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60-586: MPC , Mpc or mpc may refer to: Astronomy [ edit ] Megaparsec (Mpc), unit of length used in astronomy Minor Planet Center , Smithsonian Astrophysical Observatory Minor Planet Circulars (MPC, M.P.C. or MPCs), astronomical publication from the Minor Planet Center Businesses [ edit ] Mai-Liao Power Corporation , Taiwan Model Products Corporation , model kit manufacturer Moving Picture Company ,

120-469: A u ≈ 206 264.81   a u . {\displaystyle {\begin{aligned}\mathrm {SD} &={\frac {\mathrm {ES} }{\tan 1''}}\\&={\frac {\mathrm {ES} }{\tan \left({\frac {1}{60\times 60}}\times {\frac {\pi }{180}}\right)}}\\&\approx {\frac {1\,\mathrm {au} }{{\frac {1}{60\times 60}}\times {\frac {\pi }{180}}}}={\frac {648\,000}{\pi }}\,\mathrm {au} \approx 206\,264.81~\mathrm {au} .\end{aligned}}} Because

180-793: A u = 180 × 60 × 60 × 149 597 870 700   m = 96 939 420 213 600 000   m {\displaystyle \pi ~\mathrm {pc} =180\times 60\times 60~\mathrm {au} =180\times 60\times 60\times 149\,597\,870\,700~\mathrm {m} =96\,939\,420\,213\,600\,000~\mathrm {m} } (exact by the 2015 definition) Therefore, 1   p c = 96 939 420 213 600 000 π   m = 30 856 775 814 913 673   m {\displaystyle 1~\mathrm {pc} ={\frac {96\,939\,420\,213\,600\,000}{\pi }}~\mathrm {m} =30\,856\,775\,814\,913\,673~\mathrm {m} } (to

240-526: A phthalocyanine used in dyeing Milk protein concentrate Multi-particle collision dynamics , a particle-based mesoscale simulation technique for complex fluids Mitochondrial pyruvate carrier Other uses [ edit ] Most placeable candidate , recruiting industry term MPC Computers Bowl , a football bowl game Myanmar Press Council Macedonian Orthodox Church (Macedonian: Македонска православна црква , romanized:  Makedonska pravoslavna crkva ) Topics referred to by

300-410: A degree), the parsec is defined as the length of the adjacent leg. The value of a parsec can be derived through the rules of trigonometry . The distance from Earth whereupon the radius of its solar orbit subtends one arcsecond. One of the oldest methods used by astronomers to calculate the distance to a star is to record the difference in angle between two measurements of the position of the star in

360-447: A distance d using the formula d ≈ ⁠ c / H ⁠ × z . One gigaparsec (Gpc) is one billion parsecs — one of the largest units of length commonly used. One gigaparsec is about 3.26 billion ly, or roughly ⁠ 1 / 14 ⁠ of the distance to the horizon of the observable universe (dictated by the cosmic microwave background radiation ). Astronomers typically use gigaparsecs to express

420-403: A dual-mode approach can provide significant reduction in online computations while maintaining comparative performance to a non-altered implementation. The proposed algorithm solves N convex optimization problems in parallel based on exchange of information among controllers. MPC is based on iterative, finite-horizon optimization of a plant model. At time t {\displaystyle t}

480-550: A model predictive controller often looks at fixed length, often graduatingly weighted sets of error functions, the linear-quadratic regulator looks at all linear system inputs and provides the transfer function that will reduce the total error across the frequency spectrum, trading off state error against input frequency. Due to these fundamental differences, LQR has better global stability properties, but MPC often has more locally optimal[?] and complex performance. The main differences between MPC and LQR are that LQR optimizes across

540-413: A nonlinear model directly in the control application. The nonlinear model may be in the form of an empirical data fit (e.g. artificial neural networks) or a high-fidelity dynamic model based on fundamental mass and energy balances. The nonlinear model may be linearized to derive a Kalman filter or specify a model for linear MPC. An algorithmic study by El-Gherwi, Budman, and El Kamel shows that utilizing

600-610: A quadratic cost function for optimization is given by: without violating constraints (low/high limits) with etc. Nonlinear model predictive control, or NMPC, is a variant of model predictive control that is characterized by the use of nonlinear system models in the prediction. As in linear MPC, NMPC requires the iterative solution of optimal control problems on a finite prediction horizon. While these problems are convex in linear MPC, in nonlinear MPC they are not necessarily convex anymore. This poses challenges for both NMPC stability theory and numerical solution. The numerical solution of

