1.1. Product overview

ABS is delivered in mounted form. The mounting frame makes a support of the system. It is ready to operate after installation of its software.

KEY FEATURES

• Double-wheel laboratory model of ABS equipped with powerful, flat dc motor.
• Three high-resolution measuring encoders.
• Full integration with MATLAB^®/ Simulink^®. Operation in real-time in MS Windows^® 98/NT/2000/XP.
• Complete model of the car-road relations.
• Library of pre-programmed braking control algorithms familiarize the user with ABS technique in a fast way.
• Rapid prototyping of real-time control algorithms. No C-code programming.
• Ideal illustration of nonlinear control algorithms.

KEY BENEFITS

• Enables to provide laboratory tests of the antilock braking system in the car velocity range from 0 to 50 km/h.
• Accelerates implementation of new slip control algorithms.
• Demonstrates slip control under different road conditions.

SETUP COMPONENTS

hardware

• mechanical unit (frame, double wheel, DC flat motor),
• interface and Power Interface Unit
• I/O RT-DAC/PCI-D board (the PWM control logic is stored in a XILINX chip)

software

• ABS Control/Simulation Toolbox operating in MATLAB^®/Simulink^® environment

manuals

• Installation Manual
• Getting Started Manual

1.2. Requirements

• INTEL or AMD based PC,
• Video card resolution 1024 x 768 pixels
• MATLAB^® 6.x /Simulink^® 4.x,
• Real Time Workshop and Real Time Windows Target toolboxes
• Compiler: MS Visual C ++

The ABS toolbox supports Matlab 6.x with the MS Visual C++ compiler.

3.1. Starting procedure

Combine the acquisition board, Power Interface and ABS together. In the WINDOWS environment invoke MATLAB by double clicking on the MATLAB icon. The MATLAB command window opens. Then simply type:

abs_main

MATLAB brings up the ABS Main Control Window (see Fig. 3.1). Pushbuttons indicate an action that executes callback routines when the user selects a menu item.

The Main Control Window contains testing tools, drivers, models and demo applications. You can see a number of pushbuttons ready to use.

3.2. Testing

Double click the Manual Setup button to check connections of all components of the system. The screen given in Fig. 3.2 opens. In the left upper corner box there are two text information fields: Base Address andBitstream Version. Non zero data in these fields indicates that the RT-DAC4/PCI-D board has been correctly detected by the system. We can notice that the measurement data in this window are equal to zero. Now the following test is recommended. Change slightly the position of the Acceleration slider. The DC motor turns around. Click the Update button and Stop button. You can notice that new measurement data have appeared (see Fig. 3.3). If the new data are not visible it means that the system is assembled in a wrong way. In such a case please come back to the Installation Manual and check the connections again.

Remember Car in Fig. 3.2 and Fig. 3.3 denotes the lower wheel of the system. Wheel denotes the upper wheel.

3.3. Stopping procedure

The system is equipped with the hardware stop pushbutton. It cuts off the control transfer signal to the system drive. The pushbutton does not terminate the real-time process running in the background. Therefore to stop the task you have to use Simulation/Stop from the pull-down menus in the model window.

4.1. Tools

One can change the ABS MATLAB structure using the Manual Setup – GUI interface. Double click the Manual Setup button and the screen given in Fig. 4.1 opens.

Remember Car in Fig. 4.1 denotes the lower wheel of the system. Wheel denotes the upper wheel.

There are numerical data in the window read from the XILINX chip placed on the RTDAC4/PCI-D board. These data reflects the MATLAB structure, which includes measurements and constants assumed in the system.

In the first frame there is the basic information:

• Base Address – the autodetected base address of the RT-DAC/PCI-D board,
• Bitstream ver. − the version of the logic design for the RT-DAC/PCI-D board.

The second frame contains the information corresponding to the acceleration and brake PWM settings:

Acceleration PWM

• Mode – 12-bits or 8-bits acceleration PWM mode.
• Prescaler – the frequency of the acceleration PWM (pulse width modulation) waves. Brake PWM
• Mode – 12-bits or 8-bits brake PWM mode.

• Prescaler – the frequency of the brake PWM (pulse width modulation) waves. The next frame includes the control sliders for the acceleration and brake processes.

