FEED FORWARD AND BACKWARD CONTROL STRATEGIES

                           FEED FORWARD AND BACKWARD CONTROL STRATEGIES


Feedforward control
A feedback controller responds only after it detects a deviation in the value of the controlled output from its desired set point. On the other hand, a feedforward controller detects the disturbance directly and takes an appropriate control action in order to eliminate its effect on the process output. 
Consider the distillation column shown in Fig (V.1) The control objective is to keep the distillate concentration at a desired set point despite any changes in the inlet feed stream. 

(a) Feedback control configuration

(b) Feedforward control configuration

Fig V.1: Feedback and Feedforward control configuration of a distillation column 
Fig.V.1(a) shows the conventional feedback loop, which measures the distillate concentration and after comparing it with the desired setpoint, increases or decreases the reflux ratio. A feedforward control system uses a different approach. It measures the changes in the inlet feed stream (disturbance) and adjusts the reflux ratio appropriately. Fig V.1(b) shows the feedforward control configuration. 

Fig V.2: The comparative schematic of feedback and feedforward control structure
Fig V.2 shows the general form of a feedforward control system. It directly measures the disturbance to the process and anticipates its effect on the process output. Eventually it alters the manipulated input in such a way that the impact of the disturbance on the process output gets eliminated. In other words, where the feedback control action starts after the disturbance is “felt” through the changes in process output, the feedforward control action starts immediately after the disturbance is “measured” directly. Hence, feedback controller acts in a compensatory manner whereas the feedforward controller acts in an anticipatory manner. 
V.I.I Design of feedforward controller 
Let us consider the block diagram of a process shown in Fig V.3. The Fig V.3(a) presents the open-loop diagram of the process. The process and disturbance transfer functions are represented by and  respectively. The controlled output, manipulated input and the disturbance variable are indicated as  and  respectively. 

(a) Open-loop process diagram 
(b) Process diagram with feedforward controller


(c) Process diagram with feedforward controller, sensor and valve 
Fig V.3: The schematic of a feedforward controller mechanism

The process output is represented by
(V.1) 
The control objective is to maintain  at the desired setpoint . Hence the eq (V.1) can be rewritten as
(V.2) 
The eq. (V.2) can be rearranged in the following manner:
or 
.....................................................(V.3)
The eq. (V.3) can be schematically represented by Fig V.3(b).
For the sake of simplicity, measuring element and final control element were not considered as parts of the feedforward control configuration as shown in Fig V.3(b). In a more generalized case, when such elements are added in the controller configuration, the resulting control structure takes the form of Fig V.3(c). A generalized form of controller equation can be written as
 .......................................................................................................(V.4)
And
 (V.5)
In case of regulatory problem (disturbance rejection) i.e. when , the controller should be able to reject the effect of disturbance and ensure no deviation in the output, i.e. . In other words,
................................................................................................................(V.6)
or
 .........................................................................................................................(V.7)
In case of servo problem (setpoint tracking), i.e. when , the controller should be able to ensure that output tracks the setpoint, i.e. . In other words,
.......................................................................................................................(V.8)
or
 ....................................................................................(V.9)
V.I.2 Example of design of feedforward controller 
Consider an overflow type continuous stirred tank heater shown in Fig V.4. The fluid inside the tank is heated with steam whose flow rate is Fst and supplying heat at a rate of to the fluid. Temperatures of the inlet and outlet streams are Ti and respectively. is the volume of liquid which is practically constant in an overflow type reactor. A control valve in the steam line indicates that the steam flow rate can be manipulated in order to keep the liquid temperature at a desired setpoint. Temperature of the inlet stream flow is the source of disturbance (change in Ti ) to the process.
(a) Process without a controller 
(b) Process with feedforward controller 

Fig V.4: Feedforward control configuration of an overflow type continuous stirred tank heater
A simple energy balance exercise will yield the model equation of the above process as:
(V.10)
All the variables are assumed to be in the deviation form. Hence, taking Laplace transform on both sides we obtain:
(V.11)
or, 
(V.12)
or,
(V.13)
or, 
(V.14)
The feedforward controller is meant for ensuring . Hence,
(V.15)
or 
(V.16)
Hence, one needs to set Fst in such a way that Q amount of heat as given in eq.(V.16) is transferred to the process. Fig V.4(b) represents the feedforward structure of the controller.

