As a typical example of cyber-physical systems, intelligent vehicles are receiving increasing attention, and the obstacle avoidance problem for such vehicles has become a hot topic of discussion. This paper presents a simultaneous trajectory planning and tracking controller for use under cruise conditions based on a model predictive control (MPC) approach to address obstacle avoidance for an intelligent vehicle. The reference trajectory is parameterized as a cubic function in time and is determined by the lateral position and velocity of the intelligent vehicle and the velocity and yaw angle of the obstacle vehicle at the start point of the lane change maneuver. Then, the control sequence for the vehicle is incorporated into the expression for the reference trajectory that is used in the MPC optimization problem by treating the lateral velocity of the intelligent vehicle at the end point of the lane change as an intermediate variable. In this way, trajectory planning and tracking are both captured in a single MPC optimization problem. To evaluate the effectiveness of the proposed simultaneous trajectory planning and tracking approach, joint veDYNA-Simulink simulations were conducted in the unconstrained and constrained cases under leftward and rightward lane change conditions. The results illustrate that the proposed MPC-based simultaneous trajectory planning and tracking approach achieves acceptable obstacle avoidance performance for an intelligent vehicle.

Simultaneous Trajectory Planning and Tracking Using an MPC Method for Cyber-Physical Systems: A Case Study of Obstacle Avoidance for an Intelligent Vehicle

In this paper, a model predictive controller for the position control of an electrical drive with an elastic connection is presented. The control methodology enables the drive's safety and physical limitations to be directly incorporated into control synthesis. The effect of the predictive horizon on the drive performance is examined. Also, the influence of parameter changes is tested in this paper. The simulation study is supported by experimental results.

Application of the MPC to the Position Control of the Two-Mass Drive System

A new method for electrical motor drive self-commissioning, with elastic couplings and backlash, is presented. The heuristic algorithm particle swarm optimization (PSO) has been used for the identification and optimization of parameters. Initially, a model-based identification procedure is performed to evaluate the parameters of the system. Then, the parameters of a proportional–integral–derivative (PID)-based controller are optimized by using a time-domain performance criterion. Experimental results, obtained by testing three different laboratory permanent magnet synchronous motor (PMSM) drive prototypes, are also presented to confirm the validity of the proposed approach.

PSO-Based Self-Commissioning of Electrical Motor Drives

In this paper, issues related to the design of a fuzzy Luenberger observer for a drive system with a flexible joint is presented. The proposed estimator ensures shifting observer closed-loop poles in accordance with the present condition of the plant. The dynamic states are recognized on the basis of the error between the plant and estimator outputs (classical approach), as well as additional signal (difference between electromagnetic, and shaft torque and its derivative). Depending on these signals, the fuzzy systems determine the location of the observer poles. The proposed control structure is investigated through a number of experimental tests.

A Modified Fuzzy Luenberger Observer for a Two-Mass Drive System

This paper proposes a method that estimates the parameters of a velocity-controlled servo. A proportional-integral controller, which uses only position measurements, closes the loop. The proposed approach uses the steady-state response produced by steps and sine-wave signals; they do not produce high levels of vibration on the servo compared with random signals commonly used with the least squares algorithm; moreover, it relies on simple numerical calculations. The method, which is called in the sequel as the steady-state response method (SSRM), consists of two steps. The first step uses three constant reference inputs in order to identify a constant disturbance and the viscous and Coulomb friction coefficients of the servo. In the second step, the SSRM estimates the servo inertia using a sine wave plus a constant signal as a velocity reference input and employs the estimate of the viscous friction coefficient obtained in the first step. Experiments on a testbed employing a brushless servomotor allow comparing the results obtained using the SSRM and those produced by a standard recursive least squares method (RLSM).

Inertia and Friction Estimation of a Velocity-Controlled Servo Using Position Measurements

In this paper, low-order integral-proportional (IP), modified IP (m-IP), and modified integral-proportional-derivative (m-IPD) controllers are designed for the speed control of a two-mass system based on a normalized model and polynomial method. In order to have sufficient damping, the parameters of the controllers are determined through characteristic-ratio assignment under the principle that all the characteristic ratios should be larger than two. It is found that for an inertia ratio smaller than one-third, an IP controller can effectively suppress the vibrations with proper damping, while for a relatively larger inertia ratio, an m-IP controller (i.e., IP controller with an additional low-pass filter) is effective. m-IPD control is theoretically effective for a large inertia ratio. However, the necessity of a negative derivative gain leads to a very poor robustness. Both simulation and experimental results verified the effectiveness of the designed IP and m-IP controllers when the inertia ratio is relatively small. For the m-IPD controller, its poor robustness is demonstrated by introducing a large gear backlash in experiments, while the IP and m-IP controllers show promising results of a much better robustness against the gear backlash nonlinearity.

