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INTRODUCTION
In the last years, the automotive industry has looked for innovative brake-by-wire (BBW) solutions. This to increase the vehicle performance and safety. The possibility of smoothlyand precisely applying a desired braking torque is at the basis of many vehicle dynamics control and autonomous vehicles. Different technological solutions have been proposed the electrohydraulic one (EHB) is based on a hydraulic system, which is activated by an electric motor or pump controlled by an electronic unit. The electromechanical brake (EMB) solution does not have the hydraulic part but there is an electric motor as actuator that provides the braking torque. A particular EMB technology is known as wedge brake, where an electric motor controls the force on a wedge that pushes backward and forward the braking pads. A modified EHB solution first presented in an electromechanical actuator that pushes backward and forward the piston of a master cylinder connected to a traditional hydraulic brake. Compared to well-known EMB and EHB solutions, this one has the advantage to keep the usual hydraulic layout adding just the actuator. This saves weight, space, and cost. With this architecture, the actuator control problem consists intracking a desired pressure reference. The control problem is made nontrivial by the nonlinearities of the system (friction, presence of the brake fluid reservoir, temperature variation, and oil compressibility) and by the very demanding performance specifications. Commonly using system of breaking in a motor cycle is disc brake system. A disc brake is a type of brake that uses callipers to squeeze pairs of pads against a disc in order to create friction that retards the rotation of a shaft, such as a vehicle axle, either to reduce its rotational speed or to hold it stationary. The energy of motion is converted into waste heat which must be dispersed. Hydraulic disc brakes are the most commonly used form of brake for motor vehicles but the principles of a disc brake are applicable to almost any rotating shaft. Compared to drum brakes, disc brakes offer better stopping performance because the disc is more readily cooled. As a consequence, discs are less prone to the brake fade caused when brake components overheat. Disc brakes also recover more quickly from immersion.
Motorcycles are statically unstable. During riding, they are stabilized mainly by two mechanisms. Both stabilizing effects require a possible increase in side force. They do not work with sliding wheels, which happens on slippery surface. In the event of a locking front wheel, the motorcycle becomes kinematically unstable. A coupled yawing and rolling motion is induced that lets the motorcycle tumble in fractions of seconds. For technological constraints, at the end of the braking event the master cylinder piston must retract before the brake reservoir inlet so that a proper fluid compensation can be achieved. This introduces a nonlinearity in the system to be controlled. Furthermore, the control law must be robust to the so-called knock-off. In racing applications, at times, the brake disk pushes back the pads at the end of the braking event. This leads to a variation in the position-pressure characteristic: during the following braking action, the master cylinder must move further than in the previous one. Then, after this anomalous braking event, the system returns to the normal behaviour. This happens in traditional brake too. Professional pilots feel the knock-offfrom the return force on the lever, and once detected, they compensate it by pressing the brake lever more theclosed-loop response with a direct pressure controller shows abig overshoot that prevents its usage in this application.
The issue is addressed by simply avoiding to completely retract the piston. In this way, a good pressure tracking performance is achieved at the cost of the risk of not compensating fluid volume changes.Moreover, a small pressure is always applied to the brake pads: This causes a loss of energy and a continuous brake pad wear. In and, a hybrid position pressure switching control strategy has been proposed, in this way, through the position control, it is possible to compensate the fluid volume variation at the end of each braking event. The main problem of such an architecture is that in the first phase of the braking action when the position controller is enabled the pressure is not directly controlled. So, if there is a small error in the identified position–pressure map, the control performances are affected. Moreover, the architecture proposed in suffers from robustness issues. the aforementioned shortcomings are addressedby an adaptive cascade control architecture, which guarantees the required performance and improves robustness with respect to external disturbances.
CHAPTER 2
LITERATURE REVIEW
[1] G. Panzani, M. Corno, F.Todeschini, S. Fiorenti, and S. Savaresi, “Analysis and control of a brake by wire actuator for sport motorcycles,” presentedat the 13th Mechatronics Forum Int. Conf., Linz, Austria, Sep. 17–19, 2012.