660-697: A regional political party in Mizoram, India Model Penal Code Movement for Progressive Change , a political party in Liberia Multi-Party Charter , political party alliance in South Africa Myanmar Peace Centre Military [ edit ] Marine Personnel Carrier , a US armored personnel carrier Military payment certificate , US military currency Military Police Corps (United States) RAF Mount Pleasant , an RAF base in

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720-511: A star is defined as half of the angular distance that a star appears to move relative to the celestial sphere as Earth orbits the Sun. Equivalently, it is the subtended angle, from that star's perspective, of the semimajor axis of the Earth's orbit. Substituting the star's parallax for the one arcsecond angle in the imaginary right triangle, the long leg of the triangle will measure the distance from

780-427: A suitably shifted guess from the previously computed optimal solution, saving considerable amounts of computation time. The similarity of subsequent problems is even further exploited by path following algorithms (or "real-time iterations") that never attempt to iterate any optimization problem to convergence, but instead only take a few iterations towards the solution of the most current NMPC problem, before proceeding to

840-591: A theoretical model for massively parallel computation Economics [ edit ] Marginal propensity to consume Monetary Policy Committee (United Kingdom) Government and politics [ edit ] Central African Patriotic Movement (MPC), a rebel group in the Central African Republic Member of Provincial Council , a member of provincial councils in Sri Lanka Mizoram People's Conference ,

900-562: A visual effects company, London, UK MPC , maker of encrypted mobile phones Computing and electronics [ edit ] Media Player Classic , a software media player MPC Computers , a former US computer maker Multimedia PC Multi Project Chip , sharing costs across projects Musepack , an audio codec Command-line client for the Music Player Daemon Akai MPC , series of music workstations Secure multi-party computation MPC model ,

960-489: Is also called receding horizon control . Although this approach is not optimal, in practice it has given very good results. Much academic research has been done to find fast methods of solution of Euler–Lagrange type equations, to understand the global stability properties of MPC's local optimization, and in general to improve the MPC method. Model predictive control is a multivariable control algorithm that uses: An example of

1020-470: Is being increasingly applied, with advancements in controller hardware and computational algorithms, e.g., preconditioning , to applications with high sampling rates, e.g., in the automotive industry, or even when the states are distributed in space ( Distributed parameter systems ). As an application in aerospace, recently, NMPC has been used to track optimal terrain-following/avoidance trajectories in real-time. Explicit MPC (eMPC) allows fast evaluation of

1080-419: Is determined in a similar fashion. To determine the number of galaxies in superclusters , volumes in cubic megaparsecs (Mpc ) are selected. All the galaxies in these volumes are classified and tallied. The total number of galaxies can then be determined statistically. The huge Boötes void is measured in cubic megaparsecs. In physical cosmology , volumes of cubic gigaparsecs (Gpc ) are selected to determine

1140-487: Is different from Wikidata All article disambiguation pages All disambiguation pages Megaparsec The parsec (symbol: pc ) is a unit of length used to measure the large distances to astronomical objects outside the Solar System , approximately equal to 3.26 light-years or 206,265 astronomical units (AU), i.e. 30.9  trillion kilometres (19.2 trillion miles ). The parsec unit

1200-411: Is formed by lines from the Sun and Earth to the star at the distant vertex . Then the distance to the star could be calculated using trigonometry. The first successful published direct measurements of an object at interstellar distances were undertaken by German astronomer Friedrich Wilhelm Bessel in 1838, who used this approach to calculate the 3.5-parsec distance of 61 Cygni . The parallax of

1260-506: Is intended to measure one billion stellar distances to within 20 microarcsecond s, producing errors of 10% in measurements as far as the Galactic Centre , about 8000 pc away in the constellation of Sagittarius . Distances expressed in fractions of a parsec usually involve objects within a single star system. So, for example: Distances expressed in parsecs (pc) include distances between nearby stars, such as those in

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1320-492: Is obtained by the use of parallax and trigonometry , and is defined as the distance at which 1 AU subtends an angle of one arcsecond ( ⁠ 1 / 3600 ⁠ of a degree ). The nearest star, Proxima Centauri , is about 1.3 parsecs (4.2 light-years) from the Sun : from that distance, the gap between the Earth and the Sun spans slightly less than ⁠ 1 / 3600 ⁠ of one degree of view. Most stars visible to

