Anti‐windup controller design for singularly perturbed systems subject to actuator saturation

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/166157/1/cth2bf00153.pd

Chattering-Free Sliding Mode Control with Unmodeled Dynamics

Sliding mode control systems are valued for their robust accommodation of uncertainties and their ability to reject disturbances. In this paper, a design methodology is proposed to eliminate the chattering phenomenon affecting sliding mode controlled plants with input unmodeled actuator dynamics of second order or greater. The proposed controller design is based on the relative degrees of the plant and the unmodeled actuator dynamics and the ranges of the uncertainties of the plant and actuator. The controller utilizes the pass filter characteristics of the physical actuating device to provide a smoothing effect on the discontinuous control signal rather than introducing any artificial dynamics into the controller design thus eliminating chattering in the system's output response

Spacecraft formation flying using bifurcating potential fields

The distributed control of spacecraft flying in formation has been shown to have advantages over conventional single spacecraft systems. These include scalability, flexibility and robustness to failures. This paper considers the real problem of actuator saturation and shows how bound control laws can be developed that allow pattern formation and reconfigurability in a formation of spacecraft using bifurcating potential fields. In addition the stability of the system is ensured mathematically through dynamical systems theory

Pattern transition in spacecraft formation flying using bifurcating potential field

Many new and exciting space mission concepts have developed around spacecraft formation flying, allowing for autonomous distributed systems that can be robust, scalable and flexible. This paper considers the development of a new methodology for the control of multiple spacecraft. Based on the artificial potential function method, research in this area is extended by considering the new approach of using bifurcation theory as a means of controlling the transition between different formations. For real, safety or mission critical applications it is important to ensure that desired behaviours will occur. Through dynamical systems theory, this paper also aims to provide a step in replacing traditional algorithm validation with mathematical proof, supported through simulation. This is achieved by determining the non-linear stability properties of the system, thus proving the existence or not of desired behaviours. Practical considerations such as the issue of actuator saturation and communication limitations are addressed, with the development of a new bounded control law based on bifurcating potential fields providing the key contribution of this paper. To illustrate spacecraft formation flying using the new methodology formation patterns are considered in low-Earth-orbit utilising the Clohessy-Wiltshire relative linearised equations of motion. It is shown that a formation of spacecraft can be driven safely onto equally spaced projected circular orbits, autonomously reconfiguring between them, whilst satisfying constraints made regarding each spacecraft

Two dimensional agonistic control

The conventional method of precise multiple-axis motion control entails use of a multiple axis positioning system with each axis carrying not only the workpiece but also the positioning system of the remaining axes. The resultant structure is heavy, sluggish, and expensive. An alternative positioning technique is being investigated in which the motion of the workpiece is controlled by pulling it with tendons, each of which has its own actuator. Since the actuators can be mounted on the base of the structure instead of being carried by motion system of the other axes, they can be relatively large and powerful without the need for a massive structure such as is found in a conventional motion control system. This method of control is given the appellation agonistic, based on the usages of the word suggesting tension or a contest. Agonistic control system can be used for low cost accurate positioning of workpiece. The control task can be moving the workpiece from one point to another point and kept there or tracking a given trajectory. While the workpiece moves, the tendons should be always kept in tension. In this thesis, the model of two dimensional agonistic control (in the case of tendons of infinite elastic modulus) is established. It leads to a nonlinear multi-variable control problem. Based on this nonlinear model, a full-state feedback control law is synthesized. It is composed of two parts. The first part is a feedforward control to cancel the nonlinear dynamics. The second part is a PD control term which requires velocity information. In the practice, velocity measurement may be contaminated by noise. In order of only using position measurement in the control law, a nonlinear observer is designed to provide the velocity information. Numerical simulation is performed to verify the ability of the proposed control law. In reality, the tendon has some elasticity. This finite elasticity, if not accounted for, can render the closed-loop system unstable. The investigation shows that the effect of elastic tendons can be compensated for by appropriately modifying the control law designed for inelastic tendons. In particular, the control law is synthesized using the singular perturbation method. It consists of a fast control and a slow control. The fast control is used to stablize the oscillations incurred by the finite elasticity of the tendon. The slow control drives the system to track the desired trajectory. Robustness of the controller is enhanced by using sliding mode control. In the chapter 4, the design of observer in the elastic case is addressed. Linear uncertain system theory is used. The observer is globally stable. The use of decentralized control scheme makes very simple the controller design and reduces the computational complexity. It is very useful for real time agonistic control. A design approach is presented for the decentralized control scheme. A simple linear second order model is used instead of complex nonlinear model used in centralized version. In this approach, the tension in each tendon is treated as disturbance, estimated by an observer, to be compensated