In the issue is addressed by simply avoiding to completely retract the piston. In this way, a good pressure tracking performance is achieved at the cost of the risk of not compensating fluid volume changes. Moreover, a small pressure is always applied to the brake pads: This causes a loss of energy and a continuous brake pad wear. The main problem of such an architecture is that in the first phase of the braking action when the position controller is enabled the pressure is not directly controlled. So, if there is a small error in the identified position–pressure map, the control performances are affected. Moreover, the architecture proposed in [18] and [19] suffers from robustness issues. In this paper, the aforementioned shortcomings are addressed by an adaptive cascade control architecture, which guarantees the required performance and improves robustness with respect to external disturbances. Also, experimental results that prove the effectiveness of the control law are presented.
[2] T. Johansen, I. Petersen, J. Kalkkuhl, and J. Ludemann, “Gain-scheduled wheel slip control in automotive brake systems,” IEEE Trans. ControlSyst. Technol., vol. 11, no. 6 pp. 799–811, 2007.
In this paper a wheel slip controller is developed and experimentally tested in a car equipped with electromechanical brake actuators and a brake-by-wire ABS system. A gain scheduling approach is taken, where the vehicle speed is viewed as a slowly time-varying parameter and the model is linearized about the nominal wheel slip. Gain matrices for the different operating conditions are designed using an LQR approach. Advantages of this idea is stable and robust. Whereas disadvantage is its high complexity.
[3] N. D’alfio, A. Morgando, and A. Sorniotti, “Electro-hydraulic brake systems: Design and test through hardware-in-the-loop simulation,” VehicleSyst. Dyn, Int. J. Vehicle Mech.Mobility, vol. 44, no. 1, pp. 378–392, 2006.
This paper presented the design and implementation of an electro-hydraulic braking system consisting of a pump and various valves allowing the control computer to stop the car. It is assembled in coexistence with the original circuit for the sake of robustness and to permit the two systems to halt the car independently. The most important Advantage of this paper is it have good performance. And its disadvantage is that it is less efficient.
[4]S. Anwar, “Generalized predictive control of yaw dynamics of a hybrid brake-by-wire equipped vehicle,” Mechatronics, vol. 15, no. 9, pp. 1089–1108, 2005.
In the last years, the automotive industry has looked for innovative brake-by-wire (BBW) solutions: This to increase the vehicle performance and safety. The possibility of smoothly and precisely applying a desired braking torque is at the basis of many vehicle dynamics control and autonomous vehicles. Different technological solutions have been proposed: the electrohydraulic one (EHB) is based on a hydraulic system, which is activated by an electric motor or pump controlled by an electronic unit. The electromechanical brake (EMB) solution does not have the hydraulic part but there is an electric motor as actuator that provides the braking torque. A particular EMB technology is known as wedge brake, where an electric motor controls the force on a wedge that pushes backward and forward the braking pads.
[5]R. Roberts, M. Schautt, H. Hartmann, and B. Gombert, “Modelling and validation of the mechatronic wedge brake,” SAE paper, vol. 112, pp. 2376–2386, 2003.
This paper presented a detailed analytical model development which can describe the dynamic behaviour of the electromechanical brake-by-wire (BBW) system over the entire operating range. This model is able to reproduce various nonlinear characteristics including typical structural hysteresis. But the dynamic behaviour is very complex.
CHAPTER 3
CONVENTIONAL CONTROLLERS
A control system is a device, or set of devices, that manages, commands, directs or regulates the behaviour of other devices or systems. Industrial control systems are used in industrial production for controlling equipment or machines.There are two common classes of control systems, open loop control systems and closed loop control systems. In open loop control systems output is generated based on inputs. In closed loop control systems current output is taken into consideration and corrections are made based on feedback. A closed loop system is also called a feedback control system.
