase presented above.

As the control system is expected to be utilized in the proximity of minimum control force in the final landing phase, a control system having a linear control characteristic can be treated as an on-off control system. To form a stable limit cycle, the following relation should be satisfied;

where D designates the control dead band, k indicates the rate adding ratio, a represents the control angular acceleration, and Td denotes the total delay time of the control system. It can be practical to take the entire delay to be 200 msec, approximately 50 msec margin against the delay in throttling control. The magnitude of the dead band will be influenced by, for example, the design of the landing gear, but it is left for future consideration. Allowing it to be 2 degrees provisionally, with typical adding ratio of 0.5 sec, yields a requirement for the minimum throttling level of approximately 4 % of the nominal thrust.

From the consideration of these three flight phases, the requirement for the engine throttling control can be summarized as: a throttling amplitude of 4 to 20 % of nominal thrust is necessary, and a concerned frequency response is important at about 2 Hz of the bandwidth. This should be the set of requirements for the following engine response studies, as long as this size and flight-path for the present vehicle are concerned.

The rocket engine used for the study is a small liquid hydrogen fueled engine with 1000 kg maximum thrust, which was originally designed and developed for a cryogenic upper stage3. Although this engine is not exactly identical to that assumed in the reusable rocket in the previous section, it is a good test-bed for the present study. The engine has a separate turbopump for each propellant, and employs Expander Cycle. The liquid hydrogen turbopump consists of a two-stage centrifugal pump with shroud and a two-stage reaction turbine. The liquid oxygen turbopump has a single-stage centrifugal pump with shroud and a single- stage impulse turbine. Maximum design chamber pressure is 3.8 MPa and the design MR (oxidizer/fuel mixture ratio) was 5.5. However, we adjusted the rated power level to 2.9 MPa chamber pressure by changing the flow restriction orifices and conducted the thrust throttling tests. The propellant flow schematic of the engine is shown in Figure 3. Figure 4 shows the engine configuration. The engine was set in the ground test facility horizontally. Engine start was done by main propellant tank-head, and the tank pressure was kept around 0.5 MPa for the liquid hydrogen tank and 0.4 MPa for the liquid oxygen tank in order to avoid influences caused by turbopump suction-performance problems during throttling tests. All the tests were conducted under sea level conditions. The ground test facility used for tests is a multi-purpose cryogenic test stand, which has sufficient capability for the range of this test series and for repeatable testing.

In order to change the thrust, two electrically driven valves were installed in the engine feed lines as shown in Figure 3. One is a thrust control valve (TCV), that has a function to by-pass the turbine working fluid out of both turbines. The other is an oxidizer/fuel mixture ratio control valve (OFCV) which will change the mixture ratio to the selected point. However in this test series, it is used only for the duration of the start-up transient. As a result, the oxidizer/fuel mixture ratio is influenced by the TCV actuation in the test for throttling response, which was in the predicted operating range. Liquid-line throttling could be more attractive from the standpoint of rapid thrust response, but it would increase pump discharge pressure during throttling and could create flow coefficient problems at the hydrogen pump. To augment the flow, hydrogen can be recirculated around the pump, but the ramifications of hydrogen recirculation might lead to a temperature rise of hydrogen and pump suction-performance problems. So we adopted a hot-gas side control system for thrust throttling in the present study.

The two valves were identical and had the same actuators and servo controllers. The actuators were to adjust the valve stroke and were manipulated by a rapid response AC driven motor. The servo system was constructed using a PC-based controller and servo driver for the AC motor. To obtain the valve opening stroke, a linear position sensor is attached to the valve poppet and a resolver attached to the AC motor rotational shaft. The PID servo gains of these actuators are tunable by the PC-based controller. However, PD control was employed in the present test. The valve specification is listed in Table 2. A angle-type valve was used for both valves to reduce the pressure drop. In order to control the engine thrust linearly with respect to the valve opening ratio, a linear flow characteristic was selected for both valves. In the closed-loop throttling test in the following sections, the combustion chamber pressure signal, which is proportional to the engine thrust, was used as a feedback signal. Before the testing, the signal noise level was carefully measured and a low-pass filter logic was installed in the PC-based controller. A block diagram of the closed-loop control system is shown in Figure 5.

A dynamic simulation model to evaluate the response of the engine before and after the test was constructed. Generally this type of engine system has some kinds of non-linearity, caused by turbo pump characteristics and hydrodynamic characteristics. So as to make an accurate estimate of the system behavior, a non-linear modeling of the engine dynamics is needed. A numerical simulation code was developed in accordance with the real engine plant shown in Figure 3. Many cases of simulations were executed to make sure to avoid singularities and/or any kind of oscillation before the hot run of the engine.

There is no room to describe the details of the modeling here. However after each test run, some of the specific parameters affecting the whole system characteristics were tuned for some uncertain parameters, and correlated to the previously estimated values, such as the line resistance to the fluid motion, the pump characteristics, the turbine efficiency, the turbo pump inertia and so on. This repeated correction leads to the result in which these uncertain parameters converge to certain values. Before executing the series of closed-loop tests, the prediction of the next test gives quite a good estimate of the dynamic behavior, and determination of the feedback gain was made after careful inspection of these estimates. An example of the correlation between the estimate and the real response is shown in Figure 6 which shows part of the time history of the step-response of the combustion chamber pressure to the engine throttling.