1380-576: Is one million parsecs, or about 3,260,000 light years. Sometimes, galactic distances are given in units of Mpc/ h (as in "50/ h  Mpc", also written " 50 Mpc h "). h is a constant (the " dimensionless Hubble constant ") in the range 0.5 < h < 0.75 reflecting the uncertainty in the value of the Hubble constant H for the rate of expansion of the universe: h = ⁠ H / 100 (km/s)/Mpc ⁠ . The Hubble constant becomes relevant when converting an observed redshift z into

1440-435: Is the fundamental calibration step for distance determination in astrophysics ; however, the accuracy of ground-based telescope measurements of parallax angle is limited to about 0.01″ , and thus to stars no more than 100 pc distant. This is because the Earth's atmosphere limits the sharpness of a star's image. Space-based telescopes are not limited by this effect and can accurately measure distances to objects beyond

1500-591: Is the unit preferred in astronomy and astrophysics , though the light-year remains prominent in popular science texts and common usage. Although parsecs are used for the shorter distances within the Milky Way , multiples of parsecs are required for the larger scales in the universe, including kilo parsecs (kpc) for the more distant objects within and around the Milky Way, mega parsecs (Mpc) for mid-distance galaxies, and giga parsecs (Gpc) for many quasars and

1560-780: The Falkland Islands commonly referred to as the Mount Pleasant Complex Places [ edit ] Michael Polanyi Center , Baylor University, Waco, Texas, US Mindanao Polytechnic College , Philippines Milton Peters College, Sint Maarten (operated by the Stichting Voortgezet Onderwijs van de Bovenwindse Eilanden ) Monterey Peninsula College , California, US Science and technology [ edit ] Model predictive control Magnetic particle clutch (or magnetic powder clutch) Metal phthalocyanine (MPc),

1620-455: The IAU 2012 definition of the astronomical unit). This corresponds to the small-angle definition of the parsec found in many astronomical references. Imagining an elongated right triangle in space, where the shorter leg measures one au ( astronomical unit , the average Earth – Sun distance) and the subtended angle of the vertex opposite that leg measures one arcsecond ( 1 ⁄ 3600 of

1680-537: The NMPC optimal control problems is typically based on direct optimal control methods using Newton-type optimization schemes, in one of the variants: direct single shooting , direct multiple shooting methods , or direct collocation . NMPC algorithms typically exploit the fact that consecutive optimal control problems are similar to each other. This allows to initialize the Newton-type solution procedure efficiently by

1740-471: The PWA for each a subset (control region) of the state space, where the PWA is constant, as well as coefficients of some parametric representations of all the regions. Every region turns out to geometrically be a convex polytope for linear MPC, commonly parameterized by coefficients for its faces, requiring quantization accuracy analysis. Obtaining the optimal control action is then reduced to first determining

1800-413: The Sun to the star. A parsec can be defined as the length of the right triangle side adjacent to the vertex occupied by a star whose parallax angle is one arcsecond. The use of the parsec as a unit of distance follows naturally from Bessel's method, because the distance in parsecs can be computed simply as the reciprocal of the parallax angle in arcseconds (i.e.: if the parallax angle is 1 arcsecond,

1860-493: The astronomical unit is defined to be 149 597 870 700   m , the following can be calculated: Therefore, if 1  ly ≈ 9.46 × 10  m, A corollary states that a parsec is also the distance from which a disc that is one au in diameter must be viewed for it to have an angular diameter of one arcsecond (by placing the observer at D and a disc spanning ES ). Mathematically, to calculate distance, given obtained angular measurements from instruments in arcseconds,

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1920-408: The change in the dependent variables of the modeled system that will be caused by changes in the independent variables . In a chemical process, independent variables that can be adjusted by the controller are often either the setpoints of regulatory PID controllers (pressure, flow, temperature, etc.) or the final control element (valves, dampers, etc.). Independent variables that cannot be adjusted by

1980-402: The control law for some systems, in stark contrast to the online MPC. Explicit MPC is based on the parametric programming technique, where the solution to the MPC control problem formulated as optimization problem is pre-computed offline. This offline solution, i.e., the control law, is often in the form of a piecewise affine function (PWA), hence the eMPC controller stores the coefficients of

2040-408: The control problem to a series of direct matrix algebra calculations that are fast and robust. When linear models are not sufficiently accurate to represent the real process nonlinearities, several approaches can be used. In some cases, the process variables can be transformed before and/or after the linear MPC model to reduce the nonlinearity. The process can be controlled with nonlinear MPC that uses

2100-405: The controller are used as disturbances. Dependent variables in these processes are other measurements that represent either control objectives or process constraints. MPC uses the current plant measurements, the current dynamic state of the process, the MPC models, and the process variable targets and limits to calculate future changes in the dependent variables. These changes are calculated to hold

