JP2009228605A - Method for controlling engine speed and device for controlling engine speed - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To avoid a problem wherein a calculated control input becomes an unrealizable excessive value, and to stabilize control in performing back-stepping control of engine speed. <P>SOLUTION: A controller defining a Liapunov function V<SB>1</SB>not containing an error z<SB>2</SB>of actual virtual inputs v<SB>1</SB>,<SB>2</SB>and an ideal value α<SB>1</SB>of virtual input containing an error z<SB>1</SB>in a first step setting the ideal value α<SB>1</SB>of the virtual input x<SB>2</SB>making the error z<SB>1</SB>of control output y and its target value y<SB>r</SB>zero, defining a Liapunov function V<SB>2</SB>containing the error z<SB>2</SB>and the Liapunov function V<SB>1</SB>in a second step setting true input u making the error z<SB>2</SB>zero, and making a differential value of the Liapunov function V<SB>2</SB>not greater than zero, is designed. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to control of engine speed, particularly idle speed.

  Conventionally, it is customary to employ a PI controller, an LQ controller, or the like for controlling the engine speed (see, for example, Patent Documents 1 and 2 below).

Such a servo controller usually has an integrator for integrating the deviation between the control output and the target value. The so-called internal model principle is the reason why an integrator is required (see Non-Patent Document 1 below).
Japanese Patent Laid-Open No. 08-114141 JP 2006-233941 A Edited by Kenzo Nonami and Hidekazu Nishimura, “Basics of Control Theory by MATLAB”, 1st Edition, Tokyo Denki University Press, March 30, 1998, p. 191-193

  In the control by a controller having an integrator, overshoot and hunting of the control output may be caused due to the influence of deviation integration. In order to suppress overshoot and hunting of the control output, it is effective to use a backstepping controller that is a controller having no integrator.

  However, if a backstepping controller is simply introduced, a situation may occur in which the control input in calculation exceeds the limit of the control input that can be realized. In controlling the engine speed, the controller operates an ISC (Idle Speed Control) valve, an electronic throttle valve, and the like. The upper limit of the valve opening is naturally 100%, but the value of the control input calculated by the backstepping controller sometimes exceeds 100%.

  The present invention made in view of the above is to avoid the problem that the control input in the calculation becomes an unrealizable excessive value in the backstepping control of the engine speed, and to stabilize the control. The purpose of the period.

  In the present invention, in the first step of setting the ideal value of the virtual input such that the error between the output and its target value becomes zero, the error between the output and the target value is included, while the ideal value of the virtual input and the actual value are In the second step of defining a Lyapunov function that does not include an error with the virtual input and setting a true input such that the error between the ideal value of the virtual input and the actual virtual input is 0, the ideal value of the virtual input Define a Lyapunov function including the error from the actual virtual input and the Lyapunov function defined in the first step, and design a controller with a differential value of this Lyapunov function being 0 or less to control the engine speed. I decided to do it.

  The error between the ideal value of the virtual input and the actual virtual input is always handled in the second step of the backstepping controller design process. Therefore, this error is not included in the Lyapunov function in the first step of the design process. Thereby, the problem that the input, that is, the valve opening degree becomes an excessive value exceeding the limit can be avoided. If the differential value of the Lyapunov function in the second step of the design process is set to 0 or less, the backstepping control can be stabilized.

  The number of model parameters in the system depends on the order of the model. For example, when the order of the entire system is 3, there are five model parameters. If the update gains of these parameters are made equal, that is, if each parameter is changed at the same speed, it will diverge and may cause output hunting. Therefore, it is desirable to change only the parameter corresponding to the steady gain that affects the convergence of the output to the target value, and delay the change of other parameters. For this purpose, among the parameter update gains for updating the parameters of the model, the update gains for the parameters corresponding to the numerator and denominator of the steady gain are set larger than the update gains for the other parameters.

  In addition, if the parameter corresponding to the numerator of the steady gain and the parameter corresponding to the denominator are changed at the same speed, there is still a possibility of divergence. Therefore, it is necessary to provide a difference between the change rates of the two. Therefore, the update gain for one of the parameter corresponding to the numerator of the steady gain and the parameter corresponding to the denominator is set larger than the update gain for the other.

  According to the present invention, when the engine speed is back-stepped, it is possible to avoid the problem that the calculated control input becomes an excessive value that cannot be realized, and the control is stabilized.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings. An outline of the engine speed control device of the present embodiment is shown in FIG. The servo controller 1 detects the current engine speed via a rotational speed sensor 3 attached to the engine 2 (the crankshaft thereof), and based on the deviation between this and the engine speed target value, Operate the opening to make the engine speed follow the target value.

