Hybrid Controller Design Research Articles

A Hybrid Switching and Proportional Control Framework for Planar Under-Actuated Manipulators

This paper presents a hybrid control scheme for planar under-actuated manipulators. The proposed hybrid control combines simple switching control and proportional control into one framework. The result is obtained by simplifying early discussion on hybrid control of the Pendubot (Zhang and Tarn, 2002), where derivative control part was also included as part of the hybrid control. Our recent studies show that it may not be necessary to include the derivative control part for hybrid control of planar under-actuated manipulators. The advantages of the derivative control part, such as decreasing overshoot and setting time, can be reached through switching control. However, the proportional control part is still necessary. It is helpful for decreasing the rising time. A proof of the proposed hybrid control design criteria and an example are given in this paper.

Design and analysis of a hybrid control scheme for sandwich nonsmooth nonlinear systems

This paper addresses an open control problem: the control of sandwich non-smooth nonlinear systems. Of interest are sandwiched non-smooth nonlinearities between linear dynamic blocks, as illustrated by a hydraulic valve system with a sandwiched dead-zone. A hybrid control scheme for the control of such sandwich systems is developed and presented in detail. The proposed control scheme employs an inner-loop discrete-time feedback design and an outer-loop continuous-time feedback design, combined with a nonlinearity inverse, to cancel the nonlinearity effect, for improving output tracking. The stability and tracking performance of the closed-loop control system are analyzed. Simulations are used to illustrate the effectiveness of the proposed hybrid control design.

ROBUST HYBRID CONTROL OF UNCERTAIN CONSTRAINED MECHANICAL SYSTEMS

Robust hybrid controller design is presented in this paper for motion/force control of mechanical systems subjected to a set of holonomic or classical nonholonomic constraints and in the presence of uncertainties about plant parameters. A unified and systematic procedure is employed to derive the controllers for both holonomic and nonholonomic constrained mechanical systems, respectively. The proposed controllers can guarantee the system motion asymptotically converges to the desired manifold, and the force tracking errors to be bounded. Numerical simulation has been done to show the effectiveness of the proposed controllers.

Hybrid Controller Design and Its Application to a Class of Nonholonomic Systems – Based on Complementarity Approach –

This paper is concerned with hybrid control of nonholonomic systems by hybrid controllers having complementarity system representations. At first, we consider feedback interconnections of complementarity systems, and derive a sufficient condition for the resulting closed loop systems to be well-posed. Secondary we apply the result to the design of a hybrid controller which belongs to a class of complementarity systems for a class of nonholonomic systems. In the resulting feedback system, the well-posedness is automatically guaranteed with the aid of the former conditions.

An invariant‐based approach to the design of hybrid control systems

AbstractIn this paper, a methodology for hybrid control design is presented. The hybrid systems of interest are characterized by a feedback architecture of a continuous nonlinear plant with a discrete‐event controller. The natural invariants of the continuous dynamics are used to partition the state space into regions and to synthesize simple and efficient control laws. The paper contains a complete description of the approach including a description of the hybrid control system modelling, of the invariant‐based approach for the design of the partition, and of the controller synthesis methodology illustrated by examples. The implementation and optimization of the approach are also discussed. The approach presented in this paper not only describes a viable methodology to hybrid design, but also addresses fundamental issues in hybrid system theory that arise in reachability analysis and verification approaches that are based on partitions of the continuous state space. Copyright © 2001 John Wiley & Sons, Ltd.

Issues on Nonlinear Digital Control

The purpose of this work is to show the real need to motivate theoretical research in nonlinear digital control not only for solving control problems which are specific to the context, but also for giving the intuition of new control methodologies. Digital control methods can, indeed, be used either for the design of piecewice constant feedback strategies or for the design of discontinuous and hybrid controllers.

Automotive engine control and hybrid systems: challenges and opportunities

The design of engine control systems has been traditionally carried out using a mix of heuristic techniques validated by simulation and prototyping using approximate average-value models. However, the ever increasing demands on passengers' comfort, safety, emissions, and fuel consumption imposed by car manufacturers and regulations call for more robust techniques and the use of cycle-accurate models. We argue that these models must be hybrid because of the combination of time-domain and event-based behaviors. We present a hybrid model of the engine in which both continuous and discrete time-domain as well as event-based phenomena are modeled in a separate but integrated manner. Based on this model, we formalize the specification of the overall engine control by defining a number of hybrid control problems. To cope with the difficulties arising in the design of hybrid controllers, a design methodology is proposed. This methodology consists of a relaxation of the hybrid problem by simplifying some of its components to obtain a solvable problem,and then deriving a solution to the original control problem by appropriately modifying the control law so obtained to take into consideration the original specifications and models. The effectiveness of this approach is illustrated on three challenging problems: fast force-transient control, cutoff control, and idle speed control.

