Cascade Control

−

−

Fig. 2.9:Two mass-spring-damper system block diagram

2.3 Servo Control

CNC Machine tools in industrial applications are generally controlled using independent joint control schemes [17]. In this type of control, each axis in the machine tool is modeled and con-trolled independently as a Single-Input Single-Output (SISO) system. Coupling effects among axes due to varying configurations during motion are treated as disturbance inputs. The con-trollers in use to control each axis are servo concon-trollers [18]. The basic reasons for preferring servo controllers over open loop controllers include the need to improve transient response times, reduce the steady state errors, reduce the sensitivity to changes in load and system pa-rameters and a better handling of disturbances.

2.3.1 Cascade Control

The predominant control structure in the field of CNC machine tools is the cascade control structure [15]. The simple structure and high disturbance rejection properties the cascade con-trol has, favors it over the other concon-trol schemes. In addition, the cascade configuration offers the following advantages in comparison to other methods [15]:

• Step-by-step start-up from the innermost to the outermost control loop. Each control loop can be adjusted efficiently and independently, ensuring a safe start-up of the entire system.

• The internal control variables can be easily limited via the command variable of the corre-sponding control loop.

• Effects of non-linearities are controlled and limited, i.e. the higher-level loop operates with improved non-linearities.

• If multiple delay times occur in the controlled system, they can be reduced or canceled for the higher level controller through compensation in a lower level control loop.

• Disturbance variables in lower level control loops will be cancelled there. They do not have to pass through the entire controlled system, and can therefore be more quickly compen-sated.

An example for a cascade controller structure for a feed drive system is shown in Figure 2.10.

The actuating device in Figure 2.10 is a simple transistor power converter which acts as the actuating device for the axis actuator. It supplies the motor with the necessary power to drive the system with the required acceleration.

C3 C2 C1 Feed forward control forw1

Feed forward control forw2

Referencecommandand feedforwardvariables

Motor

Fig. 2.10:Block diagram of cascade control structure for a CNC machine tool feed drive [15]

The motor in Figure 2.10 is characterized by the torque constantKT and the voltage constant KE. 1/Jtot represents the mechanical time constant of the motor withJtot as the motor total moment of inertia. The coupling effects among the machine axes are described by the distur-bance torqueML. The motor current is controlled by control loop1via controllerC1, the motor angular velocityω_M is controlled by control loop2via controllerC₂and the motor angular po-sitionθ_M is controlled by control loop3via controllerC₃.

The current controller is usually realized with Proportional-Integral (PI) controllers integrated in the motor drive system and tuned to its optimal gains before it is placed in use [2, 15]. There-fore the current control loop and the motor in Figure 2.10 are usually approximated by a first order lag element with a time constantT_Eidependent on the motor data as

G_Ei(s) = 1

TEis+ 1. (2.15)

The simplified cascade control structure with the equivalent time constant for the current con-trol loop is shown in Figure 2.11

2.3. Servo Control 17

Feed forward control forw1

Feed forward control forw2

Referencecommandand feedforwardvariables

Fig. 2.11:Block diagram of a simplified cascade control structure for a CNC machine tool feed drive

The second controllerC2 in Figure 2.11 is the velocity loop controller. This loop is one of the most important control loops in the feed drive system. It includes, besides the high noise, the most crucial mechanical disturbancesMLin the system, the ones modeling the axes interac-tion. Therefore, keeping a high performance in the velocity control loop is a priority for any successful feed drive servo controller design process. In practical applications, this loop is nor-mally controlled via PI controller, due to its immediate response to input signals and its ability to eliminate the steady state system errors.The a PI controller algorithm is described by

u(t) =Kp

u(t)is the control command signal, e(t)is the control error signal, Kpis the proportional gain, Tnis the integration time constant,

and a block diagram as shown in Figure 2.12

e(t)

Kp

Tn

u(t)

Fig. 2.12:Proportional-Integral controller

The third controllerC3 in Figure 2.11 is the position loop controller. It is common in machine tools industry to use only proportional controllers in this loop, since integration elements can

cause overshoot and this is not allowed at the position level. Moreover, as a result of the cascade control configuration, all system disturbances are well eliminated in the current and velocity loops leaving the position loop to react only according to changes in the commanded positions and a proportional controller is sufficient in this case. The most important vari-able, which describes the behavior of a position control loop is the position loop gain or the Kv−factor. It gives a measure for machine’s tracking or following error and gives an indication for the machine speed of response [19].

In addition to the cascade configuration, Figure 2.11 shows multiple feed forward control paths. The feed forward control is a common practice for minimizing the following errors of the servo controllers in CNC machine tools. The basic idea of the feed forward control is to bypass the servo controllers and pass the reference values, i.e. position, velocity and/or acceleration, directly to the corresponding control loops. The values are fed to the loops via matching elements, called conditioning in Figure 2.11, directly as additive command variables to the corresponding controllers. A correct conditioning of the feed forward variables will lead to the result that the bypassed controller must only correct the disturbance variables of its own control loop, and the end result is an over all speeding up of system response and so better tracking behavior. In this thesis we will consider two feed forward paths, namely a veloc-ity and acceleration feed forward. The different feed forward control strategies are not in the scope of this thesis, a detailed discussion of this topic can be found in [15].