  The controller 1 is mainly an electronic control device. The electronic control device includes a processor 1a, a RAM 1b, a ROM or flash memory 1c, an I / O interface 1d, and the like. The I / O interface 1d includes an A / D conversion circuit and / or a D / A conversion circuit, and is connected to the rotation speed sensor 3 and the ISC valve 4 to acquire a sensor signal and input a control signal. A control program to be executed is stored in advance in the ROM or flash memory 1c, and when it is executed, it is read into the RAM 1b and decoded by the processor 1a. Thus, the electronic control device functions as a backstepping controller that controls the engine speed according to the program.

  Here, the focus is particularly on the control of the idle speed. Decreasing the idling speed contributes to the improvement of fuel consumption. In order to avoid engine stall while reducing the idling speed, it is important to improve the disturbance suppression performance in idling speed control. Therefore, in the present embodiment, a tuning function is applied. The tuning function is an improvement of adaptive backstepping control that combines Lyapunov-based adaptive control with backstepping control.

  If the intake system and the rotation system are each considered as a first-order lag system, and the combustion system is a dead time but is assumed to be a first-order lag system by Padé approximation, the order of the model of the entire system is the third order. Assuming that the opening of the ISC valve 4 is the control input u and the engine speed is the control output y, the response of the system is expressed by the following equation (Equation 1).

  The state equation is expressed by the following equation (Equation 2).

In this embodiment, the output y itself is the state variable x ₁ . Of the state variables x ₁ , x ₂ , x ₃ , only x ₁ can be directly measured. The parameter (coefficient) vector a and the parameter vector b are unknown.

  A block diagram of the control system to which the tuning function is applied is shown in FIG. This system includes an input filter and an output filter that calculate state quantities from input and output, a reference model that determines a response speed of a tuning function, a non-linear controller, and a parameter update block.

  First, an input filter and an output filter are designed. The equation of state (Equation 2) can be transformed as the following equation (Equation 3).

  In order to separate the state quantity into a term that does not include an unknown parameter and a term that includes an unknown parameter, the ξ filter and the Ω filter shown in the following equation (Equation 4) are defined.

  The ξ filter is a filter that does not include an unknown parameter, and the Ω filter is a filter that includes an unknown parameter. When both filters are used, the state quantity can be estimated as in the following equation (Equation 5).

  From the above equation (Equation 5), the true state quantity considering the estimation error ε is represented by the following equation (Equation 6).

  The state quantity estimation error ε satisfies the following expression (Formula 7) and converges exponentially to 0.

The Ω filter can be expressed by the following equation (Equation 8) using a vector v ₁ , a vector v _0, and a matrix Ξ.

The vectors v ₁ and v _{0 that} are the _first two columns of the Ω filter depend on the input u in the matrix F (y, u), and the matrix で that is the remaining three columns depends on the output y. (Equation 9) holds.

  Thus, when the input filter and the output filter are defined as in the following expression (Expression 10), the following expression (Expression 11) is established for the ξ filter and the Ω filter.

  By the conversion using these input / output filters, the state quantity vector x can be expressed by the following equation (Equation 12) with a vector η, a vector λ, a vector k, a vector a, and a vector b.

  Next, the reference model is designed. The order of the reference model is equal to the model order of the entire system and is the third order. The response of the reference system is expressed by the following equation (Equation 13).

  r is the target idle speed. The state space model is expressed by the following equation (Formula 14).

The target input _yr and its differential value can be expressed as the following equation (Equation 15) with the state quantity of the reference model.

Continue designing backstepping controllers. In its first step, so that the output y and its follow-up error z ₁ from the target value y _r is 0, considered as a virtual input state variable x _2, sets the ideal value alpha _1. The Lyapunov function V ₁ regarding error z _1, defined by the following equation (Equation 16).

d ₁ is a gain for the state quantity estimation error. Further, Γ and γ are parameter update gains. The matrix Γ ⁻¹ is expressed by the following equation (Equation 17).

In the above equation (Expression 17), Γ ₁ is an update gain for the parameter b ₁ , Γ ₂ is an update gain for the parameter b ₀ , Γ ₃ is an update gain for the parameter a ₂ , and Γ ₄ is an update for the parameter a ₁ Gain, Γ ₅ is the update gain for parameter a ₀ . The larger the value of the update gain, the faster the parameter change speed. The update gains Γ ₂ and Γ ₅ for the steady gains b ₀ / a ₀ of the system are set larger than the update gains Γ ₁ , Γ ₃ , and Γ ₄ for the other parameters. This is because if all parameters are changed at the same speed, they diverge. In addition, even if the steady-state gain numerator b ₀ and denominator a ₀ are changed at the same speed, they diverge, so one of Γ ₂ and Γ ₅ is set larger than the other. In the present embodiment, the update gain Γ ₂ is set larger than the other update gains Γ ₁ , Γ ₃ , Γ ₄ , and Γ ₅ . Of course, conversely, the update gain Γ ₅ may be set larger than the other update gains Γ ₁ , Γ ₂ , Γ ₃ , Γ ₄ .

