what is the stability in multivariable control system?
355082
It's only as good as its links and constituent parts each breakdown can have an effect over all and any of the other parts, and potentially a catastrophic breakdown. This would require a diagnostic program to be inbuilt or connected to the system.
863763
D ( 2 or 0)\n\nThis is because the coefficients of the given cubic polynomial are real numbers and so any real zero needs be accompanied by its complex conjugate and so as stated  earlier MUST come in pairs so either there are 2 or there cannot be any.
421929
This is a basic form of feed-back controller.  You create an "error" signal, based on the difference between a desired state, and a measured state.  In your example, this would be the distance the joint is from the target position.\n\nYou apply a gain to this error signal, to provide the driver signal to the actuator.  In the case of PD, two gains; one to the Difference (the error) and one to the change in the error, since the last measurement/control cycle.\n\nThe gains are not dimensionless, and in your example, assuming voltage controlled actuators, the dimensions of Gp are volts/meter.  The dimensions of Gd are volt seconds/meter.\n\nok?  For more, see the reference source below.
331428
Can you show that T has a real eigenvalue? If so, let v be an eigenvector corresponding to this eigenvalue. Then, the line tv for all t in Reals is invariant under T :)
918456
domain\nall real x\nx intercept\nputting y=0\n0=x+rt{x]\n-x=rtx\nx^2=x\nx(x-1)=0\nx=0 or 1\nx intercept=(0,0) and (1,0)\ny intercept\nsetting x=0\ny=0\ny intercept=(0,0)\nno symmetry exhibited
268125
just investigate for example ODE y"=-y and then add to the left part increasingly small non-linearity +c*y^2 and find solution of the first order of c - you will see how different modes interact with each other.
116565
With the goal that a clock signal will not drift, \nPLL (phase locked loop) logic can be added to keep\nthe frequency constant.  It works by adding "feedback"\n(from the output back to the input) with a tuning\ncircuit to keep the two signals (the original input\nas well as the feedback) in synch.
846745
Typically you know three out of the four variables and solve for the last variable.\n\nBut sometimes they get tricky by giving you only two but one of the remaining variable is related to one or two of the given variables.
44400
A control system is a device or set of devices that manage the behavior of other devices.A control system is an interconnection of components connected or related in such a manner as to command, direct, or regulate itself or another system.\n\nThere are two common types of controllers, with many variations and combinations: logic controls, and feedback or linear controls. There is also fuzzy logic, which attempts to combine the easy design of logic with the real-world utility of feedback controls.
739296
Transfer function implies having  a mathematical formula. A gyroscope is a physical thing. What is your question ??? It's like asking for the equation of an apple.
1176294
Relatively steady with some minor fluctuation.
380854
im not sure if that first answer was clear so...........\nAnything in the emperiment that you have control for.  for example say you are testing how fast water boils at a certain temperature.  the temperature is the controlled variable because you can change the temperature yourself by increasing or decreasing the heat... the controlled variable is independent.  If you had to make a chart or graph, it would be on the x axis...  im not sure if thats any clearer
126252
Free vibration can be complex (resulting from many vibration modes) but is not random or chattery if the system is linear.  Forced vibration of a linear system can be random if the forcing function is, but will become deterministic once the FF stops.  Vibration in nonlinear systems can be "clean" or chattery depending on whether the nonlinearity is continuous (e.g., a spring whose stiffness is proportional to amplitude) or discontinuous (e.g., freeplay).\n  \nChatter has many meanings, most but not all involving nonlinearity in some form:\nOne vibration mode coupling to another so that reinforcement and beating and intermittent rattling may occur (in a theoretical linear system the modes do not couple.) \nVibration in a system with freeplay causing periodic rapping noises, automobile suspension noises, "walking" of objects on a vibrating table, etc. \nNoise in reciprocating machinery (e.g., valves, machine guns)\nRapid, random or nonrandom switching between states, either open-loop or due to feedback\nStick-slip phenomena (e.g., tool chatter, some bearing noises, creaking)\nAeroelastic effects (often called flutter)\nProbably many more...
949909
So Im guessing your have a transformation matrix.  \n\nYou have an initial state specified by matrix [A] and the linear transform specified by matrix [T].\n\nTo find the state after iteration 1 you multiply\n[A]x[T]=[y1]\n\nIf [y1] was your initial matrix you would multiply it by [T] to get the state after iteration.\n[y1]x[T]=[y2]\nby substitution\n([A] x [T]) x [T] = [y2]\nor \n[A] x [T]^2 = [y2]\n\nso what is T at the nth iteration?\n[A] x [T]^n = [yn]\n\nso what is the limit as n goes to inifinity?\n[A] x lim([T]^n,n->inf) = [y_inf]\n\nNumerical results break down, consider a rotation.  The limit as it goes to infinity is undefined.\nT(1,1)=sin(x)\nT(1,2)=cos(x)\nT(2,1)=-1*cos(x)\nT(2,2)=sin(x)\n\nWhen you square it you get\nT2(1,1)=sin(x)^2-cos(x)^2 = -cos(2*x)\nT2(1,2)=2*cos(x)*sin(x) = sin(2*x)\nT2(2,1)=-2*cos(x)*sin(x) = -sin(2*x)\nT2(2,2)=sin(x)^2-cos(x)^2 = -cos(2*x)\n\nWhen you cube it you get\nT3(1,1)=-sin(3*x)\nT3(1,2)=-cos(3*x)\nT3(2,1)=cos(3*x)\nT3(2,2)=-sin(3*x)\n\nWhen you raise it to the power of 100 (come on MatLab, dont die on me now, darnit) ... ahem.  When you raise it to the power of 10 (?)  aha\nT10(1,1)=-cos(10*x)\nT10(1,2)=sin(10*x)\nT10(2,1)=-sin(10*x)\nT10(2,2)=-cos(10*x)\n\nSee how that works?  Not bad huh?\n\nFor the pure rotation it never ends.\nWhat about a shrinking, a scaling by a matrix whose norm is less than 1? (note if you use 0.9, the norm is 1.8.)\n\nT(i,j)=0.45\nyields\nT2(i,j)=0.4050\nT3(i,j)=0.3645\nT10(i,j)=0.1743\nT1000(i,j)=0.1328*10^-4\n\nIt disappears to zero.\n\nintuitively you can also figure out that for a scaling by a matrix whose norm is larger than one the transform eventually goes to infinity as the limit is taken to infinity.\n\nyou could make a non-trigonometric rotation, like the sin(1/x)  Thats a fun expression.\n\nT(i,i)=sin(1/x) \nT(1,2)=cos(1/x)\nT(2,1)=-1*cos(1/x)\n\nAs x goes to infinity what happens?\nit becomes a reflection\nT_inf(i,i)=0\nT_inf(1,2)=1\nT_inf(2,1)=-1\n\nIm digressing.  Its a fun field with interesting applications.  Weather forecasting, deformation of solids, heat transfer, optimization, all use linear transformations to do their work.\n\nHave fun.
523969
The best controller in my opinion would be a dc chopper that smoothly reduces input voltage to the motor thus slowing it smoothly.
280380
http://www.visteon.com/utils/whitepapers/20_ccwdc.pdf#search='generalized%20predictive%20control'\n\nthis is an explanation with an example.
38340
dump is right!\nanother 1.. stable!