The steering input controls the lateral motion of the vehicle (see Figure 1). The automated vehicle steering control system uses information about the vehicle position relative to the center of the current lane to determine the steering wheel angle. A lateral force on the vehicle (and, hence, a lateral acceleration) is created as the wheels turn. The automated steering controller is designed to steer the vehicle from the center of the current lane to the center of an adjacent lane. Measurements of the vehicle's lateral position during the maneuver will be computed from the lateral acceleration measured by the accelerometer (see Figure 2). The closed loop steering control system with accelerometer feedback is shown in Figure 3. D(s) R(S) + U(s) X(5) G (8) G,(s) tot H(s) Figure 3. Automatic vehicle steering control system 10 0.1 (5+1) and The vehicle has a transfer function Go the steering actuator has transfer function Ga 100 the accelerometer has transfer function H = 34+20s +100 The signals in the Figure. 2 are: X(t): lateral postion (units: lanes) e(t): lateral postion error (units: lanes) r(t): desired lateral postion (units:lanes) u(t): steering angle (units: degrees) d(t): wind gust disturbance (units: degrees) The objective of the design project is to design an automated steering control system; that is, to design a suitable closed-loop controller. The selection of controller is based on the vehicle's motion during a lane change maneuver and on the effect of a lateral wind gust disturbance, dll). Note that there is a minus sign in the summing junction where d(t) enters because it is assumed to be acting against the motion of the car. The specifications for the steering control design are that the vehicle completes the lane change maneuver quickly and safely without causing the passengers discomfort. From a systems engineering point of view, these specifications require that the step response of the vehicle's lateral position has a small rise and/or settling time and minimal overshoot. Furthermore, the comfort of the passengers is closely related to the lateral acceleration during the lane change maneuver. Specifically, passenger comfort requires that the lateral acceleration is small. Equivalently, it can be shown that the lateral acceleration is proportional to the steering input and, therefore, passenger comfort requires that the steering input is small. The wind gust disturbance introduces a steady-state error which must be considered in the control system design. To understand the impact of the wind gust, recall that the steering input causes a lateral force on the vehicle. The wind gust disturbance creates a lateral acceleration acting against the motion of the vehicle and reduces the effect of the steering input. The specifications on the control system design can be divided into three categories: Safety: The closed loop system must have less than 10% overshoot in the unit step response. 2. Passenger comfort: The maximum steering input must be less than 4 degrees. 3. Disturbance rejection: The steady-state error for a unit disturbance must minimized. For better understanding to help us in efficient design process, we divide the complete automated vehicle steering control system into three phases with increased complexity. In Phase 1, we focus on the analysis of uncontrolled lateral position x(t) in response to unitary step input r(t) by considering the steering actuator Ge(s) as static system (that is, s-0). We then try to explore the factors that govern the system response, and aim to establish relationship among the controlling factor, controlled factor (x(t)), and the input r(t). Once the controlling and controlling factors are investigated and relationship between the two is established, we proceed to Phase 2. be In Phase 2, we include an accelerometer in the feedback path as well as consider the dynamic nature of the actuator Ga(s), giving realistic view of application under consideration. Since the inclusion of additional systems (that is accelerometer and dynamic Ga(s)) undoubtedly alters the system response, we revert to analysis stage and re-study the system in detail. At the end of Phase 2, we'll have an ultimate closed-loop transfer function of the system, but that transfer function too would be uncontrolled/uncompensated at that stage. So from Phase 1 and Phase 2, we will have complete understanding of the application, the effect of disturbance and varying input on the system response, and above all, we'll be able to answer: why to control the system output? We'll be able to have only one question at the end of Phase 1 and Phase 2: how to control the system output? Answer to this question will be addressed in final phase of the design process, Phase 3. In Phase 3, based on design requirements, we'll design a controller/compensator