  Due to the nature of the Lyapunov function, if the derivative of this can be made 0 or less, each error approaches 0. Therefore, let us consider making the derivative of the Lyapunov function negative. The differentiation of the equation (Equation 16) becomes the following equation (Equation 18).

The differential of the error z ₁ is the following equation (Equation 19).

Since y = x ₁ , the differentiation of y is equal to the differentiation of x ₁ , and the following equation (Equation 20) is obtained.

  Substituting equation (Equation 6) into the above equation (Equation 20) and rearranging results in the following equation (Equation 21).

  Further, when the above equation (Equation 21) is substituted into the equation (Equation 19) and rearranged, the following equation (Equation 22) is established.

  Substituting the above equation (Equation 22) into the differential equation (Equation 18) of the Lyapunov function yields the following equation (Equation 23).

In order to make the right side of the above equation (Equation 23) 0 or less, the filter signal v _1,2 is considered as a virtual input in place of the state variable x ₂ , and its ideal value is α ₁ . In this case, v _1,2 can be expressed by the following equation (Equation 24).

z ₂ is an error between the actual virtual input and its ideal value. In normal backstepping control, the above equation (Equation 24) is substituted into the Lyapunov function (differential equation thereof). However, in the present embodiment, the error z ₂ is deliberately ignored, and the following expression (Expression 25) not including z ₂ is substituted. Since the error z ₂ is always considered in the second step, it is thought that it is not necessary to take it into consideration in the first step.

By not adding the error z ₂ to the Lyapunov function V ₁ in the first step, the enlargement of the input u calculated by the backstepping controller can be suppressed. As a result, the possibility of giving the control input value u exceeding the physical limit of the ISC valve 4 to the ISC valve 4 can be reduced or avoided.

Then, the ideal value α ₁ of the virtual input is selected as in the following equation (Equation 26).

c ₁ is a gain for the error z ₁ . Substituting α ₁ in the above equation (Equation 26) as v _1,2 in the equation (Equation 23) and rearranging it yields the following equation (Equation 27).

  Then, update rules (Equation 28) and (Equation 29) are selected such that the second and third terms on the right side of the above equation (Equation 27) are zero.

Since δ does not appear in the second step, the update rule of Expression (Equation 28) can be used in the first step, and the influence of δ can be eliminated. On the other hand, since θ is also included in α ₁ and appears in the second step, the update rule of Expression (Equation 29) cannot be used in the first step. When z ₂ ≠ 0, the equation (Equation 29) is not guaranteed. With respect to the differential value of the Lyapunov function V ₁ , the following equation (Equation 30) holds.

In the second step of the backstepping controller design, the true input u is set so that the error z ₂ = v _1,2 −α ₁ becomes zero. Since it was not possible to guarantee that the differential value of the Lyapunov function V ₁ was negative in the first step, it is necessary to take the Lyapunov function V ₁ into consideration in this second step. The Lyapunov function V ₂ about the error z _2, defined by the following equation (Equation 31).

d ₂ is a gain for the state quantity estimation error. As in the first step, consider making the derivative of the Lyapunov function negative. The differentiation of the equation (Equation 31) becomes the following equation (Equation 32).

The differentiation of z ₂ is expressed by the following expression (Expression 33) from Expression (Expression 11) and Expression (Expression 24).

  Substituting the equation (Equation 30) and the above equation (Equation 33) into the differential equation (Equation 32) of the Lyapunov function, the following equation (Equation 34) is obtained.

  In order to make the right side of the above equation (Equation 34) 0 or less, an update rule (Equation 35) is selected so that the second term on the right side becomes 0.

  If the update rule of Formula (Equation 35) is used in the second step, the influence of θ can be eliminated. Further, when the control input u that makes the third and fourth terms on the right side of the equation (Equation 34) negative is obtained, the following equation (Equation 36) is obtained.

c ₂ is a gain with respect to the error z ₂ . By substituting the above formula (formula 36) and formula (formula 35) into the formula (formula 34) and rearranging, the following formula (formula 37) regarding the differential value of the Lyapunov function V ₂ is established.

From the above equation (Equation 37), it becomes clear that the differential value of the Lyapunov function V ₂ is negative, and the stability of the control system is guaranteed.

According to the present embodiment, since the servo control of the engine speed is performed in the backstepping control system without an integrator, it is possible to improve the disturbance suppression performance by increasing the gain c ₁ with respect to the deviation z ₁ . It becomes. However, chattering may occur in the control input u by increasing the gain c ₁ applied to the deviation z ₁ , and in this case, countermeasures are required.

