Tài liệu 3 Parameter Setting of Analog Speed Controllers pdf

3 Parameter Setting of Analog Speed Controllers

Practical speed controlled systems comprise delays in the feedback path.

Their torque actuators, with intrinsic dynamics, provide the driving torque

lagging with respect to the desired torque. Such delays have to be taken

into account when designing the structure of the speed controller and setting

the control parameters. In this chapter, an insight is given into traditional DC￾drives with analog speed controllers, along with practical gain-tuning proce￾dures used in industry, such as the double ratios and symmetrical optimum.

In the previous chapter, the speed controller basics were explained with

reference to the system given in Fig. 1.2, assuming an idealized torque ac￾tuator ( A

the parameter settings are discussed for the realistic speed-control systems,

including practical torque actuators with their internal dynamics A( ).

Traditional DC drives with analog controllers are taken as the design ex￾ample. Delays in torque actuation are derived for the voltage-fed DC drives

and for drives comprising the minor loop that controls the armature current.

Parameter-setting procedures commonly used in tuning analog speed con￾trollers are reviewed and discussed, including double ratios, symmetrical

The driving torque Tem, provided by a DC motor, is proportional to the ar￾mature current ia and to the excitation flux Φp. The torque is found as Tem =

kmΦpia, where the coefficient km is determined by the number of rotor con￾ductors NR (km = NR/2/π). The excitation flux is either constant or slowly

varying. Therefore, the desired driving torque Tref is obtained by injecting

the current ia = Tref /(kmΦp) into the armature winding. Hence, the torque re￾sponse is directly determined by the bandwidth achieved in controlling the

armature current. In cases when the response of the current is faster than

the desired speed response by an order of magnitude, neglecting the torque

3.1 Delays in torque actuation

W s

W (s) = 1). In this chapter, the structure of the speed controller and

optimum, and absolute value optimum. The limited bandwidth and perform￾ance limits are attributed to the intrinsic limits of analog implementation.

52 3 Parameter Setting of Analog Speed Controllers

actuator dynamics is justified (WA(s) = 1), and the synthesis of the speed

controller can follow the steps outlined in the previous chapter. With refer￾ence to traditional DC drives, the current loop response time is moderate.

For that reason, delays incurred in the torque actuation are meaningful and

the transfer function WA(s) cannot be neglected.

3.1.1 The DC drive power amplifiers

The armature winding of a DC motor is supplied from the drive power

converter. In essence, the drive converter is a power amplifier comprising

the semiconductor power switches (such as transistors and thyristors), in￾ductances, and capacitors. It changes the AC voltages obtained from the

mains into the voltages and currents required for the DC motor to provide

the desired torque Tem. In the current controller, the armature voltage ua is

the driving force. The voltage ua is applied to the armature winding in order

to suppress the current error ∆ia and to provide the armature current equal

to Tref /(kmΦp). The rate of change of the torque Tem and current ia are given

in Eq. 3.1, where Ra and La stand for the armature winding resistance and

inductance, respectively; km and ke are the torque and electromotive force

coefficients of the DC machine, respectively; Φp is the excitation flux; and

ω is the rotor speed. Given both polarities and sufficient amplitude of the

driving force ua, it is concluded from Eq. 3.1 that both positive and nega￾tive slopes of the controlled variable are feasible under any operating con￾dition. Therefore, any discrepancy in the ia and Tem can be readily corrected

by applying the proper armature voltage. The rate of change of the arma￾ture current (and, hence, the response time of the torque) is inversely pro￾portional to the inductance La. Therefore, for a prompt response of the

torque actuator, it is beneficial to have a servo motor with lower values of

the winding inductance.

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The power converter topologies used in conjunction with DC drives are

given in Figs. 3.1–3.3. The thyristor bridge in Fig. 3.1 is line commutated.

The firing angle is supplied by the digital drive controller (µP). An appro￾priate setting of the firing angle allows for a continuous change of the ar￾mature voltage. Both positive and negative average values of the voltage ua