A method for controlling the speed of a hypersonic engine using double differential sliding mode control

Abstract

The application provides a kind of hyper-speed engine speed method using double differential sliding mode control, which obtains low-speed error signal by setting low-speed protection speed, and then carries out exponential nonlinear transformation to obtain low-speed exponential error signal;Then design an exponential saturation progressive holder, obtain the first, second and zero order outputs of the holder through exponential hybrid nonlinear transformation and piecewise integral recursion, and further solve the approximate damping signal of speed error;Then, the error and the approximate damping signal of the error and the double differential form a nonlinear speed error sliding mode signal, and then the sliding mode approximate damping signal is solved through the exponential saturation progressive holder, and the nonlinear speed error sliding mode signal is superimposed to form the final hyper-speed engine throttle control signal, so as to control the speed of the aircraft and the engine.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of hypersonic engine control, in particular to a method for controlling the speed of a hypersonic engine by using double differential sliding mode control. BACKGROUND

[0002] The speed control of a hypersonic engine is very complex, unlike ordinary engines. When the speed is too low, the engine is prone to flameout failure. At the same time, due to the violent combustion process, the speed control requires very high rapidity. At the same time, the particularity of the hypersonic flight environment causes the combustion efficiency of the engine combustion process to fluctuate greatly under the influence of environmental changes, so that the speed change accuracy of different flight tests is different, and therefore the quality of the speed control is greatly disturbed by the external environment, so that it is difficult to achieve high-precision and rapid-response speed control. The sliding mode control has good rapidity and strong anti-interference ability. Based on the above background, the present application proposes a method for achieving high-precision control of the speed of a hypersonic vehicle engine by using double differential sliding mode and sliding mode approximate damping signal, and also realizes the function of low-speed protection to prevent flameout, thereby having high practicality and engineering value.

[0003] It should be noted that the information disclosed in the above background section of the application is only used to strengthen the understanding of the background of the present application, and therefore can include information that does not constitute prior art known to those of ordinary skill in the art. SUMMARY

[0004] The purpose of the present application is to provide a method for controlling the speed of a hypersonic engine by using double differential sliding mode, thereby at least partially overcoming the problems of insufficient speed control stability and lack of low-speed protection of a hypersonic vehicle caused by the limitations and defects of related technologies.

[0005] According to one aspect of the present application, a method for controlling the speed of a hypersonic engine by using double differential sliding mode is provided, comprising the following steps:

[0006] Step S10, install a speed sensor on the aircraft to measure the real-time speed of the aircraft, then set the desired speed signal of the aircraft according to the flight requirements of the aircraft, compare the two to obtain a speed error signal; then set a low-speed protection speed and compare it with the real-time speed of the aircraft to obtain a low-speed error signal; finally, perform an exponential nonlinear transformation on the low-speed error signal to obtain a low-speed exponential error signal.

[0007] Step S20: Based on the speed error signal, low-speed error signal, and low-speed exponential error signal, design an exponential saturated progressive hold and compare it with the zero-order output of the hold to obtain the hold error signal; then perform an exponential hybrid nonlinear transformation on the hold error to obtain the hold error exponential transformation signal; then solve for the third-order output signal of the hold based on the hold error exponential transformation signal, the first-order output signal of the hold, and the second-order output signal of the hold; then perform piecewise integration on the third-order output signal of the hold to obtain the second-order output signal of the hold; then perform recursive piecewise integration sequentially to obtain the first-order output signal and the zero-order output signal of the hold; finally, solve for the speed error approximate damping signal based on the first-order output signal of the hold.

[0008] Step S30: Integrate the speed error signal to obtain the speed error integral signal; then integrate the low-speed exponential error signal to obtain the low-speed exponential error integral signal; then superimpose the speed error approximate damping signal and the second-order output signal of the holder to form the speed error nonlinear sliding mode signal; then perform an exponential transformation on the speed error nonlinear sliding mode signal to obtain the sliding mode exponential transformation signal.