In the first step of the error z ₁ control output y and the target value y _r to set the ideal value alpha ₁ for the virtual input x ₂ such that 0, the error z ₁ between the output y and the target value y _r On the other hand, a Lyapunov function V ₁ not including an error z ₂ between the ideal value α ₁ of the virtual input and the actual virtual input v _1,2 is defined, and the ideal value α ₁ of the virtual input x ₂ and the actual virtual input v in the second step of the error z ₂ sets the true input u such that 0 and _1, and the error z ₂ and the actual virtual input v ₂ the ideal value alpha ₁ for the virtual input x ₂ The Lyapunov function V ₂ including the Lyapunov function V ₁ defined in the first step is defined, and the controller 1 is designed so that the differential value of the Lyapunov function V ₂ is 0 or less to control the engine speed. Therefore, it is possible to avoid the problem that the input u, that is, the valve opening becomes an excessive value exceeding the limit. . If the differential value of the Lyapunov function V ₂ in the second step of the design process is 0 or less, the backstepping control can be made stable.

Of the parameter update gains Γ ₁ , Γ ₂ , Γ ₃ , Γ ₄ , Γ ₅ for updating the parameters b ₁ , b ₀ , a ₂ , a ₁ , a ₀ of the model, parameters corresponding to the numerator and denominator of the steady gain Since the update gains Γ ₂ and Γ ₅ for b ₀ and a ₀ are set larger than the update gains Γ ₁ , Γ ₃ and Γ ₄ for the other parameters b ₁ , a ₂ and a ₁ , Only the steady gain b ₀ / a ₀ that affects the convergence to the target value can be changed quickly, and the changes of the other parameters b ₂ , b ₁ , a ₁ can be delayed, and the parameters b ₁ , b ₀ , a ₂ can be delayed. , A ₁ and a ₀ can be avoided. As long as the steady gain b ₀ / a ₀ converges to the true value, the engine speed can be sufficiently set to the target value even if the other parameters b ₁ , a ₂ , a ₁ cannot be converged to the true value. Can be followed.

In addition, the update gain Γ ₂ for one of the parameter b ₀ corresponding to the numerator of the steady gain and the parameter a ₀ corresponding to the denominator is set larger than the update gain Γ ₅ for the other, and the steady gain The divergence of b ₀ / a ₀ can be avoided and reliably converged.

  The present invention is not limited to the embodiment described in detail above. In particular, it is naturally possible to apply the backstepping control according to the present invention to control of the engine speed other than during idling.

  Further, the operation unit operated by the backstepping controller 1 is not limited to the ISC valve 4, and may be an electronic throttle valve 5, for example. At this time, the controller 1 calculates the opening degree of the electronic throttle valve 5 as a control input.

  Other specific configurations of each part can be variously modified without departing from the spirit of the present invention.

The hardware resource block diagram of the engine and rotation speed control apparatus in one Embodiment of this invention. The block diagram of a rotation speed control apparatus.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 ... Controller 2 ... Engine 3 ... Rotational speed sensor 4 ... ISC valve (operation part)
5 ... Electronic throttle valve (operation part)

Claims (4)

The engine speed is controlled by operating an operation unit such as an ISC (Idle Speed Control) valve by a backstepping controller having no integrator.
In the first step of setting the ideal value of the virtual input such that the error between the output and its target value is zero, the error between the output and the target value is included, while the ideal value of the virtual input and the actual virtual input Define Lyapunov function without error,
In the second step of setting a true input such that the error between the ideal value of the virtual input and the actual virtual input is 0, the error between the ideal value of the virtual input and the actual virtual input is determined in the first step. An engine speed control method characterized in that a Lyapunov function including a defined Lyapunov function is defined and a controller in which a differential value of the Lyapunov function is 0 or less is designed to control the engine speed. 2. The engine according to claim 1, wherein among the parameter update gains for updating the parameters of the system model, the update gains for the parameters corresponding to the numerator and denominator of the steady gain are set larger than the update gains for the other parameters. Speed control method. The engine speed control method according to claim 2, wherein an update gain for one of the parameter corresponding to the numerator of the steady gain and the parameter corresponding to the denominator is set to be larger than the update gain for the other. Input the valve opening of an ISC valve, etc., and output the engine speed.
In the first step of setting the ideal value of the virtual input such that the error between the output and its target value is zero, the error between the output and the target value is included, while the ideal value of the virtual input and the actual virtual input Define Lyapunov function without error,
In the second step of setting a true input such that the error between the ideal value of the virtual input and the actual virtual input is 0, the error between the ideal value of the virtual input and the actual virtual input is determined in the first step. An engine speed control device comprising a backstepping controller that defines a Lyapunov function including a defined Lyapunov function and is designed so that a differential value of the Lyapunov function is 0 or less.

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