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The Use of Complex Numbers in the Solution
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acceleration feedback actuator angular frequency angular position angular resonant frequency angular velocity applied approximately Argand diagram armature asymptotic axis Bode diagram chapter circuit closed-loop frequency response compensated system complex number control engineering D-form d.c. motor damping dB/decade Determine device differential equation driving function electrical electronic amplifier error constant error detector example exponential lags field winding forward path frequency locus frequency response frictional torque given gyroscope handwheel Hence hydraulic inertia integral inverse kg m2 Laplace transform log-modulus characteristic loop M-circle magnitude mass mechanical method motion Nichols chart Nyquist diagram Nyquist stability criterion open-loop transfer function output element parallel compensation phase angle phase margin phase-lag phase-lead network potentiometer pressure proportional rad/s radian resistance rotation servomechanism shaft shown in Fig simple sine wave sinusoidal specification speed stable on closed steady-state solution transient response type 1 system unity unstable valve vector velocity lag viscous frictional voltage zero