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A description of feedback control is presented within the context of differential equations, differential geometry, and Lie theory. Work related to the integration of differential geometry with the control techniques of feedback linearization is summarized. Particular attention is given to the application of the theory of vector field systems. Feedback invariants for control systems in state space form are also addressed.
A single cloud-radiation feedback mechanism, which may play a role in the climate changes expected from increased atmospheric concentrations of carbon dioxide and other trace greenhouse gases, is described. An improved radiative-convective model was developed and used to study the role of cirrus clouds in the optical thickness feedback mechanism. The model includes prescribed relative humidity and ozone profiles and a surface energy balance. The results suggest that the cloud optical thickness feedback mechanism can cause a substantial reduction in the surface warming due to doubling CO2, even in the presence of cirrus clouds.
A new approach for the eigenvalue assignment of linear, first-order, time-invariant systems using output feedback is developed. The approach can assign the maximum allowable number of closed-loop eigenvalues through output feedback provided that the system is fully controllable and observable, and both the input influence and output influence matrices are full rank. First, a collection of bases for the space of attainable closed-loop eigenvectors is generated using the Singular Value Decomposition or QR Decomposition techniques. Then, an algorithm based on subspace intersections is developed and used to compute the corresponding coefficients of the bases, and the required output feedback gain matrix. Moreover, the additional freedom provided by the multi-inputs and multi-outputs beyond the eigenvalue assignment is characterized for possible exploitation. A numerical example is given to demonstrate the viability of the proposed approach.
As automation increasingly takes its place in industry, especially high-risk industry, it is often blamed for causing harm and increasing the chance of human error when failures occur. It is proposed that the problem is not the presence of automation, but rather its inappropriate design. The problem is that the operations are performed appropriately under normal conditions, but there is inadequate feedback and interaction with the humans who must control the overall conduct of the task. When the situations exceed the capabilities of the automatic equipment, then the inadequate feedback leads to difficulties for the human controllers. The problem is that the automation is at an intermediate level of intelligence, powerful enough to take over control that which used to be done by people, but not powerful enough to handle all abnormalities. Moreover, its level of intelligence is insufficient to provide the continual, appropriate feedback that occurs naturally among human operators. To solve this problem, the automation should either be made less intelligent or more so, but the current level is quite inappropriate. The overall message is that it is possible to reduce error through appropriate design considerations.
The feasibility of a new Modal Positive Position Feedback (MPPF) strategy in controlling the vibration of a complex flexible structure using a single piezo-electric active structural member is demonstrated. The control strategy generates its control forces by manipulating only the modal position signals of the structure to provide a damping action to undamped modes. This is in contrast to conventional modal controllers that rely in their operation on negative feedback of both the modal position and velocity. The proposed strategy is very simple to design and implement as it designs the controller at the uncoupled modal level and utilizes simple first order filters to achieve the Positive Position Feedback effect. The performance of the new strategy is enhanced by augmenting it with a time sharing strategy to share a small number of actuators between larger number of modes. The effectiveness of the new strategy is validated experimentally on a flexible box-type structure that has four bays and its first two bending modes are 2.015 and 6.535 Hz respectively. A single piezo-electric actuator is utilized as an active structural member to control several transverse bending modes of the structure. The performance of the active control system is determined in the time and the frequency domains. The results are compared with those obtained when using the Independent Modal Space Control (IMSC) of Meirovitch. The experimental results suggest the potential of the proposed strategy as a viable means for controlling the vibration of large flexible structures in real time.
In a system having a driver, a motor, and a mechanical plant, a multiloop feedback control apparatus for controlling the movement and/or positioning of a mechanical plant, the control apparatus has a first local bridge feedback loop for feeding back a signal representative of a selected ratio of voltage and current at the output driver, and a second bridge feedback loop for feeding back a signal representative of a selected ratio of force and velocity at the output of the motor. The control apparatus may further include an outer loop for feeding back a signal representing the angular velocity and/or position of the mechanical plant.