Taking into account the results of the evaluated attitude motion and the resulting throttling requirement for the engine response, a series of ground firing tests was carried out using the engine described above. According to the throttling requirement, the parameters of the firing test were selected as 100 to 40 % of its maximum thrust and 0.5 to 2 Hz frequency range at 10 to 20 % of dynamic throttling amplitude. After confirming the static throttling characteristics in the preliminary firing tests, the open-loop step response and frequency response were investigated. Figure 7 presents the result of static throttling test in which the relation between the valve stroke and the combustion pressure is identified.

Next, tests were performed to investigate the improvement of the dynamic response by adding a feedback loop from the combustion chamber pressure signal to the thrust control valve, as presented in the previous section. A typical example of the time history of the dynamic tests is presented in Figure 8 where the frequency responses are investigated for the two parameters of throttling level and frequency in a single test run. It is clearly observed that the engine responds according to the command signal for throttling. Table 3 shows the summary of the test parameters of the engine throttling. The maximum firing time is about 1 minute in these test runs.

Figure 9 presents the resulting open-loop frequency response together with the model-derived characteristics. The resulting phase delay is about 81.5 deg. at 0.5 Hz frequency response, and the response time is over 450 msec. As shown in the figure, the open-loop frequency response at the concerned frequency shows a considerable delay. However, the model-derived responses show fairly good agreement with the results. In addition to these remarks, it is observed that differences in the central thrust level, and the oscillation amplitude do not greatly influence the delay characteristics.

After obtaining the open-loop system response, a pressure feedback closed loop test was conducted to improve the system dynamics for the purpose of meeting the requirements for the vehicle motion. Before executing the test, it was necessary to fix the proportional feedback gain, Kp, and the differential gain, Kd, under the conditions that the chamber pressure must not over-shoot, and the TCV stroke must not saturate due to the current limit for the TCV actuation. As a result, Kp=2.4 and Kd=0.05 were suggested after synthesis of model-derived simulations. However due to safety reasons and limitations of the TCV capability, most of the closed-loop tests were done with gains of Kp=0.8 and Kd=0.01, and the higher gains were used for the final test for evaluating the response at 0.5 and 1.0 Hz frequency as shown in Table 4.

The frequency responses of the closed-loop tests are summarized in Figure 10 where the results both for the lower feedback gains and for the higher gains are presented. The improvement in comparison with the open-loop characteristics is obvious. The phase delay is reduced to 65 deg. and response time is improved to 360 msec at 0.5 Hz frequency with feedback gains of Kp=0.8 and Kd=0.01. Also presented are the improvements with higher-gain feedback.

As presented in the previous sections, the dynamic throttling characteristics have been identified. Due to the limitations of the number of test runs and the performance of the thrust control valve, the results are not comprehensive. However, the augmentation of the dynamic response was demonstrated, and the model-derived simulation technique satisfactorily worked on every aspect in the testing, such as estimating the response, determining the feed-back gains, and so on. It was also demonstrated that the simulation result is valid even in evaluating closed-loop characteristics, and so further improvement by giving more optimal and higher feedback gains would be possible. Based on the test results, Figure 11 shows the simulated frequency response for the higher gains of Kp=12.0 and Kd=0.3. This would be realized by giving a much higher current to the TCV and careful selection of feed-back signal filtering parameters, because the higher feedback gain imposes larger noise-sensitiveness.

Table 4 summarizes the test results and the expected improvement by optimal feedback as described. Theoretically, higher gain feed-back makes it possible to improve the phase delay to under 15 deg., and response time to under one fifth of that in the open-loop characteristics. In comparison with the requirement based on the vehicle attitude dynamics, ie. 90 deg. phase delay at 2 Hz frequency as presented in the previous section, this improvement by closed-loop throttling control would be satisfactory. The TCV should have a wider range of stroke and better dynamic response for this purpose. In addition to these augmentation techniques, for the improvement of open-loop characteristics, in other words for a better dynamic response of the engine itself, making the inertia of the turbo pump as small as possible would be essential from the consideration by dynamic modeling.

Static and dynamic throttling capability was demonstrated from 40 % to 100 % of the maximum thrust of a liquid hydrogen/liquid oxygen rocket engine. The frequency response of the engine throttling was investigated, and good correspondence between the simulation-model-derived dynamic response and the real behavior was verified. Finally closed-loop engine thrust control by connecting the pressure signal of the engine combustion chamber to the throttling valve for better dynamic response was carried out. By changing the feedback gain, improvement of the frequency response was investigated, and the expected augmentation of the dynamic response was demonstrated in the required frequency range derived from the evaluated attitude motion of the reference vehicle. Based on the present study, good controllability by the application of differential thrust of the primary propulsion system for attitude control would be realistic. The engine dynamic simulation model was also verified, including the closed-loop characteristics, and the lessons learned from the study give a guide for further improvement including better dynamic characteristics of the engine throttling.

1. R K Weeger, 1992, " SSTO Propulsion Design", AIAA-92-1384
2. Y Inatani, Y Naruo and T Yamada, 1996, " A Concept of Reusable Sounding Rocket with Enhanced Maneuverability and Operability", Proc. 20th.International Symposium for Space Technology and Science, Gifu
3. T Ikeda et al, 1983, " LOX/LH2 Propulsion System for Launch Vehicle Upper Stage", Ishikawajimaharima Heavy Industry Technical Report No.1, vol.23