The term "control system" may be applied to the essentially manual controls that allow an operator, for example, to close and open a hydraulic press, perhaps including logic so that it cannot be moved unless safety guards are in place. An automatic sequential control system may trigger a series of mechanical actuators in the correct sequence to perform a task. For example various electric and pneumatic transducers may fold and glue a cardboard box, fill it with product and then seal it in an automatic packaging machine. Programmable logic controllers are used in many cases such as this, but several alternative technologies exist. In the case of linear feedback systems, a control loop, including sensors, control algorithms and actuators, is arranged in such a fashion as to try to regulate a variable at a set point or reference value. An example of this may increase the fuel supply to a furnace when a measured temperature drops. PID controllers are common and effective in cases such as this. Control systems that include some sensing of the results they are trying to achieve are making use of feedback and so can, to some extent, adapt to varying circumstances. Open-loop control systems do not make use of feedback, and run only in pre-arranged ways.
3.1 ON–OFF CONTROL
A thermostat is a simple negative feedback controller: when the temperature (the "process variable" or (PV) goes below a set point (SP), the heater is switched on. Another example could be a pressure switch on an air compressor. When the pressure (PV) drops below the threshold (SP), the pump is powered. Refrigerators and vacuum pumps contain similar mechanisms operating in reverse, but still providing negative feedback to correct errors.Simple on–off feedback control systems like these are cheap and effective. In some cases, like the simple compressor example, they may represent a good design choice.In most applications of on–off feedback control, some consideration needs to be given to other costs, such as wear and tear of control valves and perhaps other start-up costs when power is reapplied each time the PV drops. Therefore, practical on–off control systems are designed to include hysteresis which acts as a deadband, a region around the setpoint value in which no control action occurs. The width of deadband may be adjustable or programmable.
3.2LINEAR CONTROL
Linear control systems use linear negative feedback to produce a control signal mathematically based on other variables, with a view to maintain the controlled process within an acceptable operating range. The output from a linear control system into the controlled process may be in the form of a directly variable signal, such as a valve that may be 0 or 100% open or anywhere in between. Sometimes this is not feasible and so, after calculating the current required corrective signal, a linear control system may repeatedly switch an actuator, such as a pump, motor or heater, fully on and then fully off again, regulating the duty cycle using pulse-width modulation.
3.3PROPORTIONAL CONTROL
When controlling the temperature of an industrial furnace, it is usually better to control the opening of the fuel valve in proportion to the current needs of the furnace. This helps avoid thermal shocks and applies heat more effectively. Proportional negative-feedback systems are based on the difference between the required set point (SP) and process value (PV). This difference is called the error. Power is applied in direct proportion to the current measured error, in the correct sense so as to tend to reduce the error and therefore avoid positive feedback. The amount of corrective action that is applied for a given error is set by the gain or sensitivity of the control system. At low gains, only a small corrective action is applied when errors are detected. The system may be safe and stable, but may be sluggish in response to changing conditions. Errors will remain uncorrected for relatively long periods of time and the system is over-damped. If the proportional gain is increased, such systems become more responsive and errors are dealt with more quickly. There is an optimal value for the gain setting when the overall system is said to be critically damped. Increases in loop gain beyond this point lead to oscillations in the PV and such a system is damped. In real systems, there are practical limits to the range of the manipulated variable (MV). For example, a heater can be off or fully on, or a valve can be closed or fully open. Adjustments to the gain simultaneously alter the range of error values over which the MV is between these limits. The width of this ranges, in units of the error variable and therefore of the PV, is called the proportional band (PB). While the gain is useful in mathematical treatments, the proportional band is often used in practical situations. They both refer to the same thing, but the PB has an inverse relationship to gain – higher gains result in narrower PBs, and vice versa.
Fig 3.2: Proportional controller.
3.4 PI CONTROLLER
A proportional integral controller generates an output signal which includes two terms in which one is proportional to error signal and the other proportional to the integral of error signal. The transfer function of proportional controller is
Kp(1+1/(〖(t〗_d* s))) (3.1)
The term Kp is the proportional gain and Ti is the integral time.P-I controller has the property of eliminating the steady state error resulting from P controller. Whereas the speed of the response and overall stability of the system a PI controller has a negative impact. And hence this controller is commonly used in areas where speed of the system is having less importance. As a P-I controller has no ability to predict the future errors of the system it cannot decrease the rise time and eliminate the oscillations.
