System design of heterogeneous vehicle platoon based on multi-delay proportional-retarded controller

To effectively utilize delays to enhance system response speed and other control performances, a proportional-retarded (PR) controller was designed for the heterogeneous vehicle platoon by introducing multi-delays. The characteristic equations of each subsystem of the vehicle platoon were analyzed by applying the implicit function theorem and Cauchy-Riemann equation, and the right-most pole assignment method was proposed for these subsystems. The available assignment ranges of the right-most poles were determined, and the guidelines for designing the controller gains and delays were given. To gradually increase the stability of the subsystems that corresponded to the follower vehicles, the poles of subsystems were separated reasonably, and a right-most pole assignment method was proposed for the entire vehicle platoon. Moreover, sufficient conditions for string stability were derived. Simulation results indicate that the designed multi-delay PR controller and the proposed right-most pole assignment method can accurately assign the pole of the heterogeneous vehicle platoon at the desired location, and both the internal stability and string stability of the vehicles are ensured. Moreover, a smaller right-most pole indicates a faster system response speed. Compared to a single-delay PR controller, the right-most poles of subsystems are flexibly separated via this method, the system setting time reduces by 2.45%. Compared with traditional proportional-derivative (PD) controllers, the PR controller shows significant improvements in ride comfort and fuel economy, with enhancement ranging from 2-4 orders of magnitude. Under the disturbances of the same frequency, the amplitude ratios of the acceleration and control input for both the PR and PD controllers remain consistently below 1/3, dropping to 0.031 when the frequency of the disturbances is 9 Hz. It can be seen that the designed multi-delay PR controller has significant advantages in response speed, pole separation, and disturbance suppression.