[0009] Step S40: Design an exponentially saturated progressive sliding mode holder based on the aforementioned nonlinear sliding mode error signal and exponentially transformed sliding mode signal, and compare it with the zero-order output of the sliding mode holder to obtain the sliding mode holding error signal; then perform an exponentially hybrid nonlinear transformation on the sliding mode holding error to obtain the exponentially transformed sliding mode holding error signal; then solve for the third-order output signal of the sliding mode holder based on the exponentially transformed sliding mode holding error signal, the first-order output signal of the sliding mode holder, and the second-order output signal of the sliding mode holder; then perform piecewise integration based on the third-order output signal of the sliding mode holder to obtain the second-order output signal of the sliding mode holder; then perform recursive piecewise integration sequentially to obtain the first-order output signal and the zero-order output signal of the sliding mode holder; finally, solve for the approximate sliding mode damping signal based on the first-order output signal of the sliding mode holder.

[0010] Step S50: Combine and integrate the sliding mode exponential transformation signal and the speed error nonlinear sliding mode signal to obtain the sliding mode combined integral signal; then perform nonlinear transformation on the speed error nonlinear sliding mode signal to obtain the speed error sliding mode nonlinear signal; finally, superimpose the sliding mode approximate damping signal and the speed error nonlinear sliding mode signal to obtain the final hypersonic engine throttle control signal.

[0011] In one exemplary embodiment of the present invention, a speed sensor is installed on the aircraft to measure the real-time speed of the aircraft. Then, the flight requirements of the aircraft are set, and the desired speed signal of the aircraft is set. The two are compared to obtain a speed error signal. Then, a low-speed protection speed is set and compared with the real-time speed of the aircraft to obtain a low-speed error signal. Finally, an exponential nonlinear transformation is performed on the low-speed error signal to obtain a low-speed exponential error signal, including:

[0012] ;

[0013] ;

[0014] ;

[0015] in The real-time speed of the aircraft is calculated by the inertial navigation equipment of the aircraft control system. The desired speed signal for the aircraft. This is the speed error signal; For low-speed protection speed, This is a low-speed error signal; For constant parameters, This is a low-speed exponential error signal.

[0016] In one exemplary embodiment of the present invention, based on the speed error signal, low-speed error signal, and low-speed exponential error signal, an exponentially saturated progressive hold is designed, and compared with the zero-order output of the hold to obtain the hold error signal; then, an exponentially hybrid nonlinear transformation is performed on the hold error to obtain the hold error exponentially transformed signal; then, the third-order output signal of the hold is solved based on the hold error exponentially transformed signal, the first-order output signal of the hold, and the second-order output signal of the hold; then, piecewise integration is performed based on the third-order output signal of the hold to obtain the second-order output signal of the hold; then, recursive piecewise integration is performed sequentially to obtain the first-order output signal and the zero-order output signal of the hold; finally, the approximate speed error damping signal is solved based on the first-order output signal of the hold, including:

[0017] ;

[0018] ;

[0019] ;

[0020] ;

[0021] ;

[0022] ;

[0023] ;

[0024] in To preserve the error signal; , , , For parameters of nonlinear transformation, To preserve the error exponential transformation signal; , , , For constant parameters of the exponential hybrid nonlinear transform, The third-order output signal of the hold; For constant parameters, This is the second-order output signal of the hold; The first-order output signal of the hold circuit. The zero-order output signal of the hold; This is the approximate damping signal for velocity error.

[0025] In one exemplary embodiment of the present invention, the speed error signal is integrated to obtain a speed error integral signal; then, the low-speed exponential error signal is integrated to obtain a low-speed exponential error integral signal; then, the speed error approximate damping signal and the second-order output signal of the holder are superimposed to form a speed error nonlinear sliding mode signal; then, the speed error nonlinear sliding mode signal is exponentially transformed to obtain a sliding mode exponential transformation signal, including:

[0026] ;

[0027]

[0028] ;

[0029] ;

[0030] in The integral signal of the velocity error; This is the low-speed exponential error integral signal; , , , , These are constant parameters for sliding mode. This is a nonlinear sliding mode signal for velocity error; This is the sliding mode exponential transformation signal.