Dynamics and control of flexible manipulators

Flexible link manipulators (FLM) are well-known for their light mass and small energy consumption compared to rigid link manipulators (RLM). These advantages of FLM are even of greater importance in applications where energy efficiency is crucial, such as in space applications. However, RLM are still preferred over FLM for industrial applications. This is due to the fact that the reliability and predictability of the performance of FLM are not yet as good as those of RLM. The major cause for these drawbacks is link flexibility, which not only makes the dynamic modeling of FLM very challenging, but also turns its end-effector trajectory tracking (EETT) into a complicated control problem. The major objectives of the research undertaken in this project were to develop a dynamic model for a FLM and model-based controllers for the EETT. Therefore, the dynamic model of FLM was first derived. This dynamic model was then used to develop the EETT controllers. A dynamic model of a FLM was derived by means of a novel method using the dynamic model of a single flexible link manipulator on a moving base (SFLMB). The computational efficiency of this method is among its novelties. To obtain the dynamic model, the Lagrange method was adopted. Derivation of the kinetic energy and the calculation of the corresponding derivatives, which are required in the Lagrange method, are complex for the FLM. The new method introduced in this thesis alleviated these complexities by calculating the kinetic energy and the required derivatives only for a SFLMB, which were much simpler than those of the FLM. To verify the derived dynamic model the simulation results for a two-link manipulator, with both links being flexible, were compared with those of full nonlinear finite element analysis. These comparisons showed sound agreement. A new controller for EETT of FLM, which used the singularly perturbed form of the dynamic model and the integral manifold concept, was developed. By using the integral manifold concept the links’ lateral deflections were approximately represented in terms of the rotations of the links and input torques. Therefore the end-effector displacement, which was composed of the rotations of the links and links’ lateral deflections, was expressed in terms of the rotations of the links and input torques. The input torques were then selected to reduce the EETT error. The originalities of this controller, which was based on the singularly perturbed form of the dynamic model of FLM, are: (1) it is easy and computationally efficient to implement, and (2) it does not require the time derivative of links’ lateral deflections, which are impractical to measure. The ease and computational efficiency of the new controller were due to the use of the several properties of the dynamic model of the FLM. This controller was first employed for the EETT of a single flexible link manipulator (SFLM) with a linear model. The novel controller was then extended for the EETT of a class of flexible link manipulators, which were composed of a chain of rigid links with only a flexible end-link (CRFE). Finally it was used for the EETT of a FLM with all links being flexible. The simulation results showed the effectiveness of the new controller. These simulations were conducted on a SFLM, a CRFE (with the first link being rigid and second link being flexible) and finally a two-link manipulator, with both links being flexible. Moreover, the feasibility of the new controller proposed in this thesis was verified by experimental studies carried out using the equipment available in the newly established Robotic Laboratory at the University of Saskatchewan. The experimental verifications were performed on a SFLM and a two-link manipulator, with first link being rigid and second link being flexible.Another new controller was also introduced in this thesis for the EETT of single flexible link manipulators with the linear dynamic model. This controller combined the feedforward torque, which was required to move the end-effector along the desired path, with a feedback controller. The novelty of this EETT controller was in developing a new method for the derivation of the feedforward torque. The feedforward torque was obtained by redefining the desired end-effector trajectory. For the end-effector trajectory redefinition, the summation of the stable exponential functions was used. Simulation studies showed the effectiveness of this new controller. Its feasibility was also proven by experimental verification carried out in the Robotic Laboratory at the University of Saskatchewan