• They are used to control manually the acceleration and the brake of the wheel. Note, that after opening this window all controls are set to zero. Change the positions of the sliders and observe acceleration and brake processes in the system. To stop the experiment click the STOP button. The system will stop and all sliders return to the zero positions.

The next frame contains the encoder measurements:

• Positions of the both wheels expressed in meters and bumps of the balance lever expressed in radians.
• Velocities of the both wheels expressed in RPM. They are updated and refreshed when the UPDATE button is pushed.
• Marking the reset checkbox result in resetting of the encoder corresponding to that mark.

The consecutive frame shows the following measurements:

• Current Car Velocity and its maximal admissible value. If the car velocity reaches maximal value the accelerating is stopped and braking process starts.
• Current voltage of the Power Supply and its minimal acceptable value. If the voltage is under the minimum the power interface is turned off.
• Current Temperature value of the power supply and its upper limit. If temperature reaches the upper limit the power supply is turned off. It can be turn on again if the temperature falls down under the upper limit value.
• The Flag column shows if the suitable event occurs. The INACTIVE caption means that the corresponding limits have not been reached. The red ACTIVE caption indicates that the limit has been reached.

The next frame indicates if the acceleration resistors of the power interface are switched on.

• When the big DC motor driving the road wheel starts a starting current must be constrained. It is realized by switching on/off the R1 and R2 starting resistors involved into the power interface. They are turned on or off when the current car velocity reaches the Low Treshold and High Treshold. Too large starting current might result in a damage of the power interface.

The UPDATE button has to be clicked to read the current values of the all measurements accessible from the Manual Setup window.

4.2. RTWT Device Driver

The driver is a software go-between for the real ABS system MATLAB environment and the RT-DAC/PCI-D acquisition board. This driver serves to the control and measurement signals. Click the ABS Device Driver button and the driver window opens (Fig. 4.2)

The driver has two inputs: PWM input -Drive (DC motor control) and Brake (brake control). There are 5 outputs of the driver: Car position (Car) , Wheel position (Wheel), Car Velocity (Vcar), Wheel Velocity (VWheel) and Slip. When one wants to build ones own application one can copy this driver to a new model.

Do not do changes inside the original driver. They can be done only inside its copy!!!

4.3. Simulation model

The simulation model of the ABS is accessible from the ABS Simulation Model button. Its external (see Fig. 4.3) is very similar as the model given in the ABS Device Driver. Notice, that model has only one input denotedBrake. If we use the simulation model it is not necessary to accelerate the system. We set non zero initial velocities and begin the braking procedure. If we compare the simulation model to the ABS Device Driver we notice that four outputs are added to the model. These outputs are described in the section 6. The simulation model is used for many purposes: identification, design of controllers, etc. The interior of the simulation model is given in Fig. 4.4. There are two integrators introduced to obtain angular positions from angular velocities. Two gain blocks are used to calculate the appropriate units.

Set solver options to: Fixed step and Fixed-step size equal to 0.01. The Runge-Kutta solver is recommended.

In the mask presented in Fig. 4.5 you can set all coefficients of the model and introduce initial conditions for the model state variables. See section 6 for details.

4.4. Demo Controller

In this column examples of control systems are given. These demos can be used to familiarise the user with the ABS operation and allow to create the user-defined control systems. The examples must be rebuilt before using. Due to similarity of the examples we focus our attention on one of them. After clicking on the Relay button the model shown in Fig. 4.6 appears. Notice that this model looks like a typical Simulink model. The device driver is applied in the same way as other blocks from the Simulink library. The only difference is that the model is used by Real Time Windows Target (RTWT) to create the executable library, which runs in the real-time mode.

Click Controller block and next type Ctrl U . The interior of the Controller block shown in Fig. 4.7 appears. Pay attention that some blocks in Fig. 4.7 are the Enable type. These are: Acceleration block, ABS Controller block, Calculate braking distance and Stop experiment block. How the experiment is performed? At the beginning the Acceleration block is enabled. The DC motor is controlled and the wheel is accelerated until the angular velocity of the wheel reaches the velocity limit. The proper logic is placed in the Acceleration block. If the Acceleration block halts then it enables three next blocks: the ABS Controller block, Calculate braking distance and Stop experiment block. The names of the blocks correspond to the functions realized by them. The braking action runs until the car is stopped. The relay controller is applied. The interior of the ABS Controller block is given in Fig. 4.8.