for the steering automation system in order achieve the lane change maneuver quickly and with absolute precision. This will mark the end of the design process Phase 1: In this phase, the disturbance is not included, ideal feedback of the lateral position is assumed, and the actuator dynamics are neglected (1.e. Ge(s) = 2). R(S) U(S) X(s) -G (s) Ge(s) Go(s) Pigured. Closed loop Wock diagram for Phase ! We aim to analyze firstly the uncontrolled closed loop response of the system by equalizing Ge(s) to 1. To begin with the analysis of the uncontrolled closed loop system, 1.1 Obtain its unit step response and note down settling time and steady sate error (through calculations or using MATLAB tools). Compare those parameters with the specifications provided above and comment briefly on whether or not Safety and Disturbance rejection have been achieved. After analyzing the uncontrolled response, now include the proportional controller Ge(s) having gain K 1.2 Express the closed loop poles in terms of the proportional controller, K. 1.2 Similarly, express the damping and natural frequency as a function of K. 1.3 Thereafter, establish relationship between the K and %overshoot, and based on the relation explain how the variations in K will affect the Safety and Disturbance rejection. 1.4 Moreover, from the relation between K and overshoot, determine the value of that will lead to the worst-case Safety parameter in the form of having maximum overshoot of 10%? Note down this value of K. 1.5 Since you have already expressed damping ratio and natural frequency in terms of K, now use these equations to find the settling time (through calculations or using MATLAB tool). Does the settling time depend on K value in the application under consideration? 1.6 What is the roots sensitivity of the proportional controlled system? Predict the shift in the pole location as K is increased 9 times from that 1.4. Comment on the unit step transient and steady-state response of the closed-loop system as K is increased (through calculations or using MATLAB tool). Phase 2: In Phase I, we analyzed the system behavior when the actuator dynamics were neglected (1.e. Ga(s) = 2), and the feedback path was ideal (i.e. no sensor included), and consequently we concluded that how the proportional controller, K, value affects the output response. We also analyzed that how the vehicle Safety, and Disturbance Rejection vary as we change K. In Phase 2, we include dynamic model of the actuator (.e. Ga(s) and re-analyze the system behavior as we did in Phase 1. 2.1 After including the dynamic actuator, determine the unity-feedback closed-loop transfer function of the system (through calculations or using MATLAB tool). 2.2 Express settling time in terms of K. Did the settling time change after including the dynamic actuator? 2.3 Determine the upper-limit on K value. 2.4 Let K-10, determine dominant closed loop poles, obtain damping ratio, and natural frequency. Comment on Movershoot and settling time as K is increased from 10 to 20 (through calculations or using MATLAB tool). How does it affect the Safety factor? 2.5 By introducing the dynamics of the actuator, we get a limitation on the value of K. Determine maximum permissible value of K to have stable output? Will the system be stable if we take K-407 2.6 Now let's introduce the accelerometer, H(s), in the feedback path (Figure 5) with H(s) given on Page 4. What is the system order after including H(s)? Determine the value of K to have stable output? Will the system be stable if we take K 207 As you might have noticed that after including the accelerometer, the vehicle's Safety factor is no longer optimum, even if we set the proportional gain K at its maximum possible value. 2.7 Comment on how the settling time and movershoot change after including the accelerometer? And can we reduce the settling time and overshoot to Is and 5% respectively if we were to change the proportional controller value, K, only? R(S) U(S) X(s) Ge(s) G,() G(s H(s) Figure 5. Ulmate closed loop diagram of Automatic Steering Control System Phase 3: Till this point, we have deduced that by using only the proportional controller, the settling time and %overshoot cannot be further reduced. 