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The most important thing to know before using any controller is to know they take control action and it depends on process to process which may have different manipulated variables,disturbance variable or more than one controlled variable.I am going to explain all the controller based on the kettle heating process.
(i) Feedback Control : As the name suggests here the control action is taken after taking feedback from the process.Lets say when I sent my product to kettle boiler ,i wanted to increase its temperature by supplying steam from the outside and lets say our desired temperature is 'T'.Now,we will measure the temperature of the outlet product to check whether the temperature of outlet product is really at its set point T or not.After measurement the signal was sent to a comparator and checked with the set point.Now we assume that the measured temperature was not at its set point and hence their occurs a deviation in controlled variable and a error signal is generated which is the diffrence between the set point and measured temperature and this error signal was sent to the controller.Now the controller takes action by manipulating the flow rate of steam whatever required to bring the temperature of the product back to its set point.Hence the controller takes action after the effect of disturbance is felt i.e. after temperature was changed and thus it is called feedback control.
(ii) Cascade control : This is different from the feedback control in a way that here the disturbance variable i.e. any change in inlet temperature of the product is measured.Let's say there there was some inlet temperature 'T(i)' corresponding to which we got the exact temperature of outlet product which we require.Now due to any reason assume the temperature of this inlet product 'T(i)' is changed and hence definitely the outlet product temperature will also be changed for the same flow rate of steam.So what we do in this control system,we measure the disturbance associated with inlet temperature of product i.e. by how much the temperature has changed with respect to earlier inlet temperature(because of which we got a set point) and based on that an error signal is sent to the controller to take immediate action.But the controller doesn't manipulate the "flow rate of steam directly" but it also measures the flow rate of steam also to check whether if flow rate of steam was at its required set point or not.Now the required amount of control action based on inlet temperature change and temperature change due to any change in flow rate of steam are compared and based on that another error signal is generated which is sent to another controller which manipulates the flow rate of steam.So,in this case we have 2 measured variables(i.e. 2measurement flow rate of steam and temperature of inlet product),2 controllers and 1 manipulated variable to mainatin set point of outlet product.
(iii) Feedforward control :Feedforward control takes the control action before the effect of disturbance is felt by the process.Likewise cascade control it also measures if there occurs any change in the disturbance varible i.e. inlet temperature of the product and takes the control action by directly manipulating the flow rate of the steam.The transfer function of the feedforward controller is modelled on the basis relating manipulated variable to the inlet temperature.SO ,theoretically,it work better because it sense any changes in the disturbances before it can affect the process by taking necessary control action.But who guarantte that the model of the feedforward controller is exactly matches with experimental conditions and hence there may be some lag due to which it may not be able to control the inside temperature perfectly.
So here I conclude the Cascade control is much better and tightest among all mentioned because it measures any disturbance associated not only with the disturbance variable i.e. inlet temperature but also takes into account the change in manipulated variable i.e. flow rate of steam as well and hence take robust control action to maintain outlet temperature at its set point.