CN106647288A - Method for estimating indicating torque of engine based on nonsingular terminal sliding mode observer - Google Patents

Abstract

The invention discloses a method for estimating an indicating torque of an engine based on a nonsingular terminal sliding mode observer. The method comprises the following steps of: establishing an accurate nonlinear engine crankshaft dynamical model; performing real-time measurement on crankshaft angle and engine speed, taking as an observer input and performing differential operation; and utilizing the nonsingular terminal sliding mode observer to change an estimating value of the indicating torque, thereby causing the estimating value of the crankshaft angular velocity gradually approach to the constantly changing practical measurement value. According to the method disclosed by the invention, the nonsingular terminal sliding mode observer is utilized to online estimate the indicating torque of the engine, has excellent robustness to the modeling error and the parameter perturbation, is short in convergence time and is high in estimating precision. According to the method disclosed by the invention, the estimating precision of the indicating torque is guaranteed.

Description

Engine indication torque method of estimation based on non-singular terminal sliding mode observer

Technical field

The invention belongs to automobile engine indication torque method of estimation, and in particular to a kind of to be seen based on non-singular terminal sliding formwork Survey the engine indication torque method of estimation of device (NTSMO).

Background technology

Indication torque reliably obtains in real time indication torque and not only may be used as an important parameter of engine power performance With correctly engine evaluated service behaviour, in real time monitoring failure occurs, and can implement phase to engine and speed changer Close strategy and be optimized control.In the case of rotating speed and load change, the fuel economy of automobile can be effectively improved, driven Comfortableness and vehicle safety.Further, since engine indication torque cannot direct access, by install cylinder pressure sensors Obtaining cylinder pressure can be calculated indication torque, but the method is restricted in actual application.Therefore, how Estimate to obtain the extensive concern that indication torque causes educational circles indirectly.

In recent years, Chinese scholars have been carried out many correlative studys for the estimation of indication torque, and achieve certain Achievement.Indication torque is estimated by nonlinear observer, accuracy and robustness are preferable.However, some of them are estimated Meter method comprehensively, causes observer estimated accuracy to reach requirement due to considering model nonlinear characteristic not.Due to building Parameter uncertainty, model disturbance in mold process, observer there are problems that in itself system chatter, be required for It is adjusted in the design of observer and parameters setting process.Document [1] is proposed based on instantaneous speed of crankshaft analysis and one Cylinder pressure sensor is combined, for analyzing the fired state of each cylinder.Using with reference to cylinder correcting indication torque result, due to being independent of Complicated algorithm, precision is higher.But, because having used cylinder pressure sensor, practical application is but restricted；Document [2] adopts base Indication torque is estimated in the Cerebellar Model Articulation Controller of brief inference, it is higher to model accuracy dependency degree, and parameter is multiple When miscellaneous, the amount of calculation of system is than larger；Document [3] is estimated engine torque to be divided into two kinds of operating modes of stable state and transient state, and respectively From giving control error range；Document [4] by the use of engine speed as input, in the steady state using Orthogonal Least Square Estimate, transient state then using the recognition methods based on time domain, is estimated braking torque；Document [5] is to indication torque and bears Carry moment of torsion all to be estimated, have ignored the impact that piston excursion concentrates effective inertia to bent axle, improve the accuracy of estimation； Document [6], using High-gain observer, it is considered to the turning effect of bent axle, improves the standard of estimation by setting up nonlinear model True property；Document [7] combines sliding mode observer by theoretical " supertwist " algorithm of Second Order Sliding Mode, eliminates delayed phase and time The larger error that delay brings to estimated result, it is suppressed that jitter phenomenon, improves indication torque estimated accuracy；Document [8] will Kalman filter, using the IC engine dynamic model based on physics time-varying, improves calculating in combination with sliding mode observer Speed, enhances the stability of algorithm, but amount of calculation is excessive；The crankshaft angles reality that document [9] is obtained by crankshaft sensor When delta data, combine by non-linear pair of inertial model and based on the interference observer of I class of UKF, solve in information wrap The impact that vibration interference signal its vibration frequency for containing is estimated indication torque in combustion cycle process；Document [10] analysis is right The difference of High-gain observer, sliding mode observer and Second Order Sliding Mode observer to indication torque On-line Estimation is compared, it is contemplated that flat Estimated result under steady state operating mode different with instantaneous state, although traditional sliding mode observer degree of accuracy is somewhat seen better than high-gain Device is surveyed, but buffeting problem cannot be avoided；Document [11] using sliding mode observer estimate cylinder deviation torque, i.e. indication torque and The difference of average indication torque.Input estimation problem is converted to control tracking problem；Document [12] adopts sliding mode observer The difference of dynamic torque, i.e. indication torque and load torque is estimated, the acquisition of load torque is can be avoided, using cunning The estimation robustness of mould observer is preferable, but the time of convergence has much room for improvement.