It is widely believed that thin cirrus clouds act to enhance the greenhouse effect owing to a particular combination of their optical properties. It is demonstrated how this effect is perhaps based on inadequate resolution of the physics of cirrus clouds and that the more likely impact of cirrus clouds to climate change remains somewhat elusive. These conclusions are developed within the context of a specific feedback mechanism incorporated into a simple mechanistic climate model. A specific scientific question addressed is whether or not the observed relationship between the ice water content and temperature of cirrus provides any significant feedback to the CO2 greenhouse warming. A related question also examined concerns the specific role of cloud microphysics and radiation in this feedback. This raises several pertinent issues about the understanding of cirrus clouds and their likely role in climate change as there presently exists a considerable uncertainty about the microphysics of these clouds (size and shape of ice crystals) and their radiative influences.
A major drawback of open loop masters is a lack of force feedback, limiting their ability to perform complex tasks such as assembly and repair. Researchers present a simple dextrous force feedback master for computer assisted telemanipulation. The device is compact, portable and can be held in the operator hand, without the need for a special joystick or console. The system is capable of both position feed forward and force feedback, using electronic position sensors and a pneumatic micro-actuator. The level of forces exercised by the pneumatic actuator is such that near rigidity may be attained. Experimental results showing good system linearity and small time lag are given.
Reflected-force feedback is an important aspect of teleoperations. The objective is to determine the ability of the human operator to respond to that force. Telerobotics operation is simulated by computer control of a motor-driven device with capabilities for programmable force feedback and force measurement. A computer-controlled motor drive is developed that provides forces against the fingers as well as (angular) position control. A load cell moves in a circular arc as it is pushed by a finger and measures reaction forces on the finger. The force exerted by the finger on the load cell and the angular position are digitized and recorded as a function of time by the computer. Flexure forces of the index, long and ring fingers of the human hand in opposition to the motor driven load cell are investigated. Results of the following experiments are presented: (1) Exertion of maximum finger force as a function of angle; (2) Exertion of target finger force against a computer controlled force; and (3) Test of the ability to move to a target force against a force that is a function of position. Averaged over ten individuals, the maximum force that could be exerted by the index or long finger is about 50 Newtons, while that of the ring finger is about 40 Newtons. From the tests of the ability of a subject to exert a target force, it was concluded that reflected-force feedback can be achieved with the direct kinesthetic perception of force without the use of tactile or visual clues.
An improved radiative-convective model (RCM) has been developed and used to examine the role of cirrus clouds in the optical thickness feedback mechanism. Low and middle clouds are approximately black bodies for infrared radiative transfer, and so any increase in their optical thickness primarily increases the cloud albedo. Thus, if a climate warming is accompanied by an increase in average atmospheric absolute humidity and hence in average cloud liquid water content, low and middle cloud optical thickness and albedo may increase. The result is a negative feedback on the climate change, tending to reduce the surface temperature increase. Recent research suggests that the optical thickness feedback can depend sensitively on aspects of cirrus which are not well observed or adequately incorporated in typical present-day climate models.
Pinsker and Ebert (1970) proved that in channels with additive Gaussian noise, feedback at most doubles the capacity. Cover and Pombra (1989) proved that feedback at most adds half a bit per transmission. Following their approach, the author proves that in the limit as signal power approaches either zero (very low SNR) or infinity (very high SNR), feedback does not increase the finite block-length capacity (which for nonstationary Gaussian channels replaces the standard notion of capacity that may not exist). Tighter upper bounds on the capacity are obtained in the process. Specializing these results to stationary channels, the author recovers some of the bounds recently obtained by Ozarow.