3.5 PD CONTROLLER
A proportional derivative controller generates an output signal which includes two terms in which one is proportional to error signal and the other proportional to the derivative of error signal. The transfer function of proportional controller is
Kp(1+Td*s) (3.2)
The term Kd is the proportional gain and Td is the derivative time. Through using a P-D controller we can increase the stability of the system by improving control since it has an ability to predict the future error of the system response. For avoiding effects of the sudden change in the value of the error signal, the derivative is taken from the output response of the system variable instead of the error signal. Therefore, derivative mode is designed to be proportional to the change of the output variable to prevent the sudden changes occurring in the control output resulting from sudden changes in the error signal. Also a derivative action directly amplifies process noise and hence derivative only control is not used.
PID CONTROL
A proportional–integral–derivative controller (PID controller) is a control loopfeedback mechanism (controller) commonly used in industrial control systems. A PID controller continuously calculates an error value as the difference between a measured process variable and a desired setpoint. The controller attempts to minimize the error over time by adjustment of a control variable, such as the position of a control valve, a damper, or the power supplied to a heating element, to a new value determined by a weighted sum:
u(t)=K_p e(t)+K_i ∫_0^t▒〖e(t)dt+K_d 〗 (de(t))/dt (3.3)
where , , and , all non-negative, denote the coefficients for the proportional, integral, and derivative terms, respectively (sometimes denoted P,I, and D). In this model,
P accounts for present values of the error (e.g. if the error is large and positive, the control variable will be large and negative),
I accounts for past values of the error (e.g. if the output is not sufficient to reduce the size of the error, the control variable will accumulate over time, causing the controller to apply a stronger action), and
D accounts for possible future values of the error, based on its current rate of change.
As a PID controller relies only on the measured process variable, not on knowledge of the underlying process, it is broadly applicable.By tuning the three parameters of the model, a PID controller can deal with specific process requirements. The response of the controller can be described in terms of its responsiveness to an error, the degree to which the system overshoots a setpoint, and the degree of any system oscillation. The use of the PID algorithm does not guarantee optimal control of the system or even its stability.
Some applications may require using only one or two terms to provide the appropriate system control. This is achieved by setting the other parameters to zero. A PID controller will be called a PI, PD, P or I controller in the absence of the respective control actions. PI controllers are fairly common, since derivative action is sensitive to measurement noise, whereas the absence of an integral term may prevent the system from reaching its target value.
Derivative action
The derivative part is concerned with the rate-of-change of the error with time: If the measured variable approaches the setpoint rapidly, then the actuator is backed off early to allow it to coast to the required level; conversely if the measured value begins to move rapidly away from the setpoint, extra effort is applied—in proportion to that rapidity—to try to maintain it. Derivative action makes a control system behave much more intelligently. On control systems like the tuning of the temperature of a furnace, or perhaps the motion-control of a heavy item like a gun or camera on a moving vehicle, the derivative action of a well-tuned PID controller can allow it to reach and maintain a setpoint better than most skilled human operators could. If derivative action is over-applied, it can lead to oscillations too. An example would be a PV that increased rapidly towards SP, then halted early and seemed to "shy away" from the setpoint before rising towards it again.
Integral action
The integral term magnifies the effect of long-term steady-state errors, applying ever-increasing effort until they reduce to zero. In the example of the furnace above working at various temperatures, if the heat being applied does not bring the furnace up to setpoint, for whatever reason, integral action increasingly moves the proportional band relative to the setpoint until the PV error is reduced to zero and the setpoint is achieved.
LOOP TUNING METHODS
Tuning is a process through which control parameters of a control loop are manipulated to obtain desired control action. Stability of a system has the top importance but as the system varies with respect to their behaviour and requirements their compatibility may not be plays good.