The content of the invention

In consideration of it, the present invention exists not for available engine crankshaft dynamic model and indication torque method of estimation Foot, needs to estimate indication torque using method that is a kind of reasonable and easily realizing, so that estimate can be good at being close to Actual value.A kind of engine indication torque method of estimation based on non-singular terminal sliding mode observer (NTSMO) is provided, using song The continuous reduction of axis angular rate error come guarantee indication torque estimate precision.

To achieve these goals the present invention is adopted the following technical scheme that：Based on starting for non-singular terminal sliding mode observer Machine indication torque method of estimation, comprises the following steps：

Obtain crank shaft angle θ of engine real-time change, and Engine Instantaneous Speed Signals；Set up and be based on crank angle θ With indication torque T_i, inertia torque T_r, friction torque T_fWith load torque T_lThe non-linear crankshaft dynamic mould of multicylinder engine Type.

According to crank shaft angle θ, angular velocity of crankshaftAnd crankshaft angular accelerationBetween relation, calculate crankshaft angular acceleration.

Set up non-singular terminal sliding-mode surface s.

Estimate that equation is calculated indication torque estimate according to indication torque

When continuous injection signal can order about sliding-mode surface s to zero, then output obtains indication torque estimate

Any several ε for being more than zero are less than when sliding-mode surface s is unsatisfactory for condition, i.e. value, then angular acceleration estimateCarry out Integral operation, obtains angular velocity of crankshaft estimateReturn system recalculates indication torque estimate

The non-linear crankshaft dynamic model of the multicylinder engine is：

OrderUse angular velocity of crankshaft estimateReplace angular velocity of crankshaft ω,

In formula：

J_e=m₁r²[f(θ)]²+m₂r²

For indication torque estimate；J_eIt is the inertia equation with regard to crank shaft angle θ；m₁For equivalent reciprocal lumped mass；m₂For Equivalent rotary lumped mass；R is crank throw；D is damped coefficient；M is car mass；G is acceleration of gravity；r_wFor wheel half Footpath；i_gFor transmission ratio；i_oFor main reducing gear speed reducing ratio；η_TFor speed changer mechanical efficiency；F is road damped coefficient；I is Road grade；φ_kFor kth cylinder relative to the 1st cylinder ignition phase place；N is cylinder sum；ρ is the hollow gas of traveling process Density；δ is correction coefficient of rotating mass；A front face area of automobile；C_DFor coefficient of air resistance；f(θ-φ_k)、g(θ-φ_k)、f (θ), I (θ) is respectively the different functions of crank angle geometrical relationship.

The non-singular terminal sliding-mode surface s is：

In formula, k₁, k₂It is divided into normal number, defines system convergence speed；Sgn () is sign function,For crank shaft angle speed Degree estimate, ω is angular velocity of crankshaft.

The indication torque estimates that equation is：

In formula, J (θ) is the concentration Effective Moment of Inertia of engine； Estimation for angular velocity of crankshaft is missed Difference.

The present invention has advantages below：

(1) because engine crankshaft dynamic system is the nonlinear system of a complexity, comprising many uncertain variables, Using the suitably smooth injection signal of non-singular terminal sliding mode observer and selection, it is more beneficial for completing the instruction to measuring Moment of torsion carries out On-line Estimation.

(2) in modeling process, automobile dynamics equation is introduced according to automobile theory, load torque variable is carried out Explanation.Improve the accuracy of modeling.

Description of the drawings

Fig. 1 is indication torque controller architecture block diagram；

Fig. 2 is that indication torque estimates flow chart；

Fig. 3 is angular velocity of crankshaft tracking error curve；

Fig. 4 is indication torque aircraft pursuit course；

Fig. 5 is indication torque tracking error curve.

Specific embodiment

Below in conjunction with the accompanying drawings the invention will be further described.

Indication torque method of estimation based on non-singular terminal sliding mode observer of the present invention, indicates to turn round by changing The estimate of squareForce the estimate of angular velocity of crankshaftThe measured value ω that tracking is actually continually changing.In slip forming, The evaluated error of angular velocity of crankshaftIt is gradually reduced, it is ensured that the convergence of system.Tied by Li Yapu loves stability theorem Close sliding formwork control and select suitable injection signal, it is to avoid system chatter simultaneously eliminates steady-state error.

