# Model-Based Control and Model-Free Control Techniques for Autonomous Vehicles: A Technical Survey
## 2 Control of Autonomous Vehicle
### Longitudinal Control of Autonomous Vehicles
#### 2.2.1 Longitudinal Model-Based Control Techniques
Further, the novel adaptive cruise control (ACC) was proposed for the automated driving bus for the acceleration reduction of the vehicle. Pilot tests were used to validate the controller's performance on public roads. A methodology was proposed in [58] for selecting a longitudinal model and improving velocity control in an autonomous car. The inverse model compensates for nonlinear dynamics in the transmission system and engine. The modeling method works for any automated car with actuated throttle and braking, relying on data without prior knowledge. The control system uses two loops for throttle and braking, achieving good performance on uneven surfaces. It maintained acceleration around 2.5 m/s\({}^{2}\) in the 0-40 km/h speed range, which is suitable for passenger comfort. The methodology was validated through simulations and experiments, proving its effectiveness in enhancing safety and performance. A controller for a longitudinal ADAS system of a test vehicle was designed in [59]. A robust H\({}_{\infty}\) cruise control based on a feedforward and a feedback control design was proposed to ensure a precise velocity tracking and robustness against longitudinal disturbance  
Figure 3: Schematic of longitudinal control system. effects such as aerodynamic forces, mass parameter variations, rolling resistance, and road slopes of the vehicle. The parameter variation (dynamics) of the actuator was considered in a simplified form in the control formulation. The proposed control algorithm was implemented in CarSim. The method efficiency was illustrated during simulation scenarios on the Mulhouse-Belfort highway section. The introduced control design will be applied to various vehicles because it needs a small number of vehicle parameters. An MRAC approach for ACC systems in vehicles, which is capable of effectively managing uncertainties in low-level dynamics, was introduced by the authors of [60]. The linear longitudinal dynamic model incorporates uncertainties in the state and input matrices, and the system was designed based on error dynamics. The velocity of the lead vehicle was considered an exogenous disturbance, and the uncertainties were addressed by the control structure to maintain the desired distance. Despite model uncertainties, the proposed control demonstrated superior performance compared to a linear-state feedback control in MATLAB/Simulink. This controller is suitable for practical implementation, as it only requires a sensor in addition to vehicle velocity to measure the relative distance between the lead and controlled vehicle. In [61], a longitudinal control algorithm was developed for an autonomous vehicle without the need for vehicle parameter identification. The modified MRAC approach was studied with appropriate initial conditions, ignoring powertrain dynamics and road slope changes. Despite these simplifications, the adaptive algorithm effectively tracks speed profiles with comfortable acceleration and robustness to environmental variations. The control architecture is suitable for vehicles with approximately known parameters. Simulation using a CarSim-Simulink setup demonstrated the feasibility of the approach, evaluating vehicle performance under different dynamic conditions. In [62], a novel longitudinal control method for autonomous vehicles was presented. The approach utilizes the reverse plant model of the vehicle to address non-linearity in the powertrain at low speeds and rapid acceleration/deceleration caused by surrounding vehicles. The parameters known to original equipment manufacturers (OEMs) were used to design the complete controller, incorporating an inner controller for brake requests and accelerator pedal percentage, and an outer controller for desired speed based on the lead vehicle's speed. The inner controller employs a reverse plant model with a virtual load sensor and follows a PI control strategy, enabling the control of vehicles with non-linear powertrain dynamics.