Sensing and Quantifying a New Mechanism for Vehicle Brake Creep Groan

This paper investigates the creep groan of a vehicle’s brake experimentally, analytically, and numerically. Experimentally, the effects of acceleration on caliper and strut, noise, brake pressure, and tension are measured. The results show that the measured signals and their relevant spectra broadly capture the complex vibrations of creep groan. This includes the simple stick-slip, severe stick-slip vibrations/resonances, multiple harmonics, half-order harmonics; stick-slip-induced impulsive vibrations, steady/unstable vibrations, and their transitions. Analytically, a new mathematical model is presented to capture the unique features of half-order harmonics and the connections to fundamental stick-slip/resonant frequency and multiple harmonics. The analytical solution and the experimental results show that the vibro-impact of the brake pad-disc system can be triggered by severe stick-slip vibrations and is associated with instable, impulsive stick-slip vibration with wideband. The induced stick-slip vibro-impact can evolve into a steady and strong state with half-order, stick-slip fundamental, and multiple-order components. This new mechanism is different from all previously proposed mechanisms of creep groan in that we also view some type of creep groan as a stick-slip vibration-induced vibro-impact phenomenon in addition to conventional stick-slip phenomena. The new mechanism comprehensively explains the complex experimental phenomena reported in the literature. Numerically, the salient features of phase diagrams of instable stick-slip and vibro-impact are examined by using a seven-degree-of-freedom brake system model, which shows that the phase diagrams of the dynamics of creep groan with and without vibro-impact are substantially different. The phase diagram of the dynamics with vibro-impact is closer to the experimental results. In contrast to existing mechanisms, the proposed new mechanism encompasses the instable stick-slip nature of creep groan and elaborates the inherent connections and transition of the spectrogram. The new knowledge can be used to attain critical improvements to brake noise and vibration analysis and design. By applying the proposed new model in addition to existing models, all experimental phenomena in creep groan are elaborated and quantified

Intelligent control of miniature holonomic vertical take-off and landing robot

This paper discusses the development of a fuzzy based controller for miniaturized unmanned aerial vehicle (UAV).This controller is designed to control the center-of-gravity (CoG) in a new configuration of coaxial miniaturized flying robot (MFR). The idea is to shift the CoG by controlling two pendulums located in perpendicular directions; each pendulum ends with a small mass. A key feature of this work is that the control algorithm represents the original nonlinear function that describes the dynamics of the proposed system. The controller model incorporates two cascaded subsystems: PD and PI fuzzy logic controllers. These two controllers regulate the attitude and the position of the flying robot, respectively. A model of the proposed controllers has been developed and evaluated in terms of stability and maneuverability. The results show that the presented control system can be used efficiently for the MFR applications

A multi-objective optimal PID control for a nonlinear system with time delay

It is generally difficult to design feedback controls of nonlinear systems with time delay to meet time domain specifications such as rise time, overshoot, and tracking error. Furthermore, these time domain specifications tend to be conflicting to each other to make the control design even more challenging. This paper presents a cell mapping method for multi-objective optimal feedback control design in time domain for a nonlinear Duffing system with time delay. We first review the multi-objective optimization problem and its formulation for control design. We then introduce the cell mapping method and a hybrid algorithm for global optimal solutions. Numerical simulations of the PID control are presented to show the features of the multi-objective optimal design

MULTI-OBJECTIVE OPTIMAL DESIGN OF CONTROL SYSTEMS

Feedback controls are usually designed to achieve multiple and often conflicting performance goals. These incommensurable objectives can be found in both time and frequency domains. For instance, one may want to design a control system such that the closed-loop system response to a step input has a minimum percentage overshoot , peak time, rise time, settling time, tracking error, and control effort. Another designer may want the controlled system to have a maximum crossover frequency, maximum phase margin and minimum steady-state error . However, Most of these objectives cannot be achieved concurrently. Therefore, trade-offs have to be made when the design objective space includes two or more conflicting objectives. These compromise solutions can be found by techniques called multi-objective optimization algorithms. Unlike the single optimization methods which return only a single solution, the multi-objective optimization algorithms return a set of solutions called the Pareto set and a set of the corresponding objective function values called the Pareto front.In this thesis, we present a multi-objective optimal (MOO) design of linear and nonlinear control systems using two algorithms: the non-dominated sorting genetic algorithm (NSGA-II) and a multi-objective optimization algorithm based on the simple cell mapping. The NSGA-II is one of the most popular methods in solving multi-objective optimization problems (MOPs). The cell mapping methods were originated by Hsu in 1980s for global analysis of nonlinear dynamical systems that can have multiple steady-state responses including equilibrium states, periodic motions, and chaotic attractors. However, this method can be also used also to solve multi-objective optimization problems by using a direct search method that can steer the search into any pre-selected direction in the objective space.Four case studies of robust multi-objective/many-objective optimal control design are introduced. In the first case, the NSGA-II is used to design the gains of a PID (proportional-integral-derivative) control and an observer simultaneously. The optimal design takes into account the stability robustness of both the control system and the estimator at the same time. Furthermore, the closed-loop system's robustness against external disturbances and measurement noises are included in the objective space.The second case study investigates the MOO design of an active control system applied to an under-actuated bogie system of high speed trains using the NSGA-II. Three conflicting objectives are considered in the design: the controlled system relative stability, disturbance rejection and control energy consumption. The performance of the Pareto optimal controls is tested against the train speed and wheel-rail contact conicity, which have huge impact on the bogie lateral stability.The third case addresses the MOO design of an adaptive sliding mode control for nonlinear dynamic systems. Minimizing the rise time, control energy consumption, and tracking integral absolute error and maximizing the disturbance rejection efficiency are the objectives of the design. The solution of the MOP results in a large number of trade-off solutions. Therefore, we also introduce a post-processing algorithm that can help the decision-maker to choose from the many available options in the Pareto set. Since the PID controls are the most used control algorithm in industry and usually experience time delay, a MOO design of a time-delayed PID control applied to a nonlinear system is presented as the fourth case study. The SCM is used in the solution of this problem. The peak time, overshoot and the tracking error are considered as design objectives and the design parameters are the PID controller gains