3.1 Suggest a suitable controller and provide its transfer function that could help us decrease the settling time and overshoot to less than Is and 2%, respectively in order to ensure best-possible Safety and Disturbance Rejection 3.2 Also, verify your designed closed-loop controller for unitary step input by implementing the complete closed-loop controlled automatic steering control system in Simulink. That will be an ultimate closed-loop controller that will ensure lane changing and centering maneuver with absolute precision while keeping Safety as well as Passenger Comfort factor at top priority. The steering input controls the lateral motion of the vehicle (see Figure 1). The automated vehicle steering control system uses information about the vehicle position relative to the center of the current lane to determine the steering wheel angle. A lateral force on the vehicle (and, hence, a lateral acceleration) is created as the wheels turn. The automated steering controller is designed to steer the vehicle from the center of the current lane to the center of an adjacent lane. Measurements of the vehicle's lateral position during the maneuver will be computed from the lateral acceleration measured by the accelerometer (see Figure 2). The closed loop steering control system with accelerometer feedback is shown in Figure 3. D(s) R(S) + U(s) X(5) G (8) G,(s) tot H(s) Figure 3. Automatic vehicle steering control system 10 0.1 (5+1) and The vehicle has a transfer function Go the steering actuator has transfer function Ga 100 the accelerometer has transfer function H = 34+20s +100 The signals in the Figure. 2 are: X(t): lateral postion (units: lanes) e(t): lateral postion error (units: lanes) r(t): desired lateral postion (units:lanes) u(t): steering angle (units: degrees) d(t): wind gust disturbance (units: degrees) The objective of the design project is to design an automated steering control system; that is, to design a suitable closed-loop controller. The selection of controller is based on the vehicle's motion during a lane change maneuver and on the effect of a lateral wind gust disturbance, dll). Note that there is a minus sign in the summing junction where d(t) enters because it is assumed to be acting against the motion of the car. The specifications for the steering control design are that the vehicle completes the lane change maneuver quickly and safely without causing the passengers discomfort. From a systems engineering point of view, these specifications require that the step response of the vehicle's lateral position has a small rise and/or settling time and minimal overshoot. Furthermore, the comfort of the passengers is closely related to the lateral acceleration during the lane change maneuver. Specifically, passenger comfort requires that the lateral acceleration is small. Equivalently, it can be shown that the lateral acceleration is proportional to the steering input and, therefore, passenger comfort requires that the steering input is small. The wind gust disturbance introduces a steady-state error which must be considered in the control system design. To understand the impact of the wind gust, recall that the steering input causes a lateral force on the vehicle. The wind gust disturbance creates a lateral acceleration acting against the motion of the vehicle and reduces the effect of the steering input. The specifications on the control system design can be divided into three categories: Safety: The closed loop system must have less than 10% overshoot in the unit step response. 2. Passenger comfort: The maximum steering input must be less than 4 degrees. 3. Disturbance rejection: The steady-state error for a unit disturbance must minimized. For better understanding to help us in efficient design process, we divide the complete automated vehicle steering control system into three phases with increased complexity. In Phase 1, we focus on the analysis of uncontrolled lateral position x(t) in response to unitary step input r(t) by considering the steering actuator Ge(s) as static system (that is, s-0). We then try to explore the factors that govern the system response, and aim to establish relationship among the controlling factor, controlled factor (x(t)), and the input r(t). Once the controlling and controlling factors are investigated and relationship between the two is established, we proceed to Phase 2. be In Phase 2, we include an accelerometer in the feedback path as well as consider the dynamic nature of the actuator Ga(s), giving realistic view of application under consideration. Since the inclusion of additional systems (that is accelerometer and dynamic Ga(s)) undoubtedly alters the system response, we revert to analysis stage and re-study the system in detail. At the end of Phase 2, we'll have an ultimate closed-loop transfer function of the system, but that transfer function too would be uncontrolled/uncompensated at that stage. So from Phase 1 and Phase 2, we will have complete understanding of the application, the effect of disturbance and varying input on the system response, and above all, we'll be able to answer: why to control the system output? We'll be able to have only one question at the end of Phase 1 and Phase 2: how to control the system output? Answer to this question will be addressed in final phase of the design process, Phase 3. In Phase 3, based on design requirements, we'll design a controller/compensator