Position Control by means of a Flexible Transmission

Figure 8.44. Flexible 360° arm. Output sensitivity function (|Syp|) for various controllers




Figure 8.45. Flexible 360° arm. Input sensitivity function (|Sup|) for various controllers

1

1
between 4 and 6 Hz. A resonant pole-zero filter H_R / P₃ in |S_up| is considered. It
will be centred around 5 Hz. Choosing f₀ = 4.7 Hz, M_t = -16.4 dB and _den =0.9
one gets the desired results (Figures 8.44 and 8.45 – curves D). The characteristics,
of H_R and P₃ are given in Table 8.9.
Table 8.9. Specifications of the various controllers for the 360° flexible robot arm

	HS(q^-1)	HR(q^-1)	Closed loop poles
			Dominant	Auxiliary
A	1 - q^-1	-	0 = 2.1673  = 0.8	-
B	1 - q^-1	-	0 = 2.1673  = 0.8	(1 – 0.5q^-1)^6
C	1 - q^-1 0 = 6.28  = 0.424	-	0 = 2.1673  = 0.8	(1 – 0.5q^-1)^6 0 = 6.28  = 0.8
D	1 - q^-1 0 = 6.28  = 0.424	0 = 29.57  = 0.092	0 = 2.1673  = 0.8	(1 – 0.5q^-1)^6 0 = 6.28  = 0.8 0 = 40.1  = 0.74

Concluding Remarks

Digital controllers can be implemented on a large variety of hardware. This implementation, however, has to be done by paying attention to a number of issues listed here:

• 
  Specification of the desired performances taking into account the actuator power and band pass, the time response of the plant in open loop and the desired robustness margins.
  
• 
  Taking into account the computation delay.
  
• 
  Taking into account the characteristics of the digital to analog converter.
  
• 
  Introducing anti-saturation schemes.
  
• 
  Implementation of a bumpless transfer procedure from open loop operation to closed loop operation.
  

For applications where significant variations of the dynamic model of the plant occur with the change of the operating points, it is recommended to proceed as follows:

• 
  To identify the model of the plant in the various regions of operation.
  
• 
  To design a controller for each region of operation assuring desired performance and robustness.
  
• 
  To store the parameters of the controllers in a table.
  
• 
  To change the parameters of the controllers when the system moves in a new region of operation by downloading the values of the controller parameters stored in the table.
  

This procedure is called “open loop adaptation”.
In continuous production processes it is very useful to measure the quality of the control from the histogram of the regulated variables.
The application examples presented in this chapter (there are many others) have illustrated how the methodology for system identification and control design has to be used in order to implement a high performance control system.