Multi-Objective Optimal Design of a Cascade Control System for a Class of Underactuated Mechanical Systems

This paper presents a multi-objective optimal design of a cascade control system for an underactuated mechanical system. Cascade control structures usually include two control algorithms (inner and outer). To design such a control system properly, the following conflicting objectives should be considered at the same time: 1) the inner closed-loop control must be faster than the outer one, 2) the inner loop should fast reject any disturbance and prevent it from propagating to the outer loop, 3) the controlled system should be insensitive to measurement noise, and 4) the controlled system should be driven by optimal energy. Such a control problem can be formulated as a multi-objective optimization problem such that the optimal trade-offs among these design goals are found. To authors best knowledge, such a problem has not been studied in multi-objective settings so far. In this work, an underactuated mechanical system consisting of a rotary servo motor and a ball and beam is used for the computer simulations, the setup parameters of the inner and outer control systems are tuned by NSGA-II (Non-dominated Sorting Genetic Algorithm), and the dominancy concept is used to find the optimal design points. The solution of this problem is not a single optimal cascade control, but rather a set of optimal cascade controllers (called Pareto set) which represent the optimal trade-offs among the selected design criteria. The function evaluation of the Pareto set is called the Pareto front. The solution set is introduced to the decision-maker who can choose any point to implement. The simulation results in terms of Pareto front and time responses to external signals show the competing nature among the design objectives. The presented study may become the basis for multi-objective optimal design of multi-loop control systems

Simple cell mapping method for multi-objective optimal feedback control design

This paper introduces the simple cell mapping (SCM) method for the multi-objective optimal time domain design of feedback controls for linear systems with or without time delay. The SCM method is originally developed for the global analysis of nonlinear dynamical systems, and is extended to the multi-objective optimal design problem of feedback controls in this paper. We consider two feedback control design problems to demonstrate the method: a linear quadratic regulator based approach with the weighting matrices as design parameters, and a direct optimization with feedback control gains as design parameters. The Pareto set and Pareto front consisting of the peak time, overshoot and integrated absolute tracking error are obtained for two linear control systems, one of which has a control time delay. It is interesting to note that for the second order linear system, we have found a structure of the Pareto front, which has been very difficult to obtain using stochastic search algorithms. This study suggests that the SCM method is an effective method that can provide global and fine-structured solutions of MOPs for complex dynamical systems

Many-Objective Optimal Design of Sliding Mode Controls

This paper presents a many-objective optimal (MOO) control design of an adaptive and robust sliding mode control (SMC). A second-order system is used as an example to demonstrate the design method. The robustness of the closed-loop system in terms of stability and disturbance rejection are explicitly considered in the optimal design, in addition to the typical time-domain performance specifications such as the rise time, tracking error, and control effort. The genetic algorithm is used to solve for the manyobjective optimization problem (MOOP). The optimal solutions known as the Pareto set and the corresponding objective functions known as the Pareto front are presented. To assist the decisionmaker to choose from the solution set, we present a postprocessing algorithm that operates on the Pareto front. Numerical simulations show that the proposed many-objective optimal control design and the post-processing algorithm are promising

Sensing and Quantifying a New Mechanism for Vehicle Brake Creep Groan

This paper investigates the creep groan of a vehicle’s brake experimentally, analytically, and numerically. Experimentally, the effects of acceleration on caliper and strut, noise, brake pressure, and tension are measured. The results show that the measured signals and their relevant spectra broadly capture the complex vibrations of creep groan. This includes the simple stick-slip, severe stick-slip vibrations/resonances, multiple harmonics, half-order harmonics; stick-slip-induced impulsive vibrations, steady/unstable vibrations, and their transitions. Analytically, a new mathematical model is presented to capture the unique features of half-order harmonics and the connections to fundamental stick-slip/resonant frequency and multiple harmonics. The analytical solution and the experimental results show that the vibro-impact of the brake pad-disc system can be triggered by severe stick-slip vibrations and is associated with instable, impulsive stick-slip vibration with wideband. The induced stick-slip vibro-impact can evolve into a steady and strong state with half-order, stick-slip fundamental, and multiple-order components. This new mechanism is different from all previously proposed mechanisms of creep groan in that we also view some type of creep groan as a stick-slip vibration-induced vibro-impact phenomenon in addition to conventional stick-slip phenomena. The new mechanism comprehensively explains the complex experimental phenomena reported in the literature. Numerically, the salient features of phase diagrams of instable stick-slip and vibro-impact are examined by using a seven-degree-of-freedom brake system model, which shows that the phase diagrams of the dynamics of creep groan with and without vibro-impact are substantially different. The phase diagram of the dynamics with vibro-impact is closer to the experimental results. In contrast to existing mechanisms, the proposed new mechanism encompasses the instable stick-slip nature of creep groan and elaborates the inherent connections and transition of the spectrogram. The new knowledge can be used to attain critical improvements to brake noise and vibration analysis and design. By applying the proposed new model in addition to existing models, all experimental phenomena in creep groan are elaborated and quantified