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SAE TECHNICAL PAPER SERIES
1999-01-0399
Modeling and Analysis of an Electric
Power Steering System
Aly Badawy, Jeff Zuraski, Farhad Bolourchi and Ashok Chandy
Delphi Saginaw Steering Systems
Reprinted From: Steering and Suspension Technology Symposium 1999
(SP-1438)
International Congress and Exposition申请信
Detroit, Michigan March 1-4, 1999
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1999-01-0399 Modeling and Analysis of an Electric Power Steering System
Aly Badawy, Jeff Zuraski, Farhad Bolourchi and Ashok Chandy
Delphi Saginaw Steering Systems Copyright © 1999 Society of Automotive Engineers, Inc.
ABSTRACT
An Electric Power Steering (EPS) System will be consid-ered in this report. The modeling of this dynamic system will be achieved with both simplicity and usability taken into account. As such, a Reduced Order Model that reveals the important dynamic distinctions of the system will be developed from a more complex one. This model will be ud to analyze various clod loop effects such as torque performance, disturbance rejection, noi rejection, road feel, and stability. The fundamental effects (compromis) are ud toward the design of a desired control system. This modeling philosophy together with a comprehensive understanding of system compromis is esntial to an optimized EPS system. INTRODUCTION
Electric Power Steering is without a doubt, the most excit-ing improvement to steering systems since the introduc-tion of hydraulic power steering, some 50 years ago. It achieves the almost impossible:
simplifies the system -provides additional benefits - introduces virtually no side effects or costs. The details of all the benefits as pro-vided by Delphi’s EPS system, is outlined in [1]. Here, it suffices to merely point them out in the following catego-ries:
•Engine Independence / Fuel Economy
•T unability of Steering Feel
•Modularity / Quick Asmbly
•Compact Size
•Environmental Friendliness
In this paper, we shall take a technical dive into the c-ond bullet. Our focus will be to look at some of the model-ing techniques and other technical tools to achieve a desired steering feel. Therefore, following a brief descrip-tion of the E•Steer™ system, Reduced Order Modeling will be introduced. With this model validated, the clod loop characteristics of the system can be analyzed. Finally, with a thorough understanding of the clod loop behaviors, control system Algorithms are defined. With proper tuning a particular steering feel is achieved and demonstrated toward the end o
f this paper. Conclu-sion will look back at what has been accomplished. Some thoughts for continuous improvements are also given. SYSTEM ARCHITECTURE
Figure 1.E•Steer™ incorporated in the steering system An E•Steer™ system in its column assist configuration is shown in Figure 1. The system is made up of: a Steering Column, a Gear Assist mechanism attached to this col-umn, a Brushless Motor, a Controller and a Sensor within the assist housing. The rest of the steering system: Steering Wheel (or hand wheel, HW), Intermediate Shaft (I-Shaft), Rack & Pinion, and the Tie Rods are also shown.
The main purpo of any power steering system is, of cour, to provide assist to the driver. This is achieved by the torque nsor, which measures the driver’s torque and nds a signal to the controller proportional to this torque. The controller also receives steering position information from the position nsor that is collocated with the torque nsor and together they make up the Sensor. The torque and position information is procesd in the controller and an assist command is generated. This assist command is further modulated by the vehicle speed signal, which is also received by the controller.
This command is given to the motor, which provides the
torque to the assist mechanism. The gear mechanism amplifies this torque, and ultimately the loop is clod by applying the assist torque to the steering column. The power source from the battery and
motor position signals (i.e. Hall-effect signals coming from the motor asmbly which are ud to commutate the brushless motor) are also shown in Figure 1.
Other EPS architectures such as Rack Assist, Pinion Assist, etc. have also been propod by Delphi and oth-ers. The different configurations, while important with respect to packaging, environmental effects, etc. are of little conquence to the discussion of this paper. There-fore, the Column Assist architecture shown in Figure 1 is the primary candidate considered for the upcoming anal-ysis.
REDUCED ORDER MODELING
81年属什么From a mechanical point of view, the steering system is made of (or maybe modeled with) many mass or iner-tias lumped together with springs and dampers (or fric-tion elements). Figure 2 sketches a complete (Full Order)model of an EPS system.
