Section Thirteen Section Thirteen Section Thirteen Section Thirteen Section Thirteen Vehicle control systems 391 This page is left intentionally left blank Chapter 13.1 Vehicle motion control William Ribbens 13.2 Typical cruise control system The term vehicle motion refers to its translation along and Automotive cruise control is an excellent example of the rotation about all three axes (i., longitudinal, lateral, type of electronic feedback control system. Recall that and vertical). By the term longitudinal axis, we mean the the components of a control system include the plant, or axis that is parallel to the ground (vehicle at rest) along system being controlled, and a sensor for measuring the the length of the car. The lateral axis is orthogonal to plant variable being regulated.
It also includes an elec- the longitudinal axis and is also parallel to the ground tronic control system that receives inputs in the form of (vehicle at rest). The vertical axis is orthogonal to both the desired value of the regulated variable and the mea- the longitudinal and lateral axes. sured value of that variable from the sensor. The control Rotations of the vehicle around these three axes cor- system generates an error signal constituting the differ- respond to angular displacement of the car body in roll, ence between the desired and actual values of this vari- yaw, and pitch.
Roll refers to angular displacement about able. It then generates an output from this error signal the longitudinal axis; yaw refers to angular displacement that drives an electromechanical actuator. The actuator about the vertical axis; and pitch refers to angular dis- controls the input to the plant in such a way that the placement about the lateral axis. regulated plant variable is moved toward the desired Electronic controls have been recently developed with value.
the capability to regulate the motion along and about In the case of a cruise control, the variable being reg- all three axes. Individual car models employ various ulated is the vehicle speed. The driver manually sets the selected combinations of these controls. This chapter car speed at the desired value via the accelerator pedal.
discusses motion control electronics beginning with Upon reaching the desired speed the driver activates control of motion along the longitudinal axis in the form a momentary contact switch that sets that speed as the of a cruise control system. command input to the control system. From that point The forces that influence vehicle motion along the on, the cruise control system maintains the desired speed longitudinal axis include the powertrain (including, in automatically by operating the throttle via a throttle selected models, traction control), the brakes, the aero- actuator. dynamic drag, and tire-rolling resistance, as well as the Under normal driving circumstances, the total drag influence of gravity when the car is moving on a road with forces acting on the vehicle are such that a net positive a nonzero inclination (or grade).
In a traditional cruise traction force (from the powertrain) is required to control system, the tractive force due to the powertrain maintain a constant vehicle speed. However, when the is balanced against the total drag forces to maintain car is on a downward sloping road of sufficient grade, a constant speed. In an ACC system, brakes are also constant vehicle speed requires a negative tractive force automatically applied as required to maintain speed that the powertrain cannot deliver. In this case, the car when going down a hill of sufficiently steep grade.
will accelerate unless brakes are applied. For our initial Understanding Automotive Electronics; ISBN: 9780750675994 Copyright Ó 2003 Elsevier Ltd; All rights of reproduction, in any form, reserved.1 Vehicle motion control ACTUAL CONTROL SPEED SIGNAL THROTTLE CONTROLLER ACTUATOR S1 COMMAND SPEED ELECTRICAL POWER S2 TO DRIVE AXLES SPEED AIR ENGINE SENSOR THROTTLE Fig.1-1 Cruise control configuration. discussion, we assume this latter condition does not pedal-activated switch that disables the cruise control occur and that no braking is required. any time that the brake pedal is moved from its rest The plant being controlled consists of the powertrain position.
The throttle actuator opens and closes the (i., engine and drivetrain), which drives the vehicle throttle in response to the error between the desired and through the drive axles and wheels. As described above, actual speed. Whenever the actual speed is less than the the load on this plant includes friction and aerodynamic desired speed the throttle opening is increased by the drag as well as a portion of the vehicle weight when the actuator, which increases vehicle speed until the error is car is going up and down hills. zero, at which point the throttle opening remains fixed The configuration for a typical automotive cruise until either a disturbance occurs or the driver calls for control is shown in Fig.
The momentary contact a new desired speed. (pushbutton) switch that sets the command speed is A block diagram of a cruise control system is shown denoted S1 in Fig. Also shown in this figure is in Fig. In the cruise control depicted in this a disable switch that completely disengages the cruise figure, a proportional integral (PI) control strategy has control system from the power supply such that throttle been assumed.
However, there are many cruise control control reverts back to the accelerator pedal. This switch systems still on the road today with proportional (P) is denoted S2 in Fig.1-1 and is a safety feature. In an controllers. Nevertheless, the PI controller is repre- actual cruise control system the disable function can be sentative of good design for such a control system since activated in a variety of ways, including the master it can reduce speed errors due to disturbances (such as power switch for the cruise control system, and a brake hills) to zero.