Stop Experiment

We are ready now to return to the model window (see Fig. 4.6) and click the Controller block. The mask shown in Fig. 4.9 opens.

Relay

Fig. 4.9 Parameters of the relay controller

Velocity Treshold [RPM] equal to 2300 means: if velocity reaches 2300 RPM the wheel acceleration is stopped and the braking of the wheel starts. Switch point [)N OFF] equal to [0.1 0.1] means: if the slip is greater than 0.1 the relay turns on the brake, and if the slip is less than 0.1 the relay turns off the brake. Control When [ON OFF] equal to [0 1] means the control is equal to 0 when Switch Point is ON and the control is equal to 1 when Switch Point is OFF.

Then, choose the Tools pull-down menu in the Simulink model window. The pop-up menu provide a choice between predefined items. Choose the RTW Build item. A successful compilation and linking processes are finished with the following message:

Model ABS_Relay.rtd successfully created

### Successful completion of Real-Time Workshop build procedure for model:

ABS_Relay

If an error occurs then the message corresponding to this error is displayed in the MATLAB command window.

Now, we return to the model window and click the Simulation/Connect to Target option. Next, click the Simulation/Start real-time code item.

The system starts and the wheel accelerates. When the car velocity reaches upper limit (1700 rpm) the acceleration stops and the braking begins. This is visible in the plots in the scope. The experiment stops after 20 seconds.

Results displayed in the scope are stored as the structure with time in the variable ABSHistory (it has been set in the option of the scope ABS plots). In order to plot the results we can write in Matlab Command Window:

t=ABSHistory.time;

vcar=ABSHistory.signals(3).values;

slip=ABSHistory.signals(5).values;

plot(t,vcar);grid;title(‘Car velocity’);xlabel(‘time [sec]’);

plot(t,slip);grid;title(‘Slip’);xlabel(‘time [sec]’);

All experimental results related to acceleration and braking are shown in Fig. 4.10.

a = 1450; b = 1600;

plot(t(a:b),vcar(a:b));grid;title(‘Car velocity -braking time’);xlabel(‘time [sec]’);

plot(t(a:b),slip(a:b));grid;title(‘Slip -braking time’);xlabel(‘time [sec]’);

The braking phase of the experiment 1 in the zoomed form is shown in Fig. 4.11.

Car velocity Car velocity -braking time 2500

2500

2000

2000

1500

1500

1000

1000

500 500

0

0 0 2 4 6 8 10 12 14 16 18 14.4 14.6 14.8 15 15.2 15.4 15.6 15.8 16

time [sec] time [sec]

Slip Slip -braking time

1.5

1.5

1 1

0.5

0.5

0 0

-0.5

-0.5

-1 -1

-1.5

-1.5 0 2 4 6 8 10 12 14 16 18 14.4 14.6 14.8 15 15.2 15.4 15.6 15.8 16

time [sec] time [sec]

The braking distance, read out from the Breaking Distance scope is equal to 17.7 m. We can notice the time moments at the car velocity plot in which the starting resistors are turned off. We can also notice that negative slip values may appear in the plot. If small velocities are observed the numerical data are not accurate. Note that the slip often reaches zero (see Fig. 4.11). It means that in these moments the braking is off and the brake is released. In this case the braking distance is long and it shows that the applied control algorithm does not fit well to the braking task.

In this demo one can try to adjust the parameters of the control algorithm. Click Controller block and set Switch point to [0.7 0.7] (see Fig. 4.9). Next return to the model window and click theSimulation/Connect to Target option. Next, click the Simulation/Start real-time code item.

Acceleration and braking experimental results are shown in Fig. 4.12. The braking phase of the experiment in the zoomed form is given in Fig. 4.12.