2160-399: The current plant state is sampled and a cost minimizing control strategy is computed (via a numerical minimization algorithm) for a relatively short time horizon in the future: [ t , t + T ] {\displaystyle [t,t+T]} . Specifically, an online or on-the-fly calculation is used to explore state trajectories that emanate from the current state and find (via

2220-435: The dependent variables close to target while honoring constraints on both independent and dependent variables. The MPC typically sends out only the first change in each independent variable to be implemented, and repeats the calculation when the next change is required. While many real processes are not linear, they can often be considered to be approximately linear over a small operating range. Linear MPC approaches are used in

2280-509: The distance SD is calculated as follows: S D = E S tan ⁡ 1 ″ = E S tan ⁡ ( 1 60 × 60 × π 180 ) ≈ 1 a u 1 60 × 60 × π 180 = 648 000 π

2340-402: The distribution of matter in the visible universe and to determine the number of galaxies and quasars. The Sun is currently the only star in its cubic parsec, (pc ) but in globular clusters the stellar density could be from 100–1000 pc . The observational volume of gravitational wave interferometers (e.g., LIGO , Virgo ) is stated in terms of cubic megaparsecs (Mpc ) and is essentially

2400-476: The entire time window (horizon) whereas MPC optimizes in a receding time window, and that with MPC a new solution is computed often whereas LQR uses the same single (optimal) solution for the whole time horizon. Therefore, MPC typically solves the optimization problem in a smaller time window than the whole horizon and hence may obtain a suboptimal solution. However, because MPC makes no assumptions about linearity, it can handle hard constraints as well as migration of

2460-473: The formula would be: Distance star = Distance earth-sun tan ⁡ θ 3600 {\displaystyle {\text{Distance}}_{\text{star}}={\frac {{\text{Distance}}_{\text{earth-sun}}}{\tan {\frac {\theta }{3600}}}}} where θ is the measured angle in arcseconds, Distance earth-sun is a constant ( 1 au or 1.5813 × 10  ly). The calculated stellar distance will be in

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2520-531: The limit of ground-based observations. Between 1989 and 1993, the Hipparcos satellite, launched by the European Space Agency (ESA), measured parallaxes for about 100 000 stars with an astrometric precision of about 0.97  mas , and obtained accurate measurements for stellar distances of stars up to 1000 pc away. ESA's Gaia satellite , which launched on 19 December 2013,

2580-631: The main approaches to robust MPC are given below. Commercial MPC packages are available and typically contain tools for model identification and analysis, controller design and tuning, as well as controller performance evaluation. A survey of commercially available packages has been provided by S.J. Qin and T.A. Badgwell in Control Engineering Practice 11 (2003) 733–764. Model predictive control and linear-quadratic regulators are both expressions of optimal control, with different schemes of setting up optimisation costs. While

2640-437: The majority of applications with the feedback mechanism of the MPC compensating for prediction errors due to structural mismatch between the model and the process. In model predictive controllers that consist only of linear models, the superposition principle of linear algebra enables the effect of changes in multiple independent variables to be added together to predict the response of the dependent variables. This simplifies

2700-488: The most distant galaxies. In August 2015, the International Astronomical Union (IAU) passed Resolution B2 which, as part of the definition of a standardized absolute and apparent bolometric magnitude scale, mentioned an existing explicit definition of the parsec as exactly ⁠ 648 000 / π ⁠  au, or approximately 3.085 677 581 491 3673 × 10  metres (based on

2760-546: The naked eye are within a few hundred parsecs of the Sun, with the most distant at a few thousand parsecs, and the Andromeda Galaxy at over 700,000 parsecs. The word parsec is a portmanteau of "parallax of one second" and was coined by the British astronomer Herbert Hall Turner in 1913 to simplify astronomers' calculations of astronomical distances from only raw observational data. Partly for this reason, it

2820-426: The nearest metre ). Approximately, In the diagram above (not to scale), S represents the Sun, and E the Earth at one point in its orbit (such as to form a right angle at S ). Thus the distance ES is one astronomical unit (au). The angle SDE is one arcsecond ( ⁠ 1 / 3600 ⁠ of a degree ) so by definition D is a point in space at a distance of one parsec from the Sun. Through trigonometry,

