Quantitative Feedback Theory
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Quantitative Feedback Theory
In control theory, quantitative feedback theory (QFT), developed by Isaac Horowitz (Horowitz, 1963; Horowitz and Sidi, 1972), is a frequency domain technique utilising the Nichols chart (NC) in order to achieve a desired robust design over a specified region of plant uncertainty. Desired time-domain responses are translated into frequency domain tolerances, which lead to bounds (or constraints) on the loop transmission function. The design process is highly transparent, allowing a designer to see what trade-offs are necessary to achieve a desired performance level. Plant templates Usually any system can be represented by its Transfer Function (Laplace in continuous time domain), after getting the model of a system. As a result of experimental measurement, values of coefficients in the Transfer Function have a range of uncertainty. Therefore, in QFT every parameter of this function is included into an interval of possible values, and the system may be represented by a family of pl ...
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Control Theory
Control theory is a field of control engineering and applied mathematics that deals with the control system, control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any ''delay'', ''overshoot'', or ''steady-state error'' and ensuring a level of control Stability theory, stability; often with the aim to achieve a degree of Optimal control, optimality. To do this, a controller with the requisite corrective behavior is required. This controller monitors the controlled process variable (PV), and compares it with the reference or Setpoint (control system), set point (SP). The difference between actual and desired value of the process variable, called the ''error'' signal, or SP-PV error, is applied as feedback to generate a control action to bring the controlled process variable to the same value as the set point. Other aspects ...
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Process Control
Industrial process control (IPC) or simply process control is a system used in modern manufacturing which uses the principles of control theory and physical industrial control systems to monitor, control and optimize continuous Industrial processes, industrial production processes using control algorithms. This ensures that the industrial machines run smoothly and safely in factories and efficiently use energy to transform raw materials into high-quality finished products with reliable consistency while reducing Efficient energy use#Industry, energy waste and economic costs, something which could not be achieved purely by human manual control. In IPC, control theory provides the theoretical framework to understand system dynamics, predict outcomes and design control strategies to ensure predetermined objectives, utilizing concepts like feedback loops, stability analysis and controller design. On the other hand, the physical apparatus of IPC, based on automation technologies, cons ...
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Intelligent Control
Intelligent control is a class of control techniques that use various artificial intelligence computing approaches like neural networks, Bayesian probability, fuzzy logic, machine learning, reinforcement learning, evolutionary computation and genetic algorithms. Overview Intelligent control can be divided into the following major sub-domains: * Neural network control * Machine learning control * Reinforcement learning * Bayesian control * Fuzzy control * Neuro-fuzzy control * Expert Systems * Genetic control New control techniques are created continuously as new models of intelligent behavior are created and computational methods developed to support them. Neural network controller Neural networks have been used to solve problems in almost all spheres of science and technology. Neural network control basically involves two steps: * System identification * Control It has been shown that a feedforward network with nonlinear, continuous and differentiable activation func ...
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Robust Control
In control theory, robust control is an approach to controller design that explicitly deals with uncertainty. Robust control methods are designed to function properly provided that uncertain parameters or disturbances are found within some (typically compact) set. Robust methods aim to achieve robust performance and/or stability in the presence of bounded modelling errors. The early methods of Bode and others were fairly robust; the state-space methods invented in the 1960s and 1970s were sometimes found to lack robustness, prompting research to improve them. This was the start of the theory of robust control, which took shape in the 1980s and 1990s and is still active today. In contrast with an adaptive control policy, a robust control policy is static, rather than adapting to measurements of variations, the controller is designed to work assuming that certain variables will be unknown but bounded. (Section 1.5) In German; an English version is also available Criteria for robust ...
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Adaptive Control
Adaptive control is the control method used by a controller which must adapt to a controlled system with parameters which vary, or are initially uncertain. For example, as an aircraft flies, its mass will slowly decrease as a result of fuel consumption; a control law is needed that adapts itself to such changing conditions. Adaptive control is different from robust control in that it does not need ''a priori'' information about the bounds on these uncertain or time-varying parameters; robust control guarantees that if the changes are within given bounds the control law need not be changed, while adaptive control is concerned with control law changing itself. Parameter estimation The foundation of adaptive control is parameter estimation, which is a branch of system identification. Common methods of estimation include recursive least squares and gradient descent. Both of these methods provide update laws that are used to modify estimates in real-time (i.e., as the system operates). ...
