En este libro se aborda el análisis y diseño de sistemas de control en tiempo discreto. Se hace hincapié en la utilidad del programa MATLAB para el estudio de. LIBROS UNIVERISTARIOS Y Sistemas de Control en Tiempo Discreto – 2da Edicion – Katsuhiko Cargado. Katsuhiko Ogata Sistemas de Control en Tiempo Discreto PDF – Ebook download as PDF File .pdf) or libro de control digital para señales en tiempo discreto.

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System Dynamics Ogata 4th Help. System Dynamics by Ogata. Ogata – Solutions to Problems of System Dynamics.

Ogata Solutions to Problems of System Dynamics ogata solutions. System Dynamics An Introduction. Multibody System Dynamics modelamiento de sistemas dinamicos multicuerpos. Mm System Dynamics Hw4 Solution. Solucionario Ogata Solucionario para Ogata Control.

Solucionario para Ogata Control. Vehicle dynamics and road dynamics are two separate subjects. In vehicle dynamics, road surface roughness is generally regarded as random excitation to the vehicle, while at the same time handling Problemas solucionados del libro: Since y s1 we obtain B Assume that the W y of known mmnt of i n e r t i a J through a small angle akrout the v e r t i c a l axis and then equation of motion far the oscillation is where k is the torsfanal spring constant oE the string.

The positive direction is downward. Sowe have Then frm which w e obtain The ball reaches the ground in 2, s. The total angle rotated in semnd period is obtained from B Assume t h a t we apply force F to t h e spring system. Since the sane force transmits t h e shaft, we have where displacement z is defined in the figure Below. The following t w a equations describe the nation of the system and they are a mathematical model of the system. Referring to the figure below, we have Note that since x is m a s u r d where T is the tension i n the wire.

So we obkain The natural frequency of the system is B Assume that the direction of the static friction force F is to S the left as shown in t h e diagram below.

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So we obtain From the figure shmm to the right, we obtain To keep the bar AB horizontal when prlling the weight n gt h e rnament a b u t p i n t P must balance.

Thus, Solving this equation f o r x, we obtain B Assume that the stiffness of the shafts of the gear nite, t h a t there is neither backTash nor elastic defamation, nt.

Ikf i n e respectively. For s h a f t 2we have where T2 is the torque transmitted to gear 2. The equivalent mament of inertia J of mass m referred to the motor m s h a f t axis ogaga be obtained frcm where oE is disfreto angular acceleration of the motor shaft and 5 is the linear acceleration of mass rn.

Zi s is given by The transfer function can given in t e r n of camplw impedances Z1 and Z 2 as follows: Then Define the voltage at point A as ek.

Define the cyclic current in the left loop as il and that in t h e r l g n t Loop as i2. Then t h e equations for the circuit are which can be rewritten as Using the force-voltage analogy, we can convert the last two equations as follows: From these equations an analogous mechanical system can be obtained as shuwn to the r i g h t. We s h a l l solve t h i s problem by using ttm different approaches: Frm Figure we obtain Using the e1ect;rical-liquid analogy given below, e q a t i d n s for an analogous electrical system can be obtained.


C capacitance R resistance Analogaus equations for the electrical system are Based on Equations 5 through 81, we obtain the analogous electrical system shuwn below, B The equations for the liquid-level. So the flaw throughout the lobro is subsonic.

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If two roots are real, then the current is not osci- Ilatory. Case 1 Two roots of the characteristic equation are complex conjugate: For this case’ define Then The inverse Laplace transform of I s gives The current i t approaches zero as t approaches infinity.

Case 2 Two rmts of the characteristic equation are r e a l: The equations of motion for the system are k x.

Since we obtain the respanse eoIt as follows: The equation for the pendulum system can be given by JJ We shall linearize this nonlinear ajvaiirn 4 erruning angle 9 is small. X s ] can be written as clurve e-lfit s i n 5.

Figurewe obtain the following equations: F i r s t note t h a t Then, define and use a step comnand. The resulting response curve eo t versus t is shown below.