2880-592: The need of a name for that unit of distance. He proposed the name astron , but mentioned that Carl Charlier had suggested siriometer and Herbert Hall Turner had proposed parsec . It was Turner's proposal that stuck. By the 2015 definition, 1 au of arc length subtends an angle of 1″ at the center of the circle of radius 1 pc . That is, 1 pc = 1 au/tan( 1″ ) ≈ 206,264.8 au by definition. Converting from degree/minute/second units to radians , Therefore, π   p c = 180 × 60 × 60  

2940-474: The next one, which is suitably initialized; see, e.g.,.. Another promising candidate for the nonlinear optimization problem is to use a randomized optimization method. Optimum solutions are found by generating random samples that satisfy the constraints in the solution space and finding the optimum one based on cost function. While NMPC applications have in the past been mostly used in the process and chemical industries with comparatively slow sampling rates, NMPC

3000-481: The object is 1 pc from the Sun; if the parallax angle is 0.5 arcseconds, the object is 2 pc away; etc.). No trigonometric functions are required in this relationship because the very small angles involved mean that the approximate solution of the skinny triangle can be applied. Though it may have been used before, the term parsec was first mentioned in an astronomical publication in 1913. Astronomer Royal Frank Watson Dyson expressed his concern for

3060-401: The region containing the current state and second a mere evaluation of PWA using the PWA coefficients stored for all regions. If the total number of the regions is small, the implementation of the eMPC does not require significant computational resources (compared to the online MPC) and is uniquely suited to control systems with fast dynamics. A serious drawback of eMPC is exponential growth of

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3120-399: The same spiral arm or globular cluster . A distance of 1,000 parsecs (3,262 ly) is denoted by the kiloparsec (kpc). Astronomers typically use kiloparsecs to express distances between parts of a galaxy or within groups of galaxies . So, for example : Astronomers typically express the distances between neighbouring galaxies and galaxy clusters in megaparsecs (Mpc). A megaparsec

3180-525: The same measurement unit as used in Distance earth-sun (e.g. if Distance earth-sun = 1 au , unit for Distance star is in astronomical units; if Distance earth-sun = 1.5813 × 10  ly, unit for Distance star is in light-years). The length of the parsec used in IAU 2015 Resolution B2 (exactly ⁠ 648 000 / π ⁠ astronomical units) corresponds exactly to that derived using

3240-453: The same term [REDACTED] This disambiguation page lists articles associated with the title MPC . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=MPC&oldid=1259229922 " Category : Disambiguation pages Hidden categories: Articles containing Macedonian-language text Short description

3300-539: The sizes of large-scale structures such as the size of, and distance to, the CfA2 Great Wall ; the distances between galaxy clusters; and the distance to quasars . For example: To determine the number of stars in the Milky Way, volumes in cubic kiloparsecs (kpc ) are selected in various directions. All the stars in these volumes are counted and the total number of stars statistically determined. The number of globular clusters, dust clouds, and interstellar gas

3360-417: The sky. The first measurement is taken from the Earth on one side of the Sun, and the second is taken approximately half a year later, when the Earth is on the opposite side of the Sun. The distance between the two positions of the Earth when the two measurements were taken is twice the distance between the Earth and the Sun. The difference in angle between the two measurements is twice the parallax angle, which

3420-424: The small-angle calculation. This differs from the classic inverse- tangent definition by about 200 km , i.e.: only after the 11th significant figure . As the astronomical unit was defined by the IAU (2012) as an exact length in metres, so now the parsec corresponds to an exact length in metres. To the nearest meter, the small-angle parsec corresponds to 30 856 775 814 913 673  m . The parallax method

3480-445: The solution of Euler–Lagrange equations ) a cost-minimizing control strategy until time t + T {\displaystyle t+T} . Only the first step of the control strategy is implemented, then the plant state is sampled again and the calculations are repeated starting from the new current state, yielding a new control and new predicted state path. The prediction horizon keeps being shifted forward and for this reason MPC

3540-458: The total number of the control regions with respect to some key parameters of the controlled system, e.g., the number of states, thus dramatically increasing controller memory requirements and making the first step of PWA evaluation, i.e. searching for the current control region, computationally expensive. Robust variants of model predictive control are able to account for set bounded disturbance while still ensuring state constraints are met. Some of

3600-631: The value of the effective distance cubed. Model predictive control Generalized predictive control (GPC) and dynamic matrix control (DMC) are classical examples of MPC. The models used in MPC are generally intended to represent the behavior of complex and simple dynamical systems . The additional complexity of the MPC control algorithm is not generally needed to provide adequate control of simple systems, which are often controlled well by generic PID controllers . Common dynamic characteristics that are difficult for PID controllers include large time delays and high-order dynamics. MPC models predict

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