Servo Motors and Industrial Control Theory

In any system, if there exists a linear relationship between two variables, then it is said that it is a linear system.

In the previous chapter, the response characteristic of simple first and second order transfer functions were studied. It was shown that first order transfer function, sometimes called first order lag, has an overdamped response and the output lags input as it was shown in the frequency response. The second order transfer function as was shown in the previous chapter can have overdamped response for ζ &> 1 and can be oscillatory for ζ &< 1.

In the previous two chapters, the classical control theory was discussed and the concept of transfer function was used to describe the dynamic behavior of various systems. In practice, the transfer function of higher order than three or four becomes tedious and it is better to use state variable control theory. It was stated that with PID control, three parameters can be adjusted to design control systems. With three parameters, all roots of characteristic equation cannot be adjusted to achieve desirable transient and steady state behavior. In practice, it is only possible to make one or two roots to become dominant in response and a compromise between the transient response and steady state error has to be made. The derivative term always amplifies the noise in the practical systems and is not recommended. Instead a lead-lag network produces a better response.

It was discussed in Chap. 2 that there are various types of DC servo motors. They are available from sizes of fraction of horsepower to several hundreds of horsepower. The DC motors have two separate windings of one on the stator and the other on the armature. Depending on the design, they can be wired in series, shunt, or separately excited form. In servo motors applications, they are often designed so that the winding on stator are energized separately and the power to the armature is connected by brushes. There are several windings on the armature so that a smooth output torque is achieved. The winding on the stator is of low power nature and it is often used to generate a constant magnetic field. When the power is connected to the armature a large current flows in the winding, which develops a large initial current. A large electromotive force is developed which generates a torque to accelerate the armature. The initial current is very large and a current limiter must be designed in the power unit. As the armature accelerates, a back emf is developed which reduces the current. The operational of all DC servo motors are similar.

A stepping motor is defined as a rotary device whose output shaft moves in discrete steps when excited from a switched DC supply. Stepping motors are very practical devices for converting digital pulse inputs into analogue shaft-output (or rotary) motion as required in modern electric or electronic equipment. Each shaft revolution can be expressed in terms of a number of discrete identical steps or increments. Each step can be triggered by a single pulse. Stepping motors can be made with a rotor made of permanent magnets or DC energized. In the latter case, brushes must be used to energize the rotor. The principal operation of both types are shown in Fig. 5.1.

AC motors are the first choice for constant speed applications and where large starting torque is not required. They are available in three or single phase. The smaller motors are for household applications and they are made for single phase operations. For industrial applications, AC motors are available from a fraction to hundreds of horse power output. The principle of operation is that the rotor is made of laminated steel and bars of conducting material such as aluminium or copper are buried in the rotor which are short circuited at both ends. The stator is also made of laminated steel with properly designed slots. In the slots, a well designed number of windings is located which is connected to the power supply. The power supply generates a rotating magnetic field. When the motor is connected to the power supply, a voltage is induced in the bars located in the rotor which causes a current flow through them. As a result of the current, an electromotive torque is developed which accelerates the rotor. As the speed increases, the induced voltage reduces because the rotor approaches the synchronous speed. At synchronous speed, the torque becomes zero. Therefore, AC motors always rotate at a speed lower than the synchronous speed. The synchronous speed is determined by the frequency of the power supply and number of poles in the stator.

One major advantage fluid has over electrical power is that the former is not bound by the physical limitation of the material. For example, the saturation limit of steel limits the performance of the electro magnet, and available force per unit area from the hydraulic system is something like ten times than that of a saturated magnet. Therefore, hydraulic units are used whenever a large force for a small volume or a small weight is required. This applies particularly to heavy machinery such as mining machines and mobile equipment but it is not as important as in machine tools where accuracy and stability are the prime requirements. One main disadvantage of hydraulic power is that they are operated by high pressure oil which means that an expert must operate them and the oil must be kept clean and leakage to outside environment must be avoided.

Electro-Rheological (ER) fluids are special fluids made of base hydraulic fluids with chargeable particles suspended in the fluids. The important properties of ER fluid is that when it is put between two plates with gap h (typical of less than 1 mm) and a voltage is applied on the two plates, the fluid becomes stiffer with shear stress of typical 2 kN/m² has been reported. This is shown in Fig. 8.1. The range of the applied voltage is 4 kV/mm. The current drawn is very small and it is the range of a few milliamps.

In making a choice of the correct motor for a particular need, there are a number of factors to be considered; for example, speed of response, accuracy, and dynamic error due to an external disturbance, coupled with capital costs, reliability, and availability. In the previous chapters, dynamic properties of several types of servo motors were discussed and by obtaining the mathematical model the dynamic performance may be studied. In this chapter, a systematic approach is given for making the choice on the basis of a number of simplified graphs of performance.