Referring to Fig. 2, based on the engine indication torque method of estimation of non-singular terminal sliding mode observer, including following step Suddenly：

Obtain crank shaft angle θ of engine real-time change, and Engine Instantaneous Speed Signals；Set up and be based on crank angle θ With indication torque T_i, inertia torque T_r, friction torque T_fWith load torque T_lThe non-linear crankshaft dynamic mould of multicylinder engine Type.

According to crank shaft angle θ, angular velocity of crankshaftAnd crankshaft angular accelerationBetween relation, calculate crankshaft angular acceleration.

Set up non-singular terminal sliding-mode surface s.

Estimate that equation calculates indication torque and estimates to refer to according to indication torque

When continuous injection signal can order about sliding-mode surface s to zero, then output obtains indication torque estimate

When sliding-mode surface s is unsatisfactory for condition, i.e. value less than any several ε for being more than zero, then to crankshaft angular acceleration estimate Computing is integrated, angular velocity of crankshaft estimate is obtainedReturn system recalculates indication torque estimateCrank shaft angle adds Velocity estimation value can be obtained in indication torque estimates equation.

1) estimation of angular velocity of crankshaft

As shown in figure 1, obtaining the crank shaft angle of real-time change, and engine using crankshaft sensor and camshaft-signal sensor Transient speed signals.

According to law of conservation of energy, multicylinder engine balance equation is：

In formula, J (θ) is the concentration Effective Moment of Inertia of engine,For crankshaft angular acceleration, T_iFor indication torque, T_rFor Reciprocal inertia torque, T_fFor friction torque, T_lFor load torque.

Indication torque T_iFor total gas torque that all cylinder pressures are produced

In formula, φ_kFor kth cylinder relative to the 1st cylinder ignition phase place,A_pFor cylinder piston top cross-section Product；R is crank throw；P is cylinder pressure；N is cylinder sum.

According to the geometrical relationship of engine crankshaft corner, have

In formula, l is length of connecting rod；F (θ), g (θ) is respectively the different functions of crank angle geometrical relationship.

Inertia torque T_rEffectively move back and forth the moment of torsion for producing to concentrate：

In formula, m₁For equivalent reciprocal lumped mass.

Friction torque T_fBe by between piston and piston ring produce sliding friction, and engine pumping loss produce Total moment of torsion：

In formula, D is damped coefficient.

According to automobile dynamics equation, load torque can be obtained：

In formula, r_wFor radius of wheel, i_gFor transmission ratio, i_oFor main reducing gear speed reducing ratio, η_TImitate for speed changer machinery Rate, m is car mass, and g is acceleration of gravity, and f is road resistance coefficient, and i is road grade, and ρ is atmospheric density, and A is for windward Area, C_DFor coefficient of air resistance, δ is correction coefficient of rotating mass.

OrderBased on time domain engine dynamic bent axle rigid model expression formula be：

In formula, due to indication torque T_iCannot direct measurement.Accordingly, it would be desirable to setting up observer carries out estimation acquisition.

2) structure of non-singular terminal sliding-mode surface

Non-singular terminal sliding-mode surface s is：

In formula, k₁, k₂Respectively normal number；Sgn () is sign function,For angular velocity of crankshaft estimate, ω is bent axle Angular speed.

If system angular velocity of crankshaft estimate isDefine angular velocity of crankshaft evaluated error be

In order to realize Fast Convergent of the system mode in finite time, the non-singular terminal sliding-mode surface is：

In formula：k₁, k₂Respectively normal number.

Simultaneously differential is carried out to switching function both sides, is obtained

In the case of perfect condition, when system reaches sliding-mode surface, i.e.,

By solving the differential equation, the system convergence time is：

That is, system is convergence.

Define liapunov function：

In formula, V is the liapunov function of design, for the stability of decision-making system；S is non-singular terminal sliding formwork Face.

The injection signal is made to beHave

Then,That is system stability.

In formula, λ is postiive gain；η is the parameter that can be adjusted in injection signal.Wherein,η₀For the first of η Initial value.

During sliding formwork motion state, for the uncertain and parameter perturbation of system, most of tradition sliding formwork function Discontinuous injection signal, i.e. sign function sgn () are selected, switching function can be made to level off to zero.However, sign function category In Discontinuous Function, it is buffeted using the high frequency that can cause system.The smooth continuous injection signal that the present invention is selected, wherein including Integral term can avoid system chatter and eliminate steady-state error, robustness effect is preferable.