带生的成语Very simply put, Reduced Order Modeling, means con-sider the Full Order Model of Figure 2 and ask the follow-ing question: Can the number of mass (or inertias) be reduced by combining two or more of the mass into one? The answer to this question lies in the existence of overly stiff elements that connect the mass. If there are elements that are much stiffer than others, the answer is perhaps yes. This reduction in modeling order stems from the fact that higher stiffness contribute to higher frequency modes that usually are inconquential to the fundamental behavior of the system (dominated by lower frequency modes).
The mechanics of model reduction can be explained by considering the rack and tie rod connection of Figure 2.The rack mass (M R ) is linked to each one of the tie rods mass (M TR ) through the stiff inner ball joint stiffness K IBJ to be eliminated (e Figure 3). Note that in the Full
Order Model there are 3 degrees of freedom. In the Reduced Order Model, the tie rod mass are eliminated,
and thus, there is one degree of freedom (X R ) left. The equations of motion for the Full Order Model are:
where:
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F P
=Force from pinion
F ROBJ =Force from right outer ball joint F LOBJ =Force from left outer ball joint X R =Rack displacement X RTR =Right tie rod displacement X L TR
=Left tie tod displacement
Figure 2.Full order model of an EPS system
Figure 3.Reduced Order Model of an EPS system
LTR
TR
LTR
R
IBJ
LOBJ
RTR
兔子单词怎么读
TR RTR R IBJ ROBJ R R R RTR IBJ P X M )X
X (K F X M )X X (K F X M )X X (K 2F =−+=−+=−−
Now, to reduce this, assume X R = X RTR = X LTR (i.e. K IBJ is very stiff.) The equation of motion for the Reduced Order Model becomes:
The algebra gets a bit more complicated if power-trans-forming elements such as gears are involved in the
reduction process. The method is the same, however,and the result is simplification.
But why do we want to reduce the model anyway? What’s wrong with having a complicated (and arguably more accurate) model? The primary answer to this question is that unnecessary complexity (i.e. high frequency dynam-ics) brings with it undue confusion. Attention may be given to unimportant dynamics as oppod to important ones. In other words, “the forest may be misd for the branches.” Furthermore, with a complex model simula-tions take more time to run and even the resulting com-pensation design could become more complex than it needs to be. The latter could po all kinds of implemen-tation issues, also.
Of cour, too much reduction is dangerous too. At the end, it becomes an engineering call as to how much model reduction is just right. Perhaps, the single most important reason for model reduction is that through the arch for finding the “Optimal Reduced Order Model” an invaluable understanding of the dynamics of the system is acquired.
So far, we have been focusing on model reduction with respect to mechanical elements. The same philosophy may be applied to electrical effects. Should we include motor induction effects, or not? Can we neglect the Pul Width Modulation (PWM) effects, or not?
Figure 4 shows the step respon comparisons between the Full and Reduced Order models. As it can be en,the two simulations give identical results (solid and dashed lines are indistinguishable). Y et, the Reduced Order Model simulation took roughly one tenth of the time of the Full Order Model to finish.
CLOSED LOOP CHARACTERISTICS
Along with model reduction, the other necessary step before uful results can be deduced from the
model, is indeed, model validation. Sometimes, before decisions about model reduction can be made, preliminary model validation must be ascertained. Therefore, model reduc-tion and validation could very well be an iterative process.There are many ways of validating a model. Without get-ting into a discussion on various means of achieving this goal, we have found the frequency respon test of a vehicle equipped with the E•Steer™ to be most uful and convenient. Figure 5 helps to visualize this test. The idea is to validate the open loop plant or the Steering System Model block. This is achieved by nullifying the Control algorithms block to a known constant gain, dis-connecting (or zeroing) other inputs such as vehicle speed and position, opening the torque loop between the Sensor and the Control algorithms block. Using a signal analyzer, a sinusoidal signal is injected to the controller at the opened node of the loop and the respon of the sys-tem is measured from the nsor at the same node. The input frequency is varied (i.e. swept) through a defined range and the plots of output/input magnitudes and pha vs. the frequency is generated (e Figure 6).
Figure 4.Comparison of full and reduced order models
Figure 5.Clod Loop Block Diagram and Open Loop
validation test tup中国研究生招生信息网官网
R
R R TR R LOBJ ROBJ p X M X )M 2M (F F F eff =+=++香辣鸭脖