for the steering automation system in order achieve the lane change maneuver quickly and with absolute precision. This will mark the end of the design process Phase 1: In this phase, the disturbance is not included, ideal feedback of the lateral position is assumed, and the actuator dynamics are neglected (1.e. Ge(s) = 2). R(S) U(S) X(s) -G (s) Ge(s) Go(s) Pigured. Closed loop Wock diagram for Phase ! We aim to analyze firstly the uncontrolled closed loop response of the system by equalizing Ge(s) to 1. To begin with the analysis of the uncontrolled closed loop system, 1.1 Obtain its unit step response and note down settling time and steady sate error (through calculations or using MATLAB tools). Compare those parameters with the specifications provided above and comment briefly on whether or not Safety and Disturbance rejection have been achieved. After analyzing the uncontrolled response, now include the proportional controller Ge(s) having gain K 1.2 Express the closed loop poles in terms of the proportional controller, K. 1.2 Similarly, express the damping and natural frequency as a function of K. 1.3 Thereafter, establish relationship between the K and %overshoot, and based on the relation explain how the variations in K will affect the Safety and Disturbance rejection. 1.4 Moreover, from the relation between K and overshoot, determine the value of that will lead to the worst-case Safety parameter in the form of having maximum overshoot of 10%? Note down this value of K. 1.5 Since you have already expressed damping ratio and natural frequency in terms of K, now use these equations to find the settling time (through calculations or using MATLAB tool). Does the settling time depend on K value in the application under consideration? 1.6 What is the roots sensitivity of the proportional controlled system? Predict the shift in the pole location as K is increased 9 times from that 1.4. Comment on the unit step transient and steady-state response of the closed-loop system as K is increased (through calculations or using MATLAB tool). Phase 2: In Phase I, we analyzed the system behavior when the actuator dynamics were neglected (1.e. Ga(s) = 2), and the feedback path was ideal (i.e. no sensor included), and consequently we concluded that how the proportional controller, K, value affects the output response. We also analyzed that how the vehicle Safety, and Disturbance Rejection vary as we change K. In Phase 2, we include dynamic model of the actuator (.e. Ga(s) and re-analyze the system behavior as we did in Phase 1. 2.1 After including the dynamic actuator, determine the unity-feedback closed-loop transfer function of the system (through calculations or using MATLAB tool). 2.2 Express settling time in terms of K. Did the settling time change after including the dynamic actuator? 2.3 Determine the upper-limit on K value. 2.4 Let K-10, determine dominant closed loop poles, obtain damping ratio, and natural frequency. Comment on Movershoot and settling time as K is increased from 10 to 20 (through calculations or using MATLAB tool). How does it affect the Safety factor? 2.5 By introducing the dynamics of the actuator, we get a limitation on the value of K. Determine maximum permissible value of K to have stable output? Will the system be stable if we take K-407 2.6 Now let's introduce the accelerometer, H(s), in the feedback path (Figure 5) with H(s) given on Page 4. What is the system order after including H(s)? Determine the value of K to have stable output? Will the system be stable if we take K 207 As you might have noticed that after including the accelerometer, the vehicle's Safety factor is no longer optimum, even if we set the proportional gain K at its maximum possible value. 2.7 Comment on how the settling time and movershoot change after including the accelerometer? And can we reduce the settling time and overshoot to Is and 5% respectively if we were to change the proportional controller value, K, only? R(S) U(S) X(s) Ge(s) G,() G(s H(s) Figure 5. Ulmate closed loop diagram of Automatic Steering Control System Phase 3: Till this point, we have deduced that by using only the proportional controller, the settling time and %overshoot cannot be further reduced. 3.1 Suggest a suitable controller and provide its transfer function that could help us decrease the settling time and overshoot to less than Is and 2%, respectively in order to ensure best-possible Safety and Disturbance Rejection 3.2 Also, verify your designed closed-loop controller for unitary step input by implementing the complete closed-loop controlled automatic steering control system in Simulink. That will be an ultimate closed-loop controller that will ensure lane changing and centering maneuver with absolute precision while keeping Safety as well as Passenger Comfort factor at top priority