R e m e BdU I Sec Note that Notice t h a t the response curve is a sum of two exponential curves and a step function of magnitude 5. The equations of motion for the system are which can be m i t t e n as I Since we are interested in the steady state behavior of the system, we can assume that all initial conditions are zero.

F m the d i a g m shown centrifuqal force gravitational force Solving for W B Since 5 is desired to be 0. If w n So the acceleration of the base is ptopartional. Define the displacement of spring k2 as y. RIPvibration amplitude X jW of ‘. Assuming ma11 angles Q1 and system rriay be obtained as fo Llm: Thus For constants A and B to be nonzero, ” ,determinant of t h e coefficients of Equations 3 and 4 must be equal t o zero, or This determinant equation determines the natural frequencies of the systemEquation 5.

Thus The first natural frequency is w l first W e and the second natural frequency is L3 second mode.

This means that both masses move the same munt in the same direction. This mode is depicted in Figure a below. This mode is depicted in Figure b shown b e l o w. Q Therefore, mupling exists between Equation 11 and Equation 2. To f i n d the natural frequencies f o r the system, assume the following harmonic motion: T3 sinWt Then, frm Equations [I and 2 we obtain For amp1itudes A and 3 to be nonzero, the determinant of the coefficients of Equations 13 and 4 must be equal to zero, or Thfs determinant equation determines t h e n a t u r a l frequencies of the system.

Equation 5 can ke rewritten as which can be simplified to Notice that this last: Notice that the ratio of the displacements of springs k and k are 1 2 ‘Ihe f i r s t mcde of vibration is sham in Figure a on next page.


The system shown in? Also, that satisfies Equations 7 – 3 8 and bcmes as follows: Figlures i3 and l u s r i m on next page d e p l c t the first mode of vibration and second mode of vibration, respectively.

The equations of motion for the system are Substituting the given numerical mlues into these two equations and simplifying, we have To find the natural frequencies of the free vibration, assume that the motion is harmonic, or Then.

Frun Equations 3 and 4! Next, we s h a U obtain the vibrations x t and y t subjected to the given initial conditions. To obtain the responses x t and y t to the given initial conditions, as follows: The resulting plots x t 1 versus t and y t versus t are shown on next page. All necessary derivations of quatians for the system are given in Problem A For the initial condition. The resulting p l o t s are shown zistemas Figure b below.

S,”x t ‘ text 3 -5, Let us define d i s p l a m n t s e, xand y as shown in the figure Fur relatively small angle 8 we can construct a block diagram as s h m below. Also, from the system diagram we see t h a t fox each m L l Mlue of yt h e r e is a corresponding value of angle dm Therefore, for each angle e of the control lever, there is a mrresponding steady-state elevator angle 8.


We B If the engine spsed increases, the sleeve of the fly-ball -mar moves upward. This movement acts as the input to the hydraulic tontroller. A positive error signal upward motion of the sleeve causes the power p i s disfreto a to move dawnward, reduces the fuel mlve apeningc and decreases the engine Referring to Figure a shorn below, a block diagram for t h e system speed.

For the first-order system the sisteemas response isstemas is an q n e n t i a l 50 duscreto the constant T can k determined from such an exponential m ily. For a second-order system: A typical response c u mwhen this thermwneter is p l a d timpo a bath held at a constant temperature, is shown below. The closed-loop transfer function of the system is For the unit-step input, w e have B So we have or Iherefore, disrceto To make the system s t a b l eit is necessary to reduce the gain o f the system or add an appropriate -nsator.

The characteristic equation is The Routh array for this equation is 3 5 6 R For the systm to be stable, there should be no sign changes in the first column. Since the system is of higher order 5th orderit is easier to contrl the range of gain K f o r stability by first plotting the r m t laci and then finding critical p i n t s for stability on the soot loci.

The resulting root-locus plat is s h m also on n page. Based on this plot, it can. Pill critical points for stability lie on the j axis. The gain values at these crossing p i n t s are obtainel a s follows: Hence, we first f i n d the crossing frquency and then find the m r r e s p d i n g gain m l u e.