*Article* **A Comparative Analysis of Brake-by-Wire Smart Actuators Using Optimization Strategies**

**Ehsan Arasteh \* and Francis Assadian \***

Department of Mechanical and Aerospace Engineering, University of California, Davis, CA 95616, USA **\*** Correspondence: earasteh@ucdavis.edu (E.A.); fassadian@ucdavis.edu (F.A.)

**Abstract:** Since the automotive industry is shifting towards electrification, brake-by-wire technologies are becoming more prevalent. However, there has been little research comparing and optimizing brake-by-wire actuators in terms of their energy expenditure and response time. This paper investigates the comparison of three different smart brake-by-wire actuators, Electro-Hydraulic Brakes (EHB), Electro-Mechanical Brakes (EMB), and Electronic Wedge Brakes (EWB), first by defining an objective metric and then using both linear and nonlinear optimization techniques. Modeling of the actuators is performed using the bond graph method. Then, the controllers are designed using a robust control strategy, Youla parameterization. After designing the controllers, two types of optimization are performed on the actuators. Optimizations are performed in two ways: 1. by linearizing the plants and optimizing using their transfer functions and 2. by nonlinear optimization of the plants in the closed-loop following a specific clamp force target. The objective metrics or the cost functions for these optimizations are chosen to be the energy usage of the plants during the closed-loop operation, maximum power requirement, and their dynamic responsiveness. Using this optimization framework, we can show a significant improvement in the energy usage of the actuators and slight improvements in their responsiveness. In the end, the actuators are compared in terms of their energy usage for sets of initial and optimized physical parameters.

**Keywords:** EHB; EMB; EWB; system modeling; bond graph; optimization; control design; Youla parameterization; robust control; nonlinear optimization; brake-by-wire; actuator; electro-mechanical brake; electronic wedge brake; electro-hydraulic brake