May be a P-I-D tuning seems not a difficult task while consisting of only 3 parameters, in practice; it is a difficult problem because the complex criteria at the P-I-D limit should be satisfied. A P-I-D tuning is mostly a heuristic concept but existence of many objectives to be met such as short transient, high stability makes this process harder. Sometimes, systems might have nonlinearity problem which means that while the parameters work properly for full load conditions, they might not work as effective for no load conditions. Also, if the P-I-D parameters are chosen wrong, control process input might be unstable, with or without oscillation; output diverges until it reaches to saturation or mechanical breakage. For a system to operate properly, the output should be stable, and the process should not oscillate in any condition of set point or disturbance. Whereas there are also situations of which bounded oscillation condition is quit acceptable. As an optimum behaviour, a process should satisfy the regulation and command breaking requirements. These two properties define how accurately a controlled variable reaches the desired values. The most important characteristics for command breaking are rise time and settling time. For some systems where overshoot is not acceptable, to achieve the optimum behaviour requires eliminating the overshoot completely and minimizing the dissipated power in order to reach a new set point. In order to achieve optimum solutions Kp, Ki and Kd gains are arranged according to the system characteristics. There are many tuning methods, of which common methods are listed below:
• Manual Tuning Method
• Ziegler-Nichols Tuning Method
• Cohen-Coon Tuning Method
• PID Tuning Software Methods (ex. MATLAB)
4.1 MANUAL TUNING METHOD
Manual tuning is done by arranging the parameters according to the system response unless the desired system response is obtained. Then Ki, Kp and Kd are changed by observing system behaviour.
An example for no system oscillation: First lower the derivative and integral value to 0 and raise the proportional value 100. Then increase the integral value to 100 and slowly lower the integral value and observe the system’s response. Since the system will be maintained around set point, change set point and verify if system corrects in an acceptable amount of time. If not acceptable or for a quick response, continue lowering the integral value. If the system begins to oscillate again, record the integral value and raise value to 100. After raising the integral value to 100, return to the proportional value and raise this value until oscillation ceases. Finally, lower the proportional value back to 100.0 and then lower the integral value slowly to a value that is 10% to 20% higher than the recorded value when oscillation started (recorded value times 1.1 or 1.2). Although manual tuning method seems simple it requires a lot of time and experience.
4.2 ZIEGLER-NICHOLS TUNING METHOD
At early years P-I controllers were more widely used than P-I-D controllers. Despite the fact that P-I-D controller is faster and has no oscillation, it tends to be unstable in the condition of even small changes in the input set point or any disturbances to the process than P-I controllers. Ziegler-Nichols Method is one of the most effective methods that increase the usage of P-I-D controllers.
MATHEMATICAL MODELING
Starting from the physical elements composing the BBW actuator, the complete model can be derived.
Consider the following assumptions:
1) The motor current loop, which isan order of magnitude faster than the pressure dynamics,the electrical dynamics can be discarded. Therefore, thecurrent is considered as the control variable;
2) The pressure in the master cylinder and the pressure in thebrake calliper are the same. In other words, we neglect thepressure wave propagation dynamics (the first resonancemode is usually around hundreds of hertz);
3) The amount of fluid volume in the system is not influencedby master cylinder position changes;
4) The static Coulomb friction is disregarded. This can bedone if a dithering signal is applied to the control variable or if a suitable friction compensation techniqueis applied. Under this assumption, weconsider just the viscous friction contribution.It is then possible to derive a second-order control-orientedmodel.
As the system has two operating regions we have two transfer functions
The model parameters are listed Table II. Note that they canbe found from the BBW physical components, the only unknownparameter is Kdamp. In order to model the relationshipbetween position and pressure, we exploit the quasi-static experimentalresponse of the system when an increasing currentramp followed by a decreasing one is applied.
This is anonlinear static map.The position–pressure map can be divided in two differentzones. In the dead zone, where the master cylinderis before the brake reservoir, the piston moves with no pressurevariation. The dead zone is not affected by temperature andbrake pad wear. The second part of the position–pressure curveis the operative zone; the master cylinder is after the brakereservoir and a position increment corresponds to a pressureincrement. This part of the position–pressure curve is stronglyaffected by temperature and brake pads wear. Note that theposition–pressure map depicted in Fig. 2 presents an hysteresis.
The average curve is considered for modeling purpose. Theposition–pressure curve introduces a time varying nonlinearityin the model (1), as it changes with temperature and pads wear.