Car velocity

2500

2000

1500

1000

500

0

0 2 4 6 8 10 12 14 16 18 time [sec]

Slip

1.5

1

0.5

0

-0.5

-1

-1.5

0 2 4 6 8 10 12 14 16 18 time [sec]

Car velocity -braking time

2500

2000

1500

1000

500

14.4 0	14.6	14.8	15	15.2 time [sec]	15.4	15.6	15.8	16
1.5			Slip -braking time

1

0.5

0

-0.5

-1

-1.5

14.4 14.6 14.8 15 15.2 15.4 15.6 15.8 time [sec]

Comparing the experimental results of Experiment 1 to Experiment 2 we can notice the similar car velocity plots and very different slip plots. The braking distance read from the Breaking Distance scope is equal to 12 m. This result is better than that obtained in the previous experiment. Note that the slip is equal to zero or negative only at the end of the braking zone when the car velocity is very small.

rtvdp

Next, build and run the real-time model. For details refer to the Real-Time Windows Target help, section Installation and Configuration.

To build the system that operates in the real-time mode the user has to:

• create a Simulink model of the control system which consists of the ABS system Device Driver and other blocks chosen from the Simulink library,
• built the executable file under RTWT (see the pop-up menu in Fig. 5.1)
• start the real-time code to run from the Simulation/Start real-time code pull-down menu.

5.1. Creating a model

The simplest way to create a Simulink model of the control system is to use one of the models included in the Main Control Window as a template. For example, click on the Relay button and save it asMySystem.mdl name. The MySystem Simulink model is shown in Fig.

5.2.

Now, you can modify the model. You have absolute freedom to develop your own controller. Remember to leave the ABS system driver model in the window. Though it is not obligatory, we recommend to you to live the scope block. You need a scope to watch how the system runs. Other blocks remaining in the window are not necessary for our new project. Creating your own model on the basis of an old example ensures that all-internal options of the model are set properly. These options are required to proceed with compiling and linking in a proper way. To put the ABS system Device Driver into the real-time code a special make-file is required. This file is included into the ABS system software. You can apply almost all of the blocks from the Simulink library. However, some of them cannot be used (see MathWorks references manual). The scope block properties are important for an appropriate data acquisition and watching how the system runs. The Scope block properties are defined in the Scope property window (see Fig. 5.3). This window opens after the selection of theScope/Properties tab. You can gather measurement data to the Matlab Workspace marking the Save data to workspace checkbox. The data is placed under Variable name. The variable format can be set as structureor matrix. The default Sampling Decimation parameter value is set to 1. This means that each measured point is plotted and saved. Often we choose the Decimation parameter value equal to 5 or 10. This is a good choice to get enough points to describe the signal behaviour and simultaneously to save the computer memory.

5.2. Code generation and the build process

Once a model of the system has been designed the code for real-time mode can be generated, compiled, linked and downloaded into the processor. The code is generated by the use of Target Language Compiler (TLC) (see description of the Simulink Target Language). The make-file is used to build and download object files to the target hardware automatically. First, you have to specify the simulation parameters of your Simulink model in the Simulation parameters dialog box. The RTW page appears when you select the RTW tab (Fig. 5.4). The RTW page allows you to set the real-time build options and then to start the building process of the RTW.DLLexecutable file.

The system target file name is rtwin.tlc. It manages the code generation process. Notice that the abs_win_vc.tmf template make-file is also included to the software. It is ready to be used by the Microsoft Visual C++ 6.0 compiler.

There is additional option Generate code only which have to be properly marked as shown in Fig. 5.4. If marked, a code is generated but compilation is not performed.

The Solver page appears when you select the Solver tab (Fig. 5.5). The Solver page allows you to set the simulation parameters. Several parameters and options are available in the window. The Fixed-step sizeeditable text box is set to 0.01 (this is the sampling period in seconds).

The Fixed-step solver is obligatory for real-time applications. If you use an arbitrary block from the discrete Simulink library remember that different

sampling periods must have a common divider.

The Start time has to be set to 0. The solver has to be selected. In our example the fifth-order integration method − ode5 is chosen.

If all parameters are set properly you can start the DLL executable building process. For this purpose press the Build push button on the RTW page (Fig. 5.4). Successful compilation and linking processes generate the following message:

Model MyModel.rtd successfully created ### Successful completion of Real-Time Workshop build procedure for model: MyModel

Otherwise, an error massage is displayed in the MATLAB command window.

