**1. Introduction**

By-wire technologies are becoming more in demand because of their contribution to the vehicle's fuel efficiency and electrification. They are well suited for autonomous vehicles, Electric Vehicles (EVs), and Hybrid Electric Vehicles (HEVs) due to their electronic interface and architectures. Between all these by-wire technologies, brake-by-wires are essential since they play a critical role in the vehicle's safety [1–3].

Brake-by-wire systems can reduce the overall component weight due to the reduction in the number of parts and integrated packaging. They also improve energy consumption because they would only use energy when required. The reduction of energy usage by different components is an essential aspect of reducing the CO2 emissions of vehicles. This type of reduction is significant in reducing fleet CO2 emissions. When the brake pedal is released, the brake pad may not release entirely, causing caliper drag. Brakeby-wire is even more energy-efficient by eliminating caliper drag through sensors and control methods. To enhance vehicle safety, individual wheel braking and faster activation times of BBW actuators can be utilized by the vehicle's Electronic Stability Control (ESC) system. The biggest barriers to brake-by-wire systems gaining popularity in the automotive industry are the reliability of new actuators, as well as the risk and cost of deploying new braking technology [4].

**Citation:** Arasteh, E.; Assadian, F. A Comparative Analysis of Brake-by-Wire Smart Actuators Using Optimization Strategies. *Energies* **2022**, *15*, 634. https:// doi.org/10.3390/en15020634

Academic Editor: Silvio Simani

Received: 18 November 2021 Accepted: 7 January 2022 Published: 17 January 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

#### *1.1. Brake-by-Wire Actuators*

Wet and dry brakes are the two types of braking systems. Dry brakes are simply mechanical systems that rely on electric motors, whereas wet brakes employ fluids to produce pressure on the piston and the caliper. A type of wet brake is electro-hydraulic brakes, which include solenoid valves that can be operated with an electronic signal to vary the braking pressure. These types of brakes require an accumulator and a pump, and usually a vacuum booster to maintain their high pressure throughout the braking operation. There are also a few different types of dry brakes. In a pure electro-mechanical brake, a small electric motor, planetary gear set, and roller screw energizes the brake pad [5–8]. For this type of brake, however, a 42 volt motor is needed, which is energy intensive [4]. On the other hand, a wedge mechanism is used in electronic wedge brakes to create a brake caliper, which is drawn into the brake and uses less energy because it utilizes the wheel's rotation. They usually need a 14 V supply as opposed to the 42 V of the electro-mechanical brake. However, this comes at the cost of more complicated mechanics and control [5,8–16]. Vienna Engineering has created a brake system based on a crank-shaft mechanism that reduces the complexity of dealing with the reduction gears and roller screws [17].

Purely dry brakes are expensive compared to conventional electro-hydraulic brakes since they are new technologies and need more testing and research before they can be reliable enough to go into production. The reliability of purely dry brakes is a challenge since they have more electronic components, and these components need to work reliably in an environment where vibration, shock, and temperature can significantly affect their nominal performance [4].

On the other hand, EHBs have been used by manufacturers for a while. For example, an integrated electro-hydraulic brake system utilizes an electro-mechanical actuator (similar to an electro-mechanical brake) as a modulator of a master cylinder. This electro-mechanical actuator uses a motor to rotate a gear mechanism and a ball-screw that pushes the piston. This axial force pressurizes the brake fluid inside the master cylinder. The pressurized brake fluid is then transferred to the wheel chamber using a high-pressure pipeline, where this pressure displaces the caliper (similar to an EHB). This integrated electro-hydraulic brake uses most of the EHB parts that the automotive manufacturers are already familiar with and removes the need for a pump, vacuum booster, and accumulator [18,19]. It also seems that this type of brake actuator is gaining popularity among car manufacturers. Bosch GmbH developed the iBooster and ESP hev (electronic stability program for hybrid and electric vehicles), which are integrated electro-hydraulic and Hydraulic Control Units (HCU) in 2013. In 2017, Continental AG introduced MK C1, which is an integrated EHB with fast actuation and without any vacuum booster or accumulator along with emergency brake functionalities [20]. ZF TRW (with the IBC) and Hyundai Mobis (with iMEB) are among the more recent suppliers who developed and manufactured integrated electro-hydraulic brake actuators.