[0031] In one exemplary embodiment of the present invention, an exponentially saturated progressive sliding mode holder is designed based on the aforementioned nonlinear sliding mode error signal and the sliding mode exponential transformation signal, and compared with the zero-order output of the sliding mode holder to obtain the sliding mode holding error signal; then, an exponentially hybrid nonlinear transformation is performed on the sliding mode holding error to obtain the sliding mode holding error exponential transformation signal; then, the third-order output signal of the sliding mode holder is solved based on the sliding mode holding error exponential transformation signal, the first-order output signal of the sliding mode holder, and the second-order output signal of the sliding mode holder; then, piecewise integration is performed based on the third-order output signal of the sliding mode holder to obtain the second-order output signal of the sliding mode holder; then, recursive piecewise integration is performed sequentially to obtain the first-order output signal and the zero-order output signal of the sliding mode holder; finally, the approximate sliding mode damping signal is solved based on the first-order output signal of the sliding mode holder, including:

[0032] ;

[0033] ;

[0034] ;

[0035] ;

[0036] ;

[0037] ;

[0038] ;

[0039] in To maintain the error signal for sliding mode; The sliding mode maintains the error exponential transformation signal; For constant parameters of integral decomposition, This is the third-order output signal of the sliding mode retainer; This is the second-order output signal of the sliding mode retainer; For the first-order output signal of the sliding mode retainer, This is the zero-order output signal of the sliding mode retainer; To solve the approximate damping signal of the sliding mode.

[0040] In one exemplary embodiment of the present invention, the sliding mode exponential transformation signal and the speed error nonlinear sliding mode signal are combined and integrated to obtain a sliding mode combined integral signal; then, a nonlinear transformation is performed on the speed error nonlinear sliding mode signal to obtain a speed error sliding mode nonlinear signal; finally, the sliding mode approximate damping signal and the speed error nonlinear sliding mode signal are superimposed to obtain the final hypersonic engine throttle control signal as follows:

[0041] ;

[0042] ;

[0043] ;

[0044] in , For constant integration parameters, The integral signal is the sliding mode combination signal; This is a sliding mode nonlinear signal for velocity error; , , , , For constant control parameters, This is the throttle control signal for a hypersonic engine.

[0045] By providing the hypersonic engine throttle control signal to the hypersonic vehicle engine and controlling the fuel supply valve to regulate the fuel supply, rapid and precise speed control can be achieved.

[0046] Beneficial effects

[0047] This invention provides a method for controlling the speed of a hypersonic engine using dual differential sliding mode, which has the following three advantages. First, it incorporates a low-speed protection function. By feeding back the low-speed error signal, it provides a larger throttle when the aircraft's speed falls into the low-speed region, allowing it to quickly escape the low-speed zone. Second, it designs an exponential saturated progressive hold, obtaining the first, second, and zeroth-order outputs of the hold through exponential hybrid nonlinear transformation and piecewise integral recursion, and further solves for the approximate speed error damping signal, thus providing a dual differential damping signal for the nonlinear sliding surface. Third, by passing the sliding surface through the exponential saturated progressive hold, an approximate sliding mode damping signal is obtained, providing damping for the entire throttle and speed control, resulting in smoother overall speed control.

[0048] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit the invention. Attached Figure Description

[0049] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0050] Figure 1 This is a flowchart of a method for controlling the speed of a hypersonic engine using dual differential sliding mode, provided by the present invention.

[0051] Figure 2 This is the real-time velocity signal curve (unit: meters per second) of the hypersonic vehicle provided by the embodiment of the present invention.

[0052] Figure 3 This is the speed error curve (unit: meters per second) of the method provided in the embodiments of the present invention.

[0053] Figure 4 This is the approximate damping signal curve of the velocity error provided in the embodiment of the present invention (unitless).

[0054] Figure 5 This is the velocity error integral signal curve (unitless) of the method provided in the embodiment of the present invention.