Performance benefits of hybrid control design for linear and nonlinear systems

This paper provides an overview of recent developments on design of hybrid controllers for continuous-time control systems that can be described by linear or nonlinear differential state equations. Hybrid controllers provide a generalization of classical feedback controllers for linear and nonlinear systems. The benefit of hybrid controllers, that they can be used to achieve closed-loop performance objectives that cannot be achieved using classical linear or nonlinear controllers, is emphasized. This paper introduces hybrid controllers in the form of a switching control architecture and provides a summary of recently developed control approaches that utilize this control architecture. We provide a conceptual framework for these results, identify limitations of the results, and discuss the current status of hybrid control design approaches.

HYBRID H2CONTROL DESIGN FOR VIBRATION ISOLATION

Combined feedforward and feedback (hybrid) controller design has recently been shown to be an effective approach for acoustic and structural vibration control. This paper extends previous analysis of this architecture to investigate the strong coupling that typically exists between the feedforward and feedback components for a system having noise on the feedforward sensor. One shows with a simple structural isolation example that the optimal hybrid H2controller offers the benefit of simultaneous improvement in vibration performance along with a reduction in closed loop control bandwidth.

Verified hybrid controllers for automated vehicles

The objective of an automated highway system (AHS) is to increase the safety and throughput of the existing highway infrastructure by introducing traffic automation. AHS is an example of a large scale, multiagent complex dynamical system and is ideally suited for a hierarchical hybrid controller. We discuss the design of safe and efficient hybrid controllers for regulation of vehicles on an AHS. We use game theoretic techniques to deal with the multiagent and multiobjective nature of the problem. The result is a hybrid controller that by design guarantees safety, without the need for further verification. The calculations also provide an upper bound on the performance that can be expected in terms of throughput at various levels of centralization.

A framework for hybrid control design

This paper presents a hybrid system framework which considers simultaneously the control and decision-making issues. This reconfigurable framework can accommodate a wide range of situations, from aircraft control systems to mobile manipulators. A continuous-state plant is supervised by a discrete-event system which is based on a theory of linked finite state machines. The composite system is viewed as an iterative process where a task is carried out by changing the structure of the continuous-state plant. An algorithm for a hybrid control design is provided and illustrated through a mobile manipulator example.

An Invariant based Approach to the Design of Hybrid Control Systems

In this paper, a methodology for hybrid control design is presented. The hybrid systems of interest are characterized by a feedback architecture of a continuous nonlinear plant with a discrete-event controller. The natural invariants of the continuous dynamics are used to partition the state space into regions and to synthesize simple and eAEcient control laws. The paper contains a complete description of the approach including a description of the hybrid control system modeling, of the invariant based approach for the design of the partition, and of the controller synthesis methodology illustrated by examples. The implementation and optimization of the approach are also discussed. The approach presented in this paper not only describes a viable methodology to hybrid design, but also addresses fundamental issues in hybrid system theory that arise in reachability analysis and veri cation approaches that are based on partitions of the continuous state space.

Adaptive hybrid control strategies for constrained robots

The problem of adaptive hybrid controller design for constrained roots with the consideration of computational efficiency is addressed. Two efficient control schemes based, respectively, on Lagrange and Newton-Euler dynamics formulation are presented. Detailed analyses on tracking properties of joint positions, velocities, and constrained forces are derived for both the Lagrange approach and the Newton-Euler approach. Although control laws in these two approaches are developed independently, a tight connection between them is found, indicating a possible bridge between general adaptive approaches based, respectively, on the two dynamics formulations. >

Hybrid control: A constrained motion perspective

AbstractControl of manipulators during execution of tasks that require the end‐effector to come into contact with objects in its work environment represents an important class of control problem. Hybrid control, a concept which defines the architecture of a class of control laws has been proposed as a method with which to solve this control problem. One interpretation of the hybrid control method is within the framework of constrained motion control. Constrained motion occurs during contact by the manipulator end‐effector with rigid objects in the workplace, hence the motion of the manipulator is kinematically constrained. Papers have appeared in the robotics control literature addressing hybrid control within the constrained motion context which do not explicitly use the constrained dynamic formulation that correctly describes the dynamic behaviour of the manipulator. This article serves to link results from constrained motion control and the existing literature on the hybrid control method. In this article a formulation of the constrained manipulator dynamics is presented in which the hybrid control design is most naturally carried out. This formulation of the manipulator dynamics, previously proposed in the robotics literature, is such that the generalized force and position coordinates to be controlled are mutually orthogonal. Hence, the hybrid selection matrices, a key element of the hybrid control design philosophy, are implicit in this coordinate representation. A hybrid control design methodology is then formulated based on this development. Two hybrid control laws are proposed. For each hybrid control law, the global asymptotic stability is readily established due to the natural coordinate representation. One of these hybrid control laws, a constrained motion control law already proposed in the literature, is given to illustrate the equivalence of the hybrid control design and certain existing constrained motion control methods. Finally, a concrete example of a three‐degree‐of‐freedom robotic manipulator illustrates the hybrid design methodology proposed.