Automatic control systems III Automatic control systems III. SISO Multi-loop control Cascade control Feedforward control

SISO Multi-loops The SISO means Single Input Single Output. Sometimes the pure single-loop feedback control isn‘t able to provide the appropriate quality. If we can measure a variable which contains the effect of the most important disturbance variable or we can measured it directly this disturbance, then we can use multi-loops control. If there is a measurable variable between the manipulated and controlled variables which contain the effect of the disturbance, then we can use the cascade control design. The cascade control design use two feedback loops. If we can measure directly the disturbance variable we can use the feedforward design. The feedforward design use a feedback and an open-loop control.

SISO Multi-loops The cascade and the feedforward control design require two transmitters and two compensation blocks. The third, the auxiliary feedback signal design doesn‘t require more than one compensation blocks, but these design don‘t provide as a good quality as the cascade and feedforward design. Note: Nowadays the controllers based microprocessor and so one more software block doesn‘t cause increase of cost. (compensation block equal software block.) Sometimes it‘s very difficult or costly to define the attack point and the transfer function of the disturbance. These cases a grey model of the process is needed to use the feedforward design. Note: The MIMO process control and/or the adaptive control required the state/space design.

Cascade control If there is a measurable variable between the manipulated and controlled variables which contain the effect of the disturbance, then we can use the cascade control design. The process‘s model contains three transfer function: Between the measurable and manipulated variables. Between the measurable and controlled variables. Between the measurable and disturbance variables. It is very important: The sum of the time constants of the transfer function between the measurable and manipulated variables is more less than the sum of the time constants of the transfer function between the measurable and controlled variables.

Block model of angular displacement Gear box Load 5

Block manipulation and Simpler block model 6

Example Cascade control of angular displacement The cascade control design is very popular to control angular displacement caused by electro-motor driven mechanical system, because the angular velocity and displacement are well measurable variables and not necessary to create a grey model. The time constant of the electro-motor driven mechanical system are much more less than reciprocal coefficient of the gear-box. The coefficient of gear-box will be equal KI, and so the reciprocal value of the this is TI. The example use the following parameters of the plant: 7

Structure of Cascade control Manual GW(s) GA(s) GC2(s) GC1(s) GP1(s) GP2(s) Switch1 GT1(s) Switch2 GT2(s) All switch open is the manual mode. When switch1 is closed, then slave loop is closed and the main loop remains open. All switch closed is the cascade mode.

Parameters of the example The CascadeServo mdl file is in the ExampleMultiLoopLecture3 library. The suggested parameters of the motor belongs to an 30 kW asynchronous motor which is used in the industrial process area. The time constant of the transmitter has much more less and the time constant of the actuator has less than the average time constant of the process in a well instrumented system. These parameters belongs to encoders and frequency converter in the model example. The process has an integral behaviour and in this case the appropriate simulation time is the next: Where Tj are the time constants of the process field without TI and TI is the integral time of the process. Note: Because two points on the linear part of the response are enough to determine the integral time constant so more times we can use less simulation time.

Examination of single loop system The CascadeServo mdl file is in the ExampleMultiLoopLecture3 library. First we check the status of all switches. Then set the slave controller P type with KC═1. Then we define the simulation and sample time. Note: Measured at a response of a real process we set manual mode the cascade controller and suddenly change the action signal a little bit and will wait until the response is changing constant slope. At this time we restore to the initial value of the action signal. Then we plot the appropriate trend variables from the SCADA system. In the model we use the following equitation: Checking the result with scope the simulation time and so the sample time too can be reduced. Then we plot yM2 and define the Tsum and TI* from the response.

Examination of open single loop system The Tsum and TI* from the response.

Table 1: Suggested parameters for HPT1 minimum settling time and without overshoot system performance with tracking required value Recommended by Chien-Hrones-Reswick

Table 2: Suggested parameters for HPT1 minimum settling time with maximum 20% overshoot system performance with tracking required value Recommended by Chien-Hrones-Reswick

Table 3: Suggested parameters for HPT1 minimum settling time and without overshoot system performance with disturbance rejection Recommended by Chien-Hrones-Reswick

Table 4: Suggested parameters for HPT1 minimum settling time and maximum 20% overshoot system performance with disturbance rejection Recommended by Chien-Hrones-Reswick

Table 5: Suggested parameters for IT1 minimum settling time without overshoot system performance with following trajectory of reference signal Recommended by Friedrich (PD Chien-Hrones-Reswick too)

Examination of closed single loop system From the Table 5 chosen PDT controller type TD is 2sec., and so T is 0.2sec. and KC is 11.1. Set main controller, repeat the simulation with closed main loop then plot the result. The result seems good! What will happen if a disturbance attack the closed loop system at 25 second with unit step response?

Examination of closed single loop system Disturbance attack the closed loop system at 25 second with unit step response. Increase the loop-gain decrease the steady-state error, but cause oscillatory behavior with large overshoot. It isn‘t allowed a servo system.

Cascade control compensation The CascadeServo mdl file is in the ExampleMultiLoopLecture3 library. We create the step response of the slave open loop first. Then we determine the KP, Tu and Tg parameters. Using these values and Table 1 (not allowed the overshoot with tracking required value) determine the parameters of slave controllers. Note: The fast operation and the disturbance suppression of the target, and so the quality characteristics of secondary. It means we normally choose the Table 3. Note: The strong oscillatory behaviour isn‘t allowed in a servo system.