The feasibility of a new Modal Positive Position Feedback (MPPF) strategy in controlling the vibration of a complex flexible structure using a single piezo-electric active structural member is demonstrated. The control strategy generates its control forces by manipulating only the modal position signals of the structure to provide a damping action to undamped modes. This is in contrast to conventional modal controllers that rely in their operation on negative feedback of both the modal position and velocity. The proposed strategy is very simple to design and implement as it designs the controller at the uncoupled modal level and utilizes simple first order filters to achieve the Positive Position Feedback effect. The performance of the new strategy is enhanced by augmenting it with a time sharing strategy to share a small number of actuators between larger number of modes. The effectiveness of the new strategy is validated experimentally on a flexible box-type structure that has four bays and its first two bending modes are 2.015 and 6.535 Hz, respectively. A single piezo-electric actuator is utilized as an active structural member to control several transverse bending modes of the structure. The performance of the active control system is determined in the time and the frequency domains. The results are compared with those obtained when using the Independent Modal Space Control (IMSC) of Meirovitch. The experimental results suggest the potential of the proposed strategy as a viable means for controlling the vibration of large flexible structures in real time.
A study was conducted to examine the effects of process and outcome feedback on performance during a skill acquisition phase and a transfer test phase. The research also examined the role of two moderators: self-efficacy and intrinsic motivation. Subjects were college students participating for course credit. The task involved using a computerized simulation of the Space Shuttle's Remote Manipulation System (RMS). Results provided evidence of the beneficial effects of process feedback during skill acquisition. Results also provided evidence that self-efficacy and intrinsic motivation moderate the effects of feedback type on performance.
The method of feedback linearization for control of the nonlinear nozzle and compressor components of an air breathing engine is presented. This method overcomes the need for a large number of scheduling variables and operating points to accurately model highly nonlinear plants. Feedback linearization also results in linear closed loop system performance simplifying subsequent control design. Feedback linearization is used for the nonlinear partial engine model and performance is verified through simulation.
Report discusses theoretical and experimental studies of positive-position-feedback control for suppressing vibrations in large flexible structures. Positive-position-feedback control involves placement of actuators and sensors on structure; control voltages applied to actuators in response to outputs of sensors processed via compensator algorithm. Experiments demonstrate feasibility of suppressing vibrations by positive position feedback, and spillover of vibrational energy into uncontrolled modes has stabilizing effect if control gain sufficiently small.
An active damping augmentation approach using active members in a structural system is described. The problem of maximizing the vibration damping in a lightly damped structural system is considered using the analogy of impedance matching between the load and source impedances in an electrical network. The proposed active damping augmentation approach therefore consists of finding the desired active member impedances that maximize the vibration damping, and designing a feedback control in order to achieve desired active member impedances. This study uses a bridge feedback concept that feeds back a combination of signals from sensors of the axial force and relative velocity across the active member to realize the desired active member impedance. The proposed active damping augmentation approach and bridge feedback concept were demonstrated on a three-longeron softly suspended truss structure.
In this article, the vibration control of adaptive truss structures, where the control actuation is provided by length adjustable active members, is formulated as a direct output feedback control problem. A control method named Model Truncated Output Feedback (MTOF) is presented. The method allows the control feedback gain to be determined in a decoupled and truncated modal space in which only the critical vibration modes are retained. The on-board computation required by MTOF is minimal; thus, the method is favorable for the applications of vibration control of large scale structures. The truncation of the modal space inevitably introduces spillover effect during the control process. In this article, the effect is quantified in terms of active member locations, and it is shown that the optimal placement of active members, which minimizes the spillover effect (and thus, maximizes the control performance) can be sought. The problem of optimally selecting the locations of active members is also treated.
We consider the problem of obtaining integral representation of feedback operators for damped hyperbolic control systems. We show that for the wave equation with Kelvin-Voigt damping and non-compact input operator, the feedback gain operator is Hilbert-Schmidt. This result is then used to provide an explicit integral representation for the feedback operator in terms of functional gains. Numerical results are given to illustrate the role that damping plays in the smoothness of these gains.