|
Rosenbrock System Matrix
In applied mathematics, the Rosenbrock system matrix or Rosenbrock's system matrix of a linear time-invariant system is a useful representation bridging state-space representation and transfer function matrix form. It was proposed in 1967 by Howard H. Rosenbrock. Definition Consider the dynamic system :: \dot= Ax +Bu, :: y= Cx +Du. The Rosenbrock system matrix is given by ::P(s)=\begin sI-A & -B\\ C & D \end. In the original work by Rosenbrock, the constant matrix D is allowed to be a polynomial in s. The transfer function between the input i and output j is given by ::g_=\frac where b_i is the column i of B and c_j is the row j of C. Based in this representation, Rosenbrock developed his version of the PHB test. Short form For computational purposes, a short form of the Rosenbrock system matrix is more appropriate and given by ::P\sim\begin A & B\\ C & D \end. The short form of the Rosenbrock system matrix has been widely used in H-infinity methods in control theory, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
State Space Representation
In control engineering, a state-space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations or difference equations. State variables are variables whose values evolve over time in a way that depends on the values they have at any given time and on the externally imposed values of input variables. Output variables’ values depend on the values of the state variables. The "state space" is the Euclidean space in which the variables on the axes are the state variables. The state of the system can be represented as a ''state vector'' within that space. To abstract from the number of inputs, outputs and states, these variables are expressed as vectors. If the dynamical system is linear, time-invariant, and finite-dimensional, then the differential and algebraic equations may be written in matrix form. The state-space method is characterized by significant algebraization of general syste ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transfer Function Matrix
In control system theory, and various branches of engineering, a transfer function matrix, or just transfer matrix is a generalisation of the transfer functions of single-input single-output (SISO) systems to multiple-input and multiple-output (MIMO) systems. The matrix relates the outputs of the system to its inputs. It is a particularly useful construction for linear time-invariant (LTI) systems because it can be expressed in terms of the s-plane. In some systems, especially ones consisting entirely of passive components, it can be ambiguous which variables are inputs and which are outputs. In electrical engineering, a common scheme is to gather all the voltage variables on one side and all the current variables on the other regardless of which are inputs or outputs. This results in all the elements of the transfer matrix being in units of impedance. The concept of impedance (and hence impedance matrices) has been borrowed into other energy domains by analogy, especially ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Howard Harry Rosenbrock
Howard Harry Rosenbrock (16 December 1920 – 21 October 2010) was a leading figure in control theory and control engineering. He was born in Ilford, England in 1920, graduated in 1941 from University College London with a 1st class honors degree in Electrical Engineering. He served in the Royal Air Force during World War II. He received the PhD from London University in 1955. After some time spent at Cambridge University and MIT, he was awarded a Chair at the University of Manchester Institute of Science and Technology, where he founded the Control Systems Centre. He died on 21 October 2010. Prof Rosenbrock received many awards including the IEE Premium, the IEE Heaviside Premium, and the IEE Control Achievement Award, the first IEEE Control Systems Science and Engineering Award (1982), the Rufus Oldenburger Medal (1994) and the IChemE Moulton Medal. He was a Fellow of the IEE, the IChemE, the Institute of Measurement and Control, the Royal Academy of Engineering and the Roya ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
H-infinity Methods In Control Theory
''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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kalman Decomposition
In control theory, a Kalman decomposition provides a mathematical means to convert a representation of any linear time-invariant (LTI) control system to a form in which the system can be decomposed into a standard form which makes clear the observable and controllable components of the system. This decomposition results in the system being presented with a more illuminating structure, making it easier to draw conclusions on the system's reachable and observable subspaces. Definition Consider the continuous-time LTI control system : \dot(t) = Ax(t) + Bu(t), : \, y(t) = Cx(t) + Du(t), or the discrete-time LTI control system : \, x(k+1) = Ax(k) + Bu(k), : \, y(k) = Cx(k) + Du(k). The Kalman decomposition is defined as the realization of this system obtained by transforming the original matrices as follows: : \, = TA^, : \, = TB, : \, = C^, : \, = D, where \, T^ is the coordinate transformation matrix defined as : \, T^ = \begin T_ & T_ & T_ & T_\end, and whose submat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GNU Octave
GNU Octave is a high-level programming language primarily intended for scientific computing and numerical computation. Octave helps in solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with MATLAB. It may also be used as a batch-oriented language. As part of the GNU Project, it is free software under the terms of the GNU General Public License. History The project was conceived around 1988. At first it was intended to be a companion to a chemical reactor design course. Full development was started by John W. Eaton in 1992. The first alpha release dates back to 4 January 1993 and on 17 February 1994 version 1.0 was released. Version 7.1.0 was released on Apr 6, 2022. The program is named after Octave Levenspiel, a former professor of the principal author. Levenspiel was known for his ability to perform quick back-of-the-envelope calculations. Development history Developments In additio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1967 Introductions
Events January * January 1 – Canada begins a year-long celebration of the 100th anniversary of Confederation, featuring the Expo 67 World's Fair. * January 5 ** Spain and Romania sign an agreement in Paris, establishing full consular and commercial relations (not diplomatic ones). ** Charlie Chaplin launches his last film, ''A Countess from Hong Kong'', in the UK. * January 6 – Vietnam War: USMC and ARVN troops launch ''Operation Deckhouse Five'' in the Mekong Delta. * January 8 – Vietnam War: Operation Cedar Falls starts. * January 13 – A military coup occurs in Togo under the leadership of Étienne Eyadema. * January 14 – The Human Be-In takes place in Golden Gate Park, San Francisco; the event sets the stage for the Summer of Love. * January 15 ** Louis Leakey announces the discovery of pre-human fossils in Kenya; he names the species '' Kenyapithecus africanus''. ** American football: The Green Bay Packers defeat the Kansas City Chiefs 35–10 in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Control Theory
Control theory is a field of mathematics that deals with the 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; often with the aim to achieve a degree of 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 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 which are also studied are controllability and observability. Control theory is used in control system ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
