Automatic Control System V. Compensation

If the satisfactory design of the process dynamics can’t be obtained by a gain adjustment alone, then some methods are indicated to modify the loop’s structure or compensate the loop’s dynamics. While the variety of compensation schemes is great the classical three- term controller design has been found to be particularly simple and effective. This compensation scheme has historically implemented using analogue mechanical, pneumatically and electrical controllers. Today the controllers are microprocessor based in which the compensation is implemented in a software. An extra steps is required to convert the analogue signal to digital information and the digital information to analogue signal. Nowadays in the industrial area the most popular A/D and D/A converter contain 12 bits.

The sample time If the sampling time is much more less than the sum of time constants of the process than the theory and design methodology is the same in digital and analog technologies. If one wants the digital PIDT1 compensator seems to be such as analogue must choose appropriate sample time period. Grey model (T j are the time constants.) Black model (T s is the settling time.)

Structure of classical three-term controller

Structure of classical three-term controller in sampled controller

Real combination of the three kinds Proportional P Proportional-Integral PI Proportional-Derivative PD Integral I Proportional-Integral-Derivative PID

Tuning controllers Which type of PID is the best solution? Which parameters are optimal ? The type of PID depend on transfer function of the plant (process model) The optimal parameters depend on which is the required performance specification of the feedback control If the simple feedback loop with compensation in cascade is unsatisfactory for the required performance specification than must modify the structure of control loop or exchange the classical PID scheme of control algorithm.

Position of the compensation cascade This is the most frequently when single feedback loop are used to compensate of the dynamical parameters of process or machines. G C (s)G E (s) Cascade and feedback G C1 (s)G E (s)G C2 (s)

Position of the compensation parallel feedback G C (s)G P (s)G C (s)G P (s) The parallel and the feedback arrangement are popular in the electronic circuit technique.

The PIPDT compensator P PIPDT Where the T I > 4T D ; T D > 5T It is popular in the electronic circuit technique, and the very similar lead-lag was used in the pneumatic controller.

Compensation techniques Depends on the identification of the process field transfer function Step response of the process field transfer function: Black-box model and recommendations for the controller type and value of the parameters. Frequency response of the process field transfer function: Black-box model, and fitting of PI, PDT1, or PIDT1 controller‘s frequency response to the process field transfer function. Pole replacement: Grey/box model. Poles of the process field transfer function is known.

Modelled the process from reaction curve by dead-time first order transfer function HPT1

Suggested parameters for HPT1 minimum settling time and without overshoot system performance with following trajectory of reference signal This parameters based on the absolute integral criterion of performance. There are any other parameter commendation

Modelled the process from reaction curve by “n” order transfer function PTn

Determination of system parameters

Suggested parameters for PTn minimum settling time and maximum 20% overshoot system performance with following trajectory of reference signal

Modelled the process from reaction curve by dead-time integral first order transfer function HIT1

Suggested parameter for IT1 from Friedlich

Summary questions Which transfer functions are used approaching of the real reaction curve. Interpret how the steady-state characteristics of blocks of a closed loop are fitted each other? Define the closed loop transfer functions and the opened loop transfer function of a feedback control system. Highlight what this term “system type” means. How the steady-state remaining error depends on the system type? Draw the oscillatory and the monotonic response of unit step. Explain the terms of the performance specifications of response.

Summary questions What is the goal of the compensation? What is the classical three-term controller? Outline the control actions associated with each of its constituent parts. Which transfer functions are used approaching of the real reaction curve.