3) indication torque estimates equation

Indication torque estimates that equation is

Bring formula (15) into formula (16), obtain indication torque and estimate that equation is：

Therefore, closed-loop system is

In this example, engine is the stroke of four-in-line four, and its ignition cycle order is 1-3-4-2, emulates basic parameter Value is as shown in table 1：

The engine basic parameter of table 1 is configured

Fig. 3 to Fig. 5 is the simulated effect figure based on non-singular terminal sliding mode observer using the present invention.

As a result show, the method can pass through the estimate for changing indication torque, make crank shaft angle speed estimate right well Actually enter variable signal to be tracked.Finally it is obtained in that preferable indication torque estimation effect.

Bibliography：

[1] Wang Jinli, Yang Fuyuan, Ou Yangminggao, Li Jianqiu. the internal combustion engine point cylinder combustion based on cylinder cylinder pressure and transient speed Burn state estimation. internal-combustion engine engineering, 2016 (04):20-27.

[2] Huahai's moral, Ma Ning, Ma Jie, Zhang Guichen, the Yellow River. the marine diesel moment of torsion based on CMAC Neural Network is online Estimate. internal-combustion engine engineering, 2013 (01):62-66.

[3] Du Changqing, Yan Fuwu, Li Jingsong, Hou Xianjun. engine performance measuring and moment of torsion control prototype method for building up grind Study carefully. internal-combustion engine engineering, 2010 (01):60-64.

[4]Franco,J.,M.A.Franchek and K.Grigoriadis.Real-time brake torque estimation for internal combustion engines.Mechanical systems and signal processing,2008.22(2):338-361.

[5]Zweiri,Y.H.and L.D.Seneviratne,Diesel engine indicated and load torque estimation using a non-linear observer.Proceedings of the Institution of Mechanical Engineers,Part D:Journal of Automobile Engineering,2006.220(6): 775-78.

[6]Hirahara,H.,K.Yoshida and M.Iwase.Torque estimation based on nonlinear engine model considering crankshaft torsion.in Advanced Intelligent Mechatronics(AIM),2010 IEEE/ASME International Conference on.2010:IEEE.

[7] Wang Zansong, Chu Fulei. the real-time estimation based on the theoretical automobile engine indication torque of Second Order Sliding Mode. vibration Engineering journal, 2004.17 (z1):252-255.

[8]Chauvin,J.,et al.Real-time combustion torque estimation on a diesel engine test bench using time-varying Kalman filtering.in Decision and Control,2004.CDC.43rd IEEE Conference on.2004:IEEE.

[9]Itoh,Y.,K.Higashi and M.Iwase.UKF-based estimation of indicated torque for IC engines utilizing nonlinear two-inertia model.in Decision and Control(CDC),2012IEEE 51st Annual Conference on.2012:IEEE.

[10]Wang,Y.and F.Chu,Application of non-linear observers to on-line estimation of indicated torque in automotive engines.Proceedings of the Institution of Mechanical Engineers,Part D:Journal of Automobile Engineering, 2005.219(1):65-75.

[11]Wang,Y.and F.Chu,Real-time misfire detection via sliding mode observer.Mechanical systems and signal processing,2005.19(4):900-912.

[12] king's Yun pine, Chu Fulei. the automobile engine on-line monitoring and fault diagnosis based on sliding mode tracking control. Tsing-Hua University College journal, 2005.45 (2):182-185. .

Claims (5)

1. the engine indication torque method of estimation of non-singular terminal sliding mode observer is based on, it is characterised in that including following step Suddenly：

Obtain crank shaft angle θ of engine real-time change, and Engine Instantaneous Speed Signals；Set up based on crank angle θ and finger Show torque T_i, inertia torque T_r, friction torque T_fWith load torque T_lThe non-linear crankshaft dynamic model of multicylinder engine；

According to crank shaft angle θ, angular velocity of crankshaftAnd crankshaft angular accelerationBetween relation, calculate crankshaft angular acceleration；

Set up non-singular terminal sliding-mode surface s；

Estimate that equation calculates indication torque estimate according to indication torque

When continuous injection signal can order about sliding-mode surface s to zero, then output obtains indication torque estimate

When sliding-mode surface s is unsatisfactory for condition, then angular acceleration estimateComputing is integrated, angular velocity of crankshaft estimate is obtainedReturn system recalculates indication torque estimate