[0055] Figure 6 This is a hypersonic engine throttle control signal curve (unitless) provided by the embodiment of the present invention. Detailed Implementation

[0056] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided to make the invention more comprehensive and complete, and to fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided to give a full understanding of embodiments of the invention. However, those skilled in the art will recognize that the technical solutions of the invention may be practiced with one or more of these specific details omitted, or other methods, components, apparatus, steps, etc., may be employed. In other instances, well-known technical solutions are not shown or described in detail to avoid obscuring various aspects of the invention.

[0057] This invention provides a method for controlling the speed of a hypersonic engine using a dual-differential sliding mode. The method involves setting a low-speed protection speed to obtain a low-speed error signal, which is then subjected to an exponential nonlinear transformation to obtain a low-speed exponential error signal. Next, an exponentially saturated progressive hold is designed, and the first, second, and zeroth-order outputs of the hold are obtained through an exponentially hybrid nonlinear transformation and piecewise integral recursion. The approximate speed error damping signal is then solved. Finally, the approximate damping signal of the error and the dual-differential method are used to form a nonlinear speed error sliding mode signal. This signal is then solved again using the exponentially saturated progressive hold to obtain the approximate sliding mode damping signal. Finally, the nonlinear speed error sliding mode signal is superimposed to form the final hypersonic engine throttle control signal, thereby controlling the speed of the aircraft and the engine.

[0058] The following will further explain and illustrate a method for controlling the speed of a hypersonic engine using dual differential sliding mode, in conjunction with the accompanying drawings. (Reference) Figure 1 As shown, the hypersonic engine stable fuel supply method based on adaptive fractional derivatives may include the following steps:

[0059] Step S10: Install a speed sensor on the aircraft to measure the aircraft's real-time speed. Then, install the aircraft's flight requirements and set the desired speed signal. Compare the two to obtain a speed error signal. Next, set a low-speed protection speed and compare it with the aircraft's real-time speed to obtain a low-speed error signal. Finally, perform an exponential nonlinear transformation on the low-speed error signal to obtain the following low-speed exponential error signal:

[0060] ;

[0061] ;

[0062] ;

[0063] in The real-time speed of the aircraft is calculated by the inertial navigation equipment of the aircraft control system. The desired speed signal for the aircraft. This is the speed error signal; For low-speed protection speed, This is a low-speed error signal; For constant parameters, This is a low-speed exponential error signal.

[0064] Step S20: Based on the speed error signal, low-speed error signal, and low-speed exponential error signal, design an exponential saturated progressive hold and compare it with the zero-order output of the hold to obtain the hold error signal; then perform an exponential hybrid nonlinear transformation on the hold error to obtain the hold error exponential transformation signal; then solve for the third-order output signal of the hold based on the hold error exponential transformation signal, the first-order output signal of the hold, and the second-order output signal of the hold; then perform piecewise integration on the third-order output signal of the hold to obtain the second-order output signal of the hold; then perform recursive piecewise integration sequentially to obtain the first-order output signal and the zero-order output signal of the hold; finally, solve for the speed error approximate damping signal based on the first-order output signal of the hold.

[0065] Specifically, this can be broken down into the following five steps. Step 1: Based on the aforementioned speed error signal, low-speed error signal, and low-speed exponential error signal, design an exponential saturated progressive hold, and compare it with the zero-order output of the hold to obtain the following hold error signal:

[0066] ;

[0067] in To preserve the error signal.

[0068] The second step is to perform an exponential hybrid nonlinear transformation on the hold error, resulting in the following exponentially transformed hold error signal:

[0069] ;

[0070] in , , , For the parameters of the nonlinear transformation, To preserve the error exponential transformation signal.

[0071] The third step is to calculate the third-order output signal of the hold circuit based on the hold error exponential transformation signal, the first-order output signal of the hold circuit, and the second-order output signal of the hold circuit, as follows:

[0072] ;

[0073] in , , , For constant parameters of the exponential hybrid nonlinear transform, This is the third-order output signal of the hold.

