Essentials of Control Techniques and Theory 5 docx

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... too.91239.indb 133 10/12/09 1:43 :52 PMII ESSENTIALS OF CONTROL THEORY WHAT YOU OUGHT TO KNOW91239.indb 131 10/12/09 1:43 :51 PM136 ◾ Essentials of Control Techniques and Theory there are many more ... right-hand side, we have already worked out that L{} ,5 5esaat−=+so ()() () () ,sXssxxsa2100 5 +−−=+91239.indb 142 10/12/09 1:44:10 PM128 ◾ Essentials of Control Techniques and Theory rear ... velocity.vdem=c*(command-x)if(vdem>vlim){vdem=vlim;}if(vdem<-vlim){vdem=-vlim;} and a new expression for tiltdemtiltdem=d*(vdem-vest);We add deﬁnitionsvar vlim= .5; var vdem=0;91239.indb 128 10/12/09 1:43 :50 PM126 ◾ Essentials of Control Techniques and Theory is...

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Essentials of Control Techniques and Theory_5 docx

... PM108 ◾ Essentials of Control Techniques and Theory Now we propose to apply discrete feedback around the loop, making u(n) = –k x1(n), and so we find that xnxnxn12111100 95 009 05 ()()..(++=))()..()xnaakxnx210 ... the eigenvalues, and choose a suitable value for k. e determinant gives us det ,100 05 0 0 95 0 0 95 0 9 05 0−−−−akakλλ=so we have λλ20 0 05 1 9 05 0 9 05 0 00 45 0+++=(. .)(. .).ak ... (a + 3jω)/(3a + jω).91239.indb 94 10/12/09 1:42 :53 PM118 ◾ Essentials of Control Techniques and Theory We can save a lot of typing if we define the length of the stick to be one meter.To find the characteristic...

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... pinch of salt.91239.indb 129 10/12/09 1:43 :51 PMII ESSENTIALS OF CONTROL THEORY WHAT YOU OUGHT TO KNOW91239.indb 131 10/12/09 1:43 :51 PM142 ◾ Essentials of Control Techniques and Theory Integrating ... velocity.vdem=c*(command-x)if(vdem>vlim){vdem=vlim;}if(vdem<-vlim){vdem=-vlim;} and a new expression for tiltdemtiltdem=d*(vdem-vest);We add deﬁnitionsvar vlim= .5; var vdem=0;91239.indb 128 10/12/09 1:43 :50 PM122 ◾ Essentials of Control Techniques and Theory <div ... 10.1 Illustration of mapping deﬁned in Q 10.2.1.91239.indb 1 35 10/12/09 1:43 :55 PMControlling an Inverted Pendulum ◾ 121<body style="background-color: rgb( 255 , 255 , 204);"><center><h2>...

Essentials of Control Techniques and Theory_1 pptx

... Transducers 444 .5 A Control Experiment 46 5 Adding Control 49 5. 1 Introduction 49 5. 2 Vector State Equations 49 5. 3 Feedback 52 5. 4 Another Approach 53 5. 5 A Change of Variables 55 5. 6 Systems with ... 10/12/09 1:40: 45 PM Essentials of Control Techniques and Theory 91239.indb 1 10/12/09 1:40:29 PMThis page intentionally left blank 6 ◾ Essentials of Control Techniques and Theory a small ... variables.Figure 1.3 Ball -and- plate integrator.91239.indb 7 10/12/09 1:40:43 PM8 ◾ Essentials of Control Techniques and Theory Computer simulation and discrete time control go hand in hand together. At...

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... and input magnitude, and a phase shift.–1 4j–1 2j–1 0j–1 –2j–0 .5 4j–0 .5 2j–0 .5 0j–0 .5 –2j 0 –2j 0 .5 –2j 1 –2j–1 –4j –0 .5 –4j 0 –4j 0 .5 –4j 1 –4j0 4j 0 .5 4j 1 4j1 2j1 0j0 .5 2j0 .5 ... PM78 ◾ Essentials of Control Techniques and Theory 7.2 Sine-Wave FundamentalsSine-waves and allied signals are the tools of the trade of classical control. ey can be represented in terms of their ... Linear region of the phase plane.91239.indb 71 10/12/09 1:42:11 PM82 ◾ Essentials of Control Techniques and Theory Now the derivative of a sine-wave is another sine-wave (or cosine-wave) of the same...

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... www.esscont.com/11/ladderfreq.htm and www.esscont.com/11/ladder.htm)91239.indb 155 10/12/09 1:44:33 PM 156 ◾ Essentials of Control Techniques and Theory implying from the theory of complex functions that ... 10/12/09 1:44 :53 PM 152 ◾ Essentials of Control Techniques and Theory In Figure 11 .5 we see that the Nyquist plot now sails rather closer to the critical −1 point, crossing the axis at −0. 75, and the ... = 4M = 5 M = 6Figure 11.4 M-circles.91239.indb 152 10/12/09 1:44:31 PM174 ◾ Essentials of Control Techniques and Theory To plot the progress of the poles, we must look at the roots of Ps...

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... apart to see what the system is made of. Maybe we can get the best of both worlds.91239.indb 2 15 10/12/09 1: 45: 54 PM202 ◾ Essentials of Control Techniques and Theory it can be rearranged as xxxxu3321342+++=is ... τ3)Figure 15. 4 Superposition of impulse responses.91239.indb 208 10/12/09 1: 45: 44 PM228 ◾ Essentials of Control Techniques and Theory 3. Observable but not controllable 4. Neither controllable ... dtst(–)–−∞∞∫91239.indb 2 05 10/12/09 1: 45: 39 PM210 ◾ Essentials of Control Techniques and Theory less than the resolution of the computation process. Instead of regarding the impulse response as a function of inﬁnite...

Essentials of Control Techniques and Theory_10 pptx

... 10/12/09 1:46 :54 PM244 ◾ Essentials of Control Techniques and Theory and added a controller with state z, where zKzLyMv=++We apply signals from the controller dynamics, the command input and the ... 254 ◾ Essentials of Control Techniques and Theory 18 .5 Some Properties of the z-TransformIf we have a sequence of which the z-transform is X(z), the transform ... having transfer function 15 1++ss91239.indb 244 10/12/09 1:46 :59 PM248 ◾ Essentials of Control Techniques and Theory Now we have let a computer get in on the act, and the rules must change.x(t)...

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... =τFigure 19 .5 Mapping between the z and w-planes.91239.indb 2 75 10/12/09 1:47 :58 PM 258 ◾ Essentials of Control Techniques and Theory where the components of x are position and velocity. (Here ... 1:48:00 PM276 ◾ Essentials of Control Techniques and Theory wzz=−+211τfrom which zww=+−22ττ and finally the z-plane poles and zeros of the controller enable the controller code ... effect of aliasing.91239.indb 274 10/12/09 1:47 :57 PM268 ◾ Essentials of Control Techniques and Theory are of infinite height. Could these pulses be made broader and finite? A “genuine” discrete controller...

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