Remarks: 
•  The feedforward controller ideally does not get any feedback from the process output. Hence, it solely works on the merit of the model(s). The better a model represents the behavior of a process,the better would be the performance of a feedforward controller designed on the basis of that model. Perfect control necessitates perfect knowledge of process and disturbance models and this is practically impossible. This inturn is the main drawback of a feedforward controller. 
•  The feedforward control configuration can be developed for more than one disturbance in multi-controller configuration. Any controller in that configuration would act according to the disturbance for which it is designed. 
•  External characteristics of a feedforward loop are same as that of a feedback loop. The primary measurement (disturbance in case of feedforward control and process output in case of feedback control) is compared to a setpoint and the result of the comparison is used as the actuating signal for the controller. Except the controller, all other hardware elements of the feedforward control configuration such as sensor, transducer, transmitter, valves are same as that of an equivalent feedback control configuration. 
•  Feedforward controller cannot be expressed in the feedback form such as P, PI and PID controllers. It is regarded as a special purpose computing machine 
•  Let us consider a system where process delay is higher than disturbance delay, eg.and ; in such case, . That means one needs to know the future values of disturbance in order to decide present control action. This is physically unrealizable controller. 

V.I.3 Combination of Feedforward-Feedback Controller 
The following table provides a comparative assessment of feedforward and feedback controllers. 
Table V.1: Merits and demerits of feedforward and feedback controllers 
Merits 
Demerits 
Feedforward controllers 
Takes corrective action before the process “feels” the disturbance 
Requires measurement of all disturbances affecting the system 
Good for sluggish systems and/or system with large deadtime 
Sensitive to variation in process parameters 
Does not affect the stability of the process 
Requires a “near perfect” model of the process 
Feedback controllers 
Does not require disturbance measurement 
Acts to take corrective action after the process “feels” the disturbance 
Insensitive to mild errors in modeling 
Bad for sluggish systems and/or system with large deadtime 
Insensitive to mild changes in process parameters 
May affect the stability of the process 
Let us now explore how a combination of feedforward and feedback controller would perform when they are designed to act simultaneously. The schematic of a feedforward-feedback controller is shown in Fig V.5. 

Fig V.5. The schematic of a feedforward-feedback controller 
Without losing the generality we shall ignore the transfer functions of the measuring element and the final control element. 
Now the closed loop transfer function of feedforward-feedback controller can be derived in the following manner: 
(V.17)
Rearranging the above we get, 
(V.18) 
It is observed that the stability of the closed loop response is determined by the roots of the characteristic equation: . Hence, the stability characteristics of a process does not change with the addition of a feedforward loop. 




The following numerical example demonstrates the efficacy of a feedforward-feedback controller. Consider a process having process and disturbance transfer functions as 
(V.19) 
A feedback PID controller,with , is used to control the process for disturbance rejection purpose. A feedforward controller has also been designed for the process however it has been assumed that the time constant of the process has been measured erroneously as 2.1 instead of 2. A first order filter with time constant 0.1 has been augmented to the transfer function of Gsp in order to make it causal. 
A Simulink code (Fig V.6) has been generated to simulate the process under the three types of controllers as said above.

Fig V.6: Block diagram of Simulink code for closed-loop process under three controllers 
The performance of three controllers, viz., feedforward, feedback and feedforward-feedback, are presented in Fig V.7

Fig V.7: Comparative performance analysis of three controllers.
It is clearly observed that the performance of feedforward-feedback controller is far better than the other two individual controllers. 

 

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