[0074] Fourth step: Perform piecewise integration on the third-order output signal of the hold to obtain the second-order output signal of the hold; then perform recursive piecewise integration to obtain the first-order output signal and the zeroth-order output signal of the hold as follows:

[0075] ;

[0076] ;

[0077] ;

[0078] in For constant parameters, This is the second-order output signal of the hold; The first-order output signal of the hold circuit. This is the zero-order output signal of the hold.

[0079] Fifth, based on the first-order output signal of the retainer, the approximate damping signal for the speed error is calculated as follows:

[0080] ;

[0081] in This is the approximate damping signal for velocity error.

[0082] Step S30: Integrate the speed error signal to obtain the speed error integral signal; then integrate the low-speed exponential error signal to obtain the low-speed exponential error integral signal; then superimpose the speed error approximate damping signal and the second-order output signal of the holder to form the speed error nonlinear sliding mode signal; then perform an exponential transformation on the speed error nonlinear sliding mode signal to obtain the sliding mode exponential transformation signal.

[0083] Specifically, firstly, the velocity error signal is integrated to obtain the following velocity error integral signal:

[0084] ;

[0085] in This is the integral signal of the velocity error.

[0086] Secondly, by integrating the aforementioned low-speed exponential error signal, the integrated low-speed exponential error signal is obtained as follows:

[0087] ;

[0088] in This is the low-speed exponential error integral signal.

[0089] Furthermore, the nonlinear sliding mode signal of the speed error is formed by superimposing the low-speed exponential error integral signal, the speed error approximate damping signal, and the second-order output signal of the hold, as follows:

[0090] ;

[0091] in , , , , These are constant parameters for sliding mode. This is a nonlinear sliding mode signal for velocity error.

[0092] Finally, an exponential transform is performed on the nonlinear sliding mode signal of the speed error to obtain the following sliding mode exponential transform signal:

[0093] ;

[0094] in This is the sliding mode exponential transformation signal.

[0095] Step S40: Design an exponentially saturated progressive sliding mode holder based on the aforementioned nonlinear sliding mode error signal and exponentially transformed sliding mode signal, and compare it with the zero-order output of the sliding mode holder to obtain the sliding mode holding error signal; then perform an exponentially hybrid nonlinear transformation on the sliding mode holding error to obtain the exponentially transformed sliding mode holding error signal; then solve for the third-order output signal of the sliding mode holder based on the exponentially transformed sliding mode holding error signal, the first-order output signal of the sliding mode holder, and the second-order output signal of the sliding mode holder; then perform piecewise integration based on the third-order output signal of the sliding mode holder to obtain the second-order output signal of the sliding mode holder; then perform recursive piecewise integration sequentially to obtain the first-order output signal and the zero-order output signal of the sliding mode holder; finally, solve for the approximate sliding mode damping signal based on the first-order output signal of the sliding mode holder.

[0096] Specifically, this can be broken down into the following five steps. Step 1: Based on the aforementioned nonlinear sliding mode signal and sliding mode exponential transformation signal, design an exponentially saturated progressive sliding mode holder, and compare it with the zero-order output of the sliding mode holder to obtain the sliding mode holding error signal as follows:

[0097] ;

[0098] in To maintain the error signal for sliding mode.

[0099] The second step is to perform an exponential hybrid nonlinear transformation on the sliding mode holding error, resulting in the following exponentially transformed signal of the sliding mode holding error:

[0100] ;

[0101] in This is a variable signal for the sliding mode holding error.

[0102] The third step is to calculate the third-order output signal of the sliding mode retainer based on the exponential transformation signal of the sliding mode retainer, the first-order output signal of the sliding mode retainer, and the second-order output signal of the sliding mode retainer, as follows:

[0103] ;

[0104] in This is the third-order output signal of the sliding mode retainer.