Step response of slave open loop The ratio of the time constants is 4, and so we choose PIDT compensator.

Step response of slave closed loop The counted values: KC═4 TI═4sec., TD═0.5sec. The large overshoot isn‘t allowed in servo system and so the values were required tuning KC═2.8, TI═4sec. and TD═0.8sec are used.

Step response with disturbance attack Reminder: The all changes are close to the working point. For example: The working point 50% at the saw unit and the saw unit step is 10%.

Cascade control compensation The CascadeServo mdl file is in the ExampleMultiLoopLecture3 library. We close the slave loop then we create the open loop step response of the main loop. Be carefully, the main controller type must be P with KC═1! Then we determine the TI* and Tsum parameters. Using these parameters and Table 5 define the KC and TD of main compensator not allowed the overshoot and tracking requires value of controlled variables. Finally we create the closed loop step response of cascade control. Note: A real process might be start first a little bit less gain and if the response aperiodically then increasing the counted value.

Step response of main open loop Using Table 5, chosen P type the KC═28.6 and chosen PDT type the counted controller‘s parameters: KC═28.6 and TD═ 0.7sec.

Step response of cascade closed loop The main controller is a simple P type. The PDT type isn‘t better caused by the large ratio between the TI* and Tsum time constants.

Cascade step response with disturbance attack It‘s OK, but a servo system is used to follow the required controlled variable described by reference signal.

Cascade ramp response with disturbance attack It‘s may be OK or not. Example: If the unit on the figure equal 10% in the real process, then it means 2.8% error which is much for a servo system.

Cascade control compensation for servo system The second type main loop is needed to follow the required controlled variable without steady-state error. We have already determined the parameters of main open loop, these were TI*═80sec. and Tsum═1.4sec. The PID type must be selected from Table 5 and using the parameters above the KC ═ 22.8 TI═4.5sec. and TD ═1.1sec. of main compensator. We create the closed loop step response with disturbance attack of cascade control.

Cascade ramp response with disturbance attack It‘s OK. The system follows the required value and eliminate the disturbance attack.

Feedforward control If we can measure directly the disturbance variable we can use the feedforward design. The feedforward design use a feedback and an open-loop control. Feed-forward control is an improvement over simple open-loop control, but relies on a good model of the process. If the model and especially the part of the model between disturbance variable and attack point is inaccurate, then the feedforward strategy may not work too well. If the feedforward loop works well decreases the transient time and the amplitude deflection from the required value caused by the disturbance.

Heat flow models m: the mass of the substance q2 R0 m: the mass of the substance cv: specific heat constant q1 room T1 R1 The heat flows from higher temperature to lower temperature. The net heat-energy flow into a substance: The heat energy flows through substances (across the room’s wall): 31

Simple block model of a house temperature The disturbance variable is the outdoor temperature which can be measured easy. In general is a distributed system, the entire length of it exchanging the heat. The heat flow isn‘t symmetrical. The heat losses is lees than the input heat flow. 32

Structure of Feedforward control GTW(s) uw=F(w) GW(s) GCW(s) Man/Aut GC(s) GA(s) GP1(s) GP2(s) GT(s) The uW═F(w) create an action signal at all outdoor temperature to control open-loop the internal temperature.

Action signal table 100% Uaction Toutdoor 0% +15°C 100% -35°C T The set of calibration curves depend on the required internal temperature assuming a constant water‘s temperature provided by gas boiler. This is a steady-state characteristics! The curves isn‘t always linear!

Parameters of the example The Feed_Forward mdl file is in the ExampleMultiLoopLecture3 library. The action signal table gives a constant value all temperature which is a little bit changing at a small area of working point. In the example we are disregarding this changes and using constant value. To neutralize the effect of the disturbance we choose the GCW(s) transfer function using the following formulae: Transforming the equitation:

Parameters of the example The suggested parameters of house doesn‘t belong to an real house even if the values are regarded minutes. Transforming the equitation: Not easy to create a transfer function which dynamic behaviour is similar to the above.

Examination of single loop system First we check the status of all switches. Then we define the simulation and sample time. Note: Presentation of the effect of feedforward control a steady-state working can be reached and then we can be examining the effect. This the reason that twice simulation time is required. Using the model we are examining the following: The process field step response without outdoor temperature. The process field step response with outdoor temperature. The process field step response with open-loop (feedforward) control. The closed loop step response without feedforward control and outdoor temperature disturbance. The closed loop step response with outdoor temperature disturbance and without feedforward control. The closed loop step response with outdoor temperature disturbance and feed-forward control.

Process field without outdoor effect Be Tu ═1sec. and Tg═12sec. The type of controller is PI

Process field with outdoor effect More action signal is needed to reach the required temperature

Open – loop control It‘s needed higher gain of transfer function of GCW(s) .

Simple closed loop control The parameter of PI controller are: KC═4.2, TI═14.4sec

Simple closed loop with disturbance at 40sec. The parameter of PI controller are: KC═4.2, TI═14.4sec

Feedforward control with disturbance at 40sec. The parameter setting the follow page.

Simple block model of a house temperature The disturbance variable is the water temperature of gas boiler which can be measured easy too. Transforming the equitation: Assuming first order transfer functions the resulting isn‘t proper function should therefore be replaced an approximate function: 44