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Nonlinear Control
Nonlinear control theory is the area of control theory which deals with systems that are nonlinear system, nonlinear, time-variant system, time-variant, or both. Control theory is an interdisciplinary branch of engineering and mathematics that is concerned with the behavior of dynamical systems with inputs, and how to modify the output by changes in the input using feedback, Feed forward (control), feedforward, or filter (signal processing), signal filtering. The system to be controlled is called the "plant (control theory), plant". One way to make the output of a system follow a desired reference signal is to compare the output of the plant to the desired output, and provide feedback to the plant to modify the output to bring it closer to the desired output. Control theory is divided into two branches. Linear control theory applies to systems made of devices which obey the superposition principle. They are governed by linear equation, linear differential equations. A majo ...
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Servomechanism
In mechanical and control engineering, a servomechanism (also called servo system, or simply servo) is a control system for the position and its time derivatives, such as velocity, of a mechanical system. It often includes a servomotor, and uses closed-loop control to reduce steady-state error and improve dynamic response. In closed-loop control, error-sensing negative feedback is used to correct the action of the mechanism. In displacement-controlled applications, it usually includes a built-in encoder or other position feedback mechanism to ensure the output is achieving the desired effect. Following a specified motion trajectory is called servoing, where "servo" is used as a verb. The ''servo'' prefix originates from the Latin word ''servus'' meaning slave. The term correctly applies only to systems where the feedback or error-correction signals help control mechanical position, speed, attitude or any other measurable variables. For example, an automotive power win ...
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Optimal Control
Optimal control theory is a branch of control theory that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and operations research. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the Moon with minimum fuel expenditure. Or the dynamical system could be a nation's economy, with the objective to minimize unemployment; the controls in this case could be fiscal and monetary policy. A dynamical system may also be introduced to embed operations research problems within the framework of optimal control theory. Optimal control is an extension of the calculus of variations, and is a mathematical optimization method for deriving control policies. The method is largely due to the work of Lev Pontryagin and Richard Bellman in the 1950s, after contributions to calculus of v ...
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H Infinity
''H''∞ (i.e. "''H''-infinity") methods are used in control theory to synthesize controllers to achieve stabilization with guaranteed performance. To use ''H''∞ methods, a control designer expresses the control problem as a mathematical optimization problem and then finds the controller that solves this optimization. ''H''∞ techniques have the advantage over classical control techniques in that ''H''∞ techniques are readily applicable to problems involving multivariate systems with cross-coupling between channels; disadvantages of ''H''∞ techniques include the level of mathematical understanding needed to apply them successfully and the need for a reasonably good model of the system to be controlled. It is important to keep in mind that the resulting controller is only optimal with respect to the prescribed cost function and does not necessarily represent the best controller in terms of the usual performance measures used to evaluate controllers such as settling time, ene ...
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Unicycle Cart
A unicycle is a vehicle that touches the ground with only one wheel. The most common variation has a frame with a saddle, and has a pedal-driven direct-drive. A two speed hub is commercially available for faster unicycling. Unicycling is practiced professionally in circuses, by street performers, in festivals, and as a hobby. Unicycles have also been used to create new sports such as unicycle hockey. In recent years, unicycles have also been used in mountain unicycling, an activity similar to mountain biking or trials. History US patents for single-wheeled 'velocipedes' were published in 1869 by Frederick Myers and in 1881 by Battista Scuri. Unicycle design has developed since the Penny Farthing and later the advent of the first unicycle into many variations including: the seatless unicycle (" ultimate wheel") the tall ("giraffe") unicycle and "2-wheelers" or "3-wheelers" (multiple wheels stacked directly on top of each other). During the late 1980s some extreme sportsmen too ...
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