[0105] Fourth, perform piecewise integration on the third-order output signal of the sliding mode retainer to obtain the second-order output signal of the sliding mode retainer; then, perform recursive piecewise integration sequentially to obtain the first-order output signal and the zero-order output signal of the sliding mode retainer as follows:

[0106] ;

[0107] ;

[0108] ;

[0109] in For constant parameters of piecewise integration, This is the second-order output signal of the sliding mode retainer; For the first-order output signal of the sliding mode retainer, This is the zero-order output signal of the sliding mode retainer.

[0110] Fifth, the approximate damping signal of the sliding mode is solved based on the first-order output signal of the sliding mode retainer, as follows:

[0111] ;

[0112] in To solve the approximate damping signal of the sliding mode.

[0113] Step S50: Combine and integrate the sliding mode exponential transformation signal and the speed error nonlinear sliding mode signal to obtain the sliding mode combined integral signal; then perform nonlinear transformation on the speed error nonlinear sliding mode signal to obtain the speed error sliding mode nonlinear signal; finally, superimpose the sliding mode approximate damping signal and the speed error nonlinear sliding mode signal to obtain the final hypersonic engine throttle control signal.

[0114] Specifically, the sliding mode exponential transformation signal and the velocity error nonlinear sliding mode signal are first combined and integrated to obtain the sliding mode combined integral signal as follows:

[0115] ;

[0116] in , For constant integration parameters, This is the sliding mode combination integral signal.

[0117] Secondly, a nonlinear transformation is performed on the nonlinear sliding mode signal of the velocity error to obtain the following nonlinear sliding mode signal of the velocity error:

[0118] ;

[0119] in This is the sliding mode nonlinear signal for velocity error.

[0120] Finally, the hypersonic engine throttle control signal is obtained by superimposing the speed error nonlinear sliding mode signal, the sliding mode exponential transformation signal, the sliding mode combined integral signal, the sliding mode approximate damping signal, and the speed error nonlinear sliding mode signal as follows:

[0121] ;

[0122] in , , , , For constant control parameters, This is the throttle control signal for a hypersonic engine.

[0123] Case implementation and computer simulation results analysis

[0124] To verify the correctness and effectiveness of the method provided by this invention, the following case simulation is provided.

[0125] In step S10, a speed sensor is installed on the hypersonic vehicle to measure its real-time speed, such as... Figure 2 As shown. Set the desired speed signal for the aircraft. The speed error signal is obtained as follows: Figure 3 As shown; set low-speed protection speed ,set up This is a constant parameter.

[0126] In step S20, the parameters of the nonlinear transformation are selected. , , , , , , , , The approximate damping signal of the velocity error is obtained as follows: Figure 4 As shown.

[0127] In step S30, select , , , , The velocity error integral signal is obtained as follows: Figure 5 As shown.

[0128] In step S40, In step S50, select , The final hypersonic engine throttle control signal is obtained as follows: Figure 6 As shown.

[0129] Depend on Figure 6 It can be seen that the final throttle control signal is very stable. To maintain a constant position and speed during flight, the steady-state throttle signal is between 0 and 1, which is within the normal range. Figure 2 It can be seen that although the aircraft's speed reached 4650 meters per second, Figure 3The error convergence is relatively smooth without spikes, and the convergence time is very fast, around 20 seconds, and the entire control stability period is less than 40 seconds. Figure 4 The approximate damping signal is also small, and no differential amplification phenomenon occurs; Figure 5 The peak value of the error integral signal reached approximately 70, which played a significant role in improving both speed and steady-state accuracy. Therefore, this case demonstrates that the proposed solution is correct and effective, and possesses high engineering application value for hypersonic vehicles.

[0130] Other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of such inventions. This application is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not specified herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of the invention are indicated by the claims.

