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Additional info for 347 Woodworking Patterns A Bound Set of Popular Woodworking Patterns
19) where kd is the viscous friction coefficient of the motor and load, I is the moment of inertia of the motor and load, km is the motor constant, 0(t) is the angle of the motor shaft, and v(t) is the voltage applied to the field circuit of the motor. The objective is to control the velocity 0(t) of the motor shaft; in particular, we want 0(t)---, 0oaS t ---, ~, where 0o is the desired velocity. 20) where O(s)is the LT of t3(t)and V(s) is the LT of v(t). 2 I O0 ! 1. 4 3 ,, ! ) l ! 5 Unit-step response of motor with PI controller.
We will investigate this in the next chapter. 1, determine the poles and zeros of the transfer function. 3 A linear constant continuous-variable system produces the output response y(t)= exp(-3 t) sin 5t for t > 0 when the input c(t) is equal to exp(-2t) for t > 0. (a) Find the transfer function of the system (b) Determine the poles and zeros of the transfer function. (c) Using MATLAB, plot the step response of the system. 4. (a) Using the method given in this chapter, determine a first-order model for the process.
Hence, ro is the steady-state part of the response y(t) and ytr(t) is the transient part ofy(t). 9) and thus, the error e(t) is equal t o - 1 times the transient. 9) the steady-state error ess is equal to zero, where ess = limit of e(t) as t --, oo. There are three major design requirements for tracking a step reference: To achieve zero steady-state error, it is necessary for Gp(s)Gc(s) to have a pole at s = 0. This requirement follows by applying the Final Value Theorem of the LT, but we do not consider this.