6.1. Equations of motion

There are three torques acting on the upper wheel: the braking torque M₁ , the friction torque in the upper bearing and the friction torque among the wheels. There are two torques acting on the lower wheel: the friction torque in the lower bearing and the friction torque among the wheels. Besides these we have two forces acting on the lower wheel: the gravity force of the upper wheel and the pressing force of the shock absorber.

We can write the following motion equation for the upper wheel Jx# = F rsµ(λ) − dx − sM − sM . (6.1.1)

11 n 1 11 110 11 We can write the following motion equation for the lower wheel Jx# =−Frsµ(λ) − dx − sM . (6.1.2)

22 n 2 22 220

To derive the normal force F we can write the sum of torques corresponding to the point A

n

(see Fig. 6.2).

F_nL (sin ϕ− sµ(λ) cos ϕ) = M_g + s₁M₁ + s₁M₁₀ + d₁x₁ (6.1.3)

M + sM + sM + dx

g 11 110 11

F = . (6.1.4)

n

L(sin ϕ− sµ(λ)cos ϕ) Putting formula (6.1.4) to formulas (6.1.1) and (6.1.2) we obtain

M + sM + sM + dx

g 11 110 11

Jx# = rsµ(λ) − sM − dx − sM , (6.1.5)

11 1 11 11110

L(sin ϕ− sµ(λ)cos ϕ)

M + sM + sM + dx

g 11 110 11

Jx# =− rsµ(λ) − dx − sM . (6.1.6)

22 2 22220

L(sin ϕ− sµ(λ) cos ϕ) In both equations we have the common factor sµ(λ)

S(λ) =

L(sin φ− sµ(λ)cos φ)

. (6.1.7) µ(λ) can be approximated by the following formula

p

^w4^λ 32

µ(λ) =+ w λ+ w₂λ+ w λ . (6.1.8) a +λ^p 31 It will be explained in Chapter 2 how to derive µ(λ) and S(λ) on the basis of experiments. We denote rd (sM + M )rd sMr ₁

1 10 g 1

11 1 110 1

c = ,c = , c =− , c =− , c = ,c =− ,

11 12 13 14 15 16

J J JJJJ

1 1 1111

rd (sM + M )rdsM r

1 10 g 2

21 2220 2

c =− ,c =− , c =− , c =− , c =− .

21 22 23 24 25

J J JJJ

2 2 222 The equations (6.1.1) and (6.1.2) have the forms: x# = S(λ)(cx + c )+ cx + c +(cS(λ)+ c )sM , (6.1.9)

1 11 1 12 13 1 14 15 16 1 1 x# ₂ = S(λ)(c₂₁ x₁ + c₂₂ )+ c₂₃ x₂ + c₂₄ + c₂₅ S(x₁, x₂ )s₁M₁ , (6.1.10)

The driving system of the brake is described by the following equation

#

M₁ = c (b(u) − M₁) (6.1.11)

31

Constant is equal to 20.37 [1/s]. Function b(u) (see formula (6.1.11)) may be

^c31 approximated by the formula:

b(u) =

ÀÃÕ

b

1

u + b ,u

2

≥

u

0

0,u < u

0

b = 15 .24 ,b = -6.21 ,u = 0.415.

120

6.2. Identification

15.24 u -6.21, u

ÀÃÕ

≥

0.415

0.12, u < 0.415

The model coefficients have the following values:

= 0.00158605757097, = 2.593351896228796e+002,

^c11 ^c12

== 0.01594027709515, = 0.39850692737875,

^c11 ^c13 ^c14

= 13.21714642472868, = 132.8356424595848,

^c15 ^c16

= 0.000464008124048, = 75.86965129086435,

^c21 ^c22

= 0.00878803265242, = 3.63238682966840,

^c23 ^c24

= 3.86673436706636, = 20.37,

^c25 ^c31 w₁ =− 0.04240011450454, w₂ = 0.00000000029375, w₃ = 0.03508217905067, w₄ = 0.40662691102315 a = 0.00025724985785, p = 2.09945271667129.