2. the engine indication torque method of estimation of non-singular terminal sliding mode observer is based on according to claim 1, and it is special Levy and be：The non-linear crankshaft dynamic model of the multicylinder engine is：

OrderUse angular velocity of crankshaft estimateReplace angular velocity of crankshaft ω,

$\frac{d\widehat{\mathrm{\ω}}}{dt}=\frac{1}{J\left(\mathrm{\θ}\right)}\[{\hat{T}}_i-D\widehat{\mathrm{\ω}}-I\left(\mathrm{\θ}\right){\widehat{\mathrm{\ω}}}^2-\frac{{\mathrm{mgr}}_w}{i_g{i}_o{\mathrm{\η}}_T}(f+i)\]$

In formula：

$J\left(\mathrm{\θ}\right)=J_e+m_1{r}^2\underset{k=1}{\overset{N}{\Σ}}{\[f(\mathrm{\θ}-{\mathrm{\φ}}_k)\]}^2+\frac{\mathrm{\δ}m}{{\mathrm{\η}}_T}{\left(\frac{r_w}{i_g{i}_o}\right)}^2$

$I\left(\mathrm{\θ}\right)=\frac{{\mathrm{\ρAC}}_D}{2{\mathrm{\η}}_T}{\left(\frac{r_w}{i_g{i}_o}\right)}^3{J}_e+m_1{r}^2\underset{k=1}{\overset{N}{\Σ}}{\[f(\mathrm{\θ}-{\mathrm{\φ}}_k)g(\mathrm{\θ}-{\mathrm{\φ}}_k)\]}^2$

J_e=m₁r²[f(θ)]²+m₂r²

For indication torque estimate；J_eIt is the inertia equation with regard to crank shaft angle θ；m₁For equivalent reciprocal lumped mass；m₂For equivalent Rotation lumped mass；R is crank throw；D is damped coefficient；M is car mass；G is acceleration of gravity；r_wFor radius of wheel；i_g For transmission ratio；i_oFor main reducing gear speed reducing ratio；η_TFor speed changer mechanical efficiency；F is road damped coefficient；I is road slope Degree；φ_kFor kth cylinder relative to the 1st cylinder ignition phase place；N is cylinder sum；ρ is the hollow air tightness of traveling process；δ For correction coefficient of rotating mass；A is front face area of automobile；C_DFor coefficient of air resistance.

3. the engine indication torque method of estimation based on non-singular terminal sliding mode observer according to claim 1 or claim 2, its It is characterised by：The non-singular terminal sliding-mode surface s is：

$s=(\mathrm{\ω}-\widehat{\mathrm{\ω}})+k_1{\∫}_0^t(\mathrm{\ω}-\widehat{\mathrm{\ω}})dt+k_2{\∫}_0^t{\left|\mathrm{\ω}-\widehat{\mathrm{\ω}}\right|}^{1/2}\mathrm{sgn}(\mathrm{\ω}-\widehat{\mathrm{\ω}})dt$

In formula, k₁, k₂It is divided into normal number, defines system convergence speed；Sgn () is sign function,Estimate for angular velocity of crankshaft Evaluation, ω is angular velocity of crankshaft.

4. the engine indication torque method of estimation of non-singular terminal sliding mode observer is based on according to claim 3, and it is special Levy and be：The indication torque estimates that equation is：

${\hat{T}}_i=J\left(\mathrm{\θ}\right)\[\stackrel{\·}{\mathrm{\ω}}+k_1\widetilde{\mathrm{\ω}}+k_2{\left|\widetilde{\mathrm{\ω}}\right|}^{1/2}\mathrm{sgn}\left(\widetilde{\mathrm{\ω}}\right)+\mathrm{\λ}\frac{s}{\left|s\right|+\mathrm{\η}}{\∫}_0^{t}sdt\]+D\widehat{\mathrm{\ω}}+I\left(\mathrm{\θ}\right){\widehat{\mathrm{\ω}}}^2+\frac{{\mathrm{mgr}}_w}{i_g{i}_o{\mathrm{\η}}_T}(f+i)$

In formula, J (θ) is the concentration Effective Moment of Inertia of engine； For the evaluated error of angular velocity of crankshaft.

5. the engine indication torque method of estimation of non-singular terminal sliding mode observer is based on according to claim 1 or 4, its It is characterised by：The continuous injection signal is

λ is postiive gain；η is customized parameter in injection signal, wherein,η₀For the initial value of η.