Claims

1. A method for controlling the speed of a hypersonic engine using dual differential sliding mode, characterized in that, Includes the following steps: Step S10: Install a speed sensor on the aircraft to measure the aircraft's real-time speed. Then, install the aircraft's flight requirements and set the desired speed signal. Compare the two to obtain a speed error signal. Next, set a low-speed protection speed and compare it with the aircraft's real-time speed to obtain a low-speed error signal. Finally, perform an exponential nonlinear transformation on the low-speed error signal to obtain the following low-speed exponential error signal: ； ； ； in The real-time speed of the aircraft is calculated by the inertial navigation equipment of the aircraft control system. The desired speed signal for the aircraft. This is the speed error signal; For low-speed protection speed, This is a low-speed error signal; For constant parameters, This is a low-speed exponential error signal; Step S20: Based on the speed error signal, low-speed error signal, and low-speed exponential error signal, design an exponential saturated progressive hold, and compare it with the zero-order output of the hold to obtain the hold error signal; then perform an exponential hybrid nonlinear transformation on the hold error to obtain the hold error exponential transformation signal; then solve for the third-order output signal of the hold based on the hold error exponential transformation signal, the first-order output signal of the hold, and the second-order output signal of the hold; then perform piecewise integration on the third-order output signal of the hold to obtain the second-order output signal of the hold; then perform recursive piecewise integration sequentially to obtain the first-order output signal and the zero-order output signal of the hold; finally, solve for the approximate speed error damping signal based on the first-order output signal of the hold as follows: ； ； ； ； ； ； ； in To preserve the error signal; , , , For the parameters of the nonlinear transformation, To preserve the error exponential transformation signal; , , , For constant parameters of the exponential hybrid nonlinear transform, The third-order output signal of the hold; For constant parameters, This is the second-order output signal of the hold; The first-order output signal of the hold circuit. The zero-order output signal of the hold; This is an approximate damping signal for the velocity error; Step S30: Integrate the speed error signal to obtain the speed error integral signal; then integrate the low-speed exponential error signal to obtain the low-speed exponential error integral signal; then superimpose the speed error approximate damping signal and the second-order output signal of the holder to form the speed error nonlinear sliding mode signal; then perform an exponential transformation on the speed error nonlinear sliding mode signal to obtain the sliding mode exponential transformation signal as follows: ； ； ； in The integral signal of the velocity error; This is the low-speed exponential error integral signal; , , , , These are constant parameters for sliding mode. This is a nonlinear sliding mode signal for velocity error; This is the sliding mode exponential transformation signal; Step S40: Based on the aforementioned nonlinear sliding mode signal and sliding mode exponential transformation signal, design an exponentially saturated progressive sliding mode holder and compare it with the zero-order output of the sliding mode holder to obtain the sliding mode holding error signal; then perform an exponentially hybrid nonlinear transformation on the sliding mode holding error to obtain the sliding mode holding error exponential transformation signal; then solve for the third-order output signal of the sliding mode holder based on the sliding mode holding error exponential transformation signal, the first-order output signal of the sliding mode holder, and the second-order output signal of the sliding mode holder; then perform piecewise integration based on the third-order output signal of the sliding mode holder to obtain the second-order output signal of the sliding mode holder; then perform recursive piecewise integration sequentially to obtain the first-order output signal and the zero-order output signal of the sliding mode holder; finally, solve for the approximate sliding mode damping signal based on the first-order output signal of the sliding mode holder as follows: ； ； ； ； ； ； ； in To maintain the error signal for sliding mode; The sliding mode maintains the error exponential transformation signal; For constant parameters of piecewise integration, This is the third-order output signal of the sliding mode retainer; This is the second-order output signal of the sliding mode retainer; For the first-order output signal of the sliding mode retainer, This is the zero-order output signal of the sliding mode retainer; To solve for the approximate damping signal of the sliding mode; Step S50: Combine and integrate the sliding mode exponential transformation signal and the speed error nonlinear sliding mode signal to obtain the sliding mode combined integral signal; then perform a nonlinear transformation on the speed error nonlinear sliding mode signal to obtain the speed error sliding mode nonlinear signal; finally, superimpose the sliding mode approximate damping signal and the speed error nonlinear sliding mode signal to obtain the final hypersonic engine throttle control signal as follows: ； ； ； in , For constant integration parameters, The integral signal is the sliding mode combination signal; This is a sliding mode nonlinear signal for velocity error; , , , , For constant control parameters, This is the throttle control signal for a hypersonic engine.

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