Polynomial-Method-Based Design of Low-Order Controllers for Two-Mass Systems

Wireless power transfer (WPT) working at megahertz (MHz) is widely considered a promising technology for midrange and low-power applications. A Class E 2 dc-dc converter is composed of a Class E power amplifier (PA) and a Class E rectifier. It is attractive for applications in MHz WPT due to the soft-switching properties of both the PA and the rectifier. Using the existing design, the Class E 2 dc-dc converter can only achieve optimal performance such as a high efficiency under a fixed operating condition. Meanwhile, in real applications variations in the coil relative position and the final load are common. The purpose of this paper is to analyze and develop a general design methodology for a robust Class E 2 dc-dc converter in MHz WPT applications. Component and system efficiencies are analytically derived, which serve as the basis for the determination of the design parameters. The classical matching network of the Class E PA is also improved that provides the required impedance compression capability. Then, a robust parameter design procedure is developed. Both the experimental and calculated results show that proposed design approach can significantly improve the robustness of the efficiency of the Class E 2 dc-dc converter against variations in coil relative position and final load. Finally, the experiments show that the range of variation of the system efficiency is narrowed from 47.5%-85.0% to 73.3%-83.7% using the proposed robust design.

Analysis and Design of A Robust Class $E^2$ DC–DC Converter for Megahertz Wireless Power Transfer

In this paper, a polynomial-based design of inertia ratio controllers is discussed for the vibration suppression in two-mass system A tradeoff relationship is shown to exist between damping and robustness performances in the control problem A desirable inertia ratio of 5/16 is derived at which IP control provides a proper damping Then two approaches for the control of equivalent inertia ratio are discussed without/with load velocity feedback “Resonance ratio control” is capable of providing a sufficient damping for large inertia ratios by using only drive velocity feedback However, a negative derivative gain is necessary, which leads to a poor robustness By using both drive and load velocity feedback, the equivalent inertia ratio can be exactly specified as 5/16 The proposed “inertia ratio controller” design shows an obvious improvement in terms of both damping and robustness performances All the experimental results validate the polynomial-based theoretical analysis and controller design The demonstrated generality and the explicit expression of damping indicate the promising prospect of the polynomial-based controller design for solving more complicated control problems

Polynomial-based inertia ratio controller design for vibration suppression in two-mass system

Class E rectifier is suitable for high-frequency rectification due to its soft-switching operation, which potentially improves the efficiency of wireless power transfer (WPT) systems working at MHz. In this paper, a robust optimization design is discussed for a 6.78-MHz WPT system using the Class E rectifier. In real WPT applications, the parameter variations are possible to be originated from the misalignment of coils, the change of load, and the varying equivalent resistance of rectifying diode under different power level. In this case, a robust optimization problem is formulated to find a solution of system design variables that is both optimal and insensitive to uncertainty of parameters. A genetic-based inner-outer algorithm is applied to solve this problem, where an explicit trade-off among efficiency and robustness is demonstrated in the optimization results. In the final experiments, the analytical results are proved to well match the experimental results. Compared with the WPT system using the conventional design, the proposed robust optimization can achieve an improved design with high efficiency, which is also robust against the variations of working conditions.

Robust optimization for a 6.78-MHz wireless power transfer system with Class E rectifier

This paper discusses the application of polynomial method in the transient response control of a benchmark two-mass system. It is shown that transient responses can be directly addressed by specifying the so-called characteristic ratios and the generalized time constant. The nominal characteristic ratio assignment (CRA) is a good starting point for controller design. And the characteristic ratios with lower indices have a more dominant influence. Two practical low-order control configurations, the integral-proportional (IP) and modified-integral-proportionalderivative (m-IPD) controllers are designed. The primary design strategy of the controllers is to guarantee the lower-index characteristic ratios to be equal to their nominal values, while the higher-index characteristic ratios are determined by the interaction with the generalized time constant and the limits imposed by zeros, a specific control configuration, etc. The demonstrated relationship between the transient responses and the assignments of characteristic ratios and generalized time constant in simulation and experiments explains the effectiveness of the polynomialmethod-based controller design. [DOI: 10.1115/1.4027560]

Yue Qiao

Papers

Polynomial-Method-Based Design of Low-Order Controllers for Two-Mass Systems

Analysis and Design of A Robust Class $E^2$ DC–DC Converter for Megahertz Wireless Power Transfer

Polynomial-based inertia ratio controller design for vibration suppression in two-mass system

Robust optimization for a 6.78-MHz wireless power transfer system with Class E rectifier

Transient Response Control of Two-Mass System via Polynomial Approach