In this strategy an error e is formed by PROPORTIONAL PART KPe VEHICLE DESIRED E SPEED THROTTLE ENGINE SPEED ACTUATOR DRIVETRAIN Vd Va KI∫eDT INTEGRAL PART SPEED SENSOR Fig.1-2 Cruise control block diagram. 394 Vehicle motion control CHAPTER 13.1 subtracting (electronically) the actual speed Va from activated the speed set switch. If the car is traveling on the desired speed Vd: a level road at the desired speed, then the error is zero and the throttle remains at a fixed position. e ¼ Vd Va If the car were then to enter a long hill with a steady positive slope (i., a hill going up) while the throttle is The controller then electronically generates the actuator set at the cruise position for level road, the engine will signal by combining a term proportional to the error produce less power than required to maintain that speed ðKP eÞ and a term proportional to the integral of the error: on the hill.
The hill represents a disturbance to the cruise ð control system. The vehicle speed will decrease, thereby KI e dt introducing an error to the control system. This error, in turn, results in an increase in the signal to the actuator, The actuator signal u is a combination of these two terms: causing an increase in engine power. This increased power results in an increase in speed.
However, in ð a proportional control system the speed error is not re- u ¼ KP e þ KI e dt duced to zero since a nonzero error is required so that the engine will produce enough power to balance the in- The throttle opening is proportional to the value of this creased load of the disturbance (i. The speed response to the disturbance is shown in Operation of the system can be understood by first Fig. When the disturbance occurs, the speed considering the operation of a proportional controller drops off and the control system reacts immediately to (i., imagine that the integral term is not present for the increase power. However, a certain amount of time is sake of this preliminary discussion).
We assume that the required for the car to accelerate toward the desired driver has reached the desired speed (say, 60 mph) and speed. As time progresses, the speed reaches a steady Fig.1-3 Cruise control speed performance.1 Vehicle motion control Fig.1-3 Continued value that is less than the desired speed, thereby ac- said to be underdamped, and one greater than critically counting for the steady error (es) depicted in Fig.1-3a damped is said to be overdamped., the final speed is less than the starting 60 mph). If we now consider a PI control system, we will see 13.1 Speed response curves that the steady error when integrated produces an ever- increasing output from the integrator. This increasing The curves of Fig.1-3c show the response of a cruise output causes the actuator to increase further, with control system with a PI control strategy to a sudden a resulting speed increase.
In this case the actuator disturbance. These curves are all for the same car cruising output will increase until the error is reduced to zero. initially at 60 mph along a level road and encountering an The response of the cruise control with PI control is upsloping hill. The only difference in the response of shown in Fig.
these curves is the controller gain parameters. The response characteristics of a PI controller depend Consider, first, the curve that initially drops to about strongly on the choice of the gain parameters KP and KI. 30 mph and then increases, overshooting the desired It is possible to select values for these parameters to in- speed and oscillating above and below the desired speed crease the speed of the system response to disturbance. until it eventually decays to the desired 60 mph.
This If the speed increases too rapidly, however, overshoot curve has a relatively low damping ratio as determined by will occur and the actual speed will oscillate around the the controller parameters KP and KI and takes more time desired speed. The amplitude of oscillations decreases to come to the final steady value. by an amount determined by a parameter called the Next, consider the curve that drops initially to about damping ratio. The damping ratio that produces the 40 mph, then increases with a small overshoot and fastest response without overshoot is called critical decays to the desired speed.
The numerical value for this damping. A damping ratio less than critically damped is damping ratio is about 0.7, whereas the first curve had 396 Vehicle motion control CHAPTER 13.1 a damping ratio of about 0. Finally, consider the solid the problem. This formulation correctly describes the curve of Fig.
This curve corresponds to critical concept for cruise control regardless of whether the damping. This situation involves the most rapid response implementation is by analog or digital electronics. Cruise of the car to a disturbance, with no overshoot. control is now mostly implemented digitally using a mi- The importance of these performance curves is that croprocessor-based computer.
For such a system, pro- they demonstrate how the performance of a cruise con- portional and integral control computations are trol system is affected by the controller gains. These gains performed numerically in the computer. A block diagram are simply parameters that are contained in the control for a typical digital cruise control is shown in Fig. They determine the relationship between the The vehicle speed sensor (described later in this chapter) error, the integral of the error, and the actuator control is digital.
When the car reaches the desired speed, Sd, the signal. driver activates the speed set switch. At this time, the Usually a control system designer attempts to balance output of the vehicle speed sensor is transferred to the proportional and integral control gains so that the a storage register. system is optimally damped.
However, because of The computer continuously reads the actual vehicle system characteristics, in many cases it is impossible, speed, Sa, and generates an error, en, at the sample time, impractical, or inefficient to achieve the optimal time tn (n is an integer). en ¼ Sd Sa at time tn.