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Control (optimal Control Theory)
In optimal control theory, a control is a variable chosen by the controller or agent to manipulate state variables, similar to an actual control valve. Unlike the state variable, it does not have a predetermined equation of motion. The goal of optimal control theory is to find some sequence of controls (within an admissible set) to achieve an optimal path for the state variables (with respect to a loss function). A control given as a function of time only is referred to as an ''open-loop control''. In contrast, a control that gives optimal solution during some remainder period as a function of the state variable at the beginning of the period is called a ''closed-loop control''. See also * Control loop A control loop is the fundamental building block of industrial control systems. It consists of all the physical components and control functions necessary to automatically adjust the value of a measured process variable (PV) to equal the value of ... References Control loop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimal Control Theory
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems of sorts arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a define ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Agent (economics)
In economics, an agent is an actor (more specifically, a decision maker) in a model of some aspect of the economy. Typically, every agent makes decisions by solving a well- or ill-defined optimization or choice problem. For example, ''buyers'' (consumers) and ''sellers'' ( producers) are two common types of agents in partial equilibrium models of a single market. Macroeconomic models, especially dynamic stochastic general equilibrium models that are explicitly based on microfoundations, often distinguish households, firms, and governments or central banks as the main types of agents in the economy. Each of these agents may play multiple roles in the economy; households, for example, might act as consumers, as workers, and as voters in the model. Some macroeconomic models distinguish even more types of agents, such as workers and shoppers or commercial banks. The term ''agent'' is also used in relation to principal–agent models; in this case, it refers specifically to someone de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
State Variables
A state variable is one of the set of variables that are used to describe the mathematical "state" of a dynamical system. Intuitively, the state of a system describes enough about the system to determine its future behaviour in the absence of any external forces affecting the system. Models that consist of coupled first-order differential equations are said to be in state-variable form. Examples *In mechanical systems, the position coordinates and velocities of mechanical parts are typical state variables; knowing these, it is possible to determine the future state of the objects in the system. *In thermodynamics, a state variable is an independent variable of a state function. Examples include internal energy, enthalpy, temperature, pressure, volume and entropy. Heat and work are not state functions, but process functions. *In electronic/electrical circuits, the voltages of the nodes and the currents through components in the circuit are usually the state variables. In any e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Control Valve
A control valve is a valve used to control fluid flow by varying the size of the flow passage as directed by a signal from a controller. This enables the direct control of flow rate and the consequential control of process quantities such as pressure, temperature, and liquid level. In automatic control terminology, a control valve is termed a "final control element". Operation The opening or closing of automatic control valves is usually done by electrical, hydraulic or pneumatic actuators. Normally with a modulating valve, which can be set to any position between fully open and fully closed, valve positioners are used to ensure the valve attains the desired degree of opening. Air-actuated valves are commonly used because of their simplicity, as they only require a compressed air supply, whereas electrically operated valves require additional cabling and switch gear, and hydraulically actuated valves required high pressure supply and return lines for the hydraulic fluid. The p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equation Of Motion
In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time.''Encyclopaedia of Physics'' (second Edition), R.G. Lerner, G.L. Trigg, VHC Publishers, 1991, ISBN (Verlagsgesellschaft) 3-527-26954-1 (VHC Inc.) 0-89573-752-3 More specifically, the equations of motion describe the behavior of a physical system as a set of mathematical functions in terms of dynamic variables. These variables are usually spatial coordinates and time, but may include momentum components. The most general choice are generalized coordinates which can be any convenient variables characteristic of the physical system.''Analytical Mechanics'', L.N. Hand, J.D. Finch, Cambridge University Press, 2008, The functions are defined in a Euclidean space in classical mechanics, but are replaced by curved spaces in relativity. If the dynamics of a system is known, the equations are the solutions for the differential equations describing th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is called the ''length'' of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. Formally, a sequence can be defined as a function from natural numbers (the positions of elements in the sequence) to the elements at each position. The notion of a sequence can be generalized to an indexed family, defined as a function from an ''arbitrary'' index set. For example, (M, A, R, Y) is a sequence of letters with the letter 'M' first and 'Y' last. This sequence differs from (A, R, M, Y). Also, the sequence (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence. Sequences can be ''finite'', as in these examples, or ''infi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Loss Function
In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost" associated with the event. An optimization problem seeks to minimize a loss function. An objective function is either a loss function or its opposite (in specific domains, variously called a reward function, a profit function, a utility function, a fitness function, etc.), in which case it is to be maximized. The loss function could include terms from several levels of the hierarchy. In statistics, typically a loss function is used for parameter estimation, and the event in question is some function of the difference between estimated and true values for an instance of data. The concept, as old as Laplace, was reintroduced in statistics by Abraham Wald in the middle of the 20th century. In the context of economics, for example, this i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Control Loop
A control loop is the fundamental building block of industrial control systems. It consists of all the physical components and control functions necessary to automatically adjust the value of a measured process variable (PV) to equal the value of a desired set-point (SP). It includes the process sensor, the controller function, and the final control element (FCE) which are all required for automatic control. Application The accompanying diagram shows a control loop with a single PV input, a control function, and the control output (CO) which modulates the action of the final control element (FCE) to alter the value of the manipulated variable (MV). In this example, a flow control loop is shown, but can be level, temperature, or any one of many process parameters which need to be controlled. The control function shown is an "intermediate type" such as a PID controller which means it can generate a full range of output signals anywhere between 0-100%, rather than just an on/off sign ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
