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A black dye for making shirts is injected into a stream of water. The injected dye is blended into the water flow with constant speed mixers.A detector is used to monitor the dye/water concentration. The output of the detector is sent to a controller, which then sends a signal to the dye-injection valve. One needs to be careful with the location of the detector.The sensor has to be far enough away to ensure a well-mixed stream.

However, if the detector is too far away, the transport lag can destabilize the process.The regulating valve is especially designed so that the dye input rate, in milliliters per second, varies linearly with the valve position. The regulating valve thus is a first order with a time constant of τv (seconds) and a steady state gain of Kv (mL/sec.mV).The mixing process itself can be modeled as first order with a steady-state gain of Kp (ppm.sec/mL) and a time constant of τp (seconds)

Expand your mid-term report to write a report of around 4000 words maximum, excludingreferences on: “Analysis, design and implementation of a suitable feedback control strategy for a dye injection process”
The water flowrate in the pipe is 2 L/s and the pipe has a cross-sectional area of 5 cm2 . The regulating
valve is thus first order with a time constant of 0.2 s and a steady-state gain of 0.6 mLs −1 mV−1
The mixing process itself can also be modeled as first order with a steady-state gain of 0.8 ppm s mL−1 (where ppm indicates parts per million).

A previous experiment indicated that a step change in the regulating valve resulted in a response in a dye concentration that is 99.3% complete in 20 s.The magic photodetector is extremely fast, and the response is linear over a large concentration range.The optical sensor is installed at 2 meters from Dye injection.

Industrial Automation and its benefits

Industrial automation involves the technology in which a procedure or the process is accomplished with little or no human interference or assistance. Industrial automation has cost benefits. The industrial automation has to do with the regulation and control of individual unit operations alongside accompanied units. The integration of the units and cascaded control leads into control of the larger production systems. The regulatory control maintains the process enactment at a defined level or within a set tolerance band of a given level. Index of efficiency may be computed based on several output variables. For a process to be controlled there must be an error so as to initiate a control action.

Feed forward control antedates the effect of turbulences that will distort the process by using a sensor and a compensator for them before they affect the course. Disturbances need to be established using mathematical models in the system [1]. It is quite difficult to completely compensate for the disorder due to disparities, deficiencies in the mathematical model and imperfections in the control actions. The monitoring control and feed forward regulator are used to design the control processes. Steady-state optimization is implemented in systems where the index of performance is well-defined and there is a definite relationship between the process variables and IP. Mathematical models are used to optimize the index of performance based on system parameter values.

The most commonly used controller in industrial applications is the proportional-integral-derivative controller. The PID controller computes the error value which results from the alteration between the anticipated output or yield and the measured process variable. A feedback loop is used to perform the computation. The feedback loop mainly contains a sensor which collects data from the output and relays it to the error computation point. The controller has three segments namely the proportional, the integral, the derivative.

The proportional term relies on the current errors, the integral component relies on the accumulation of the past errors, and the derivative component relies on the prediction of the future errors. The impact of these three components brings about change when implemented in the regulating valve before the mixing process commences. It is quite a crucial component in industrial implementations and the controller can deliver control action intended for specific process requirements [2].

Designers use the manipulated variable to determine the PID control scheme. The controllers are manufactured or fabricated in three different components such as the proportional, integral, and derivative modes. They could be interactive algorithms, non-Interactive algorithms and parallel algorithms such that,The interactive algorithm is defined as,It is implemented in a system such that,The non-interactive algorithm is defined as,It is implemented in a process plant system as,

  • The parallel algorithm is defined as,It is implemented in a process plant system as,

Feed forward control in industrial automation

Therefore, it is possible to build a PID controller based on all three components working together. There are several other controllers, for instance, the proportional (P) controllers, proportional-integral (PI) controllers, proportional-derivative (PD) controllers, and the proportional-integral-derivative (PID) controllers. The P controller is implemented in first order systems. Its main function is to reduce the steady state error of the system.

An increase in the gain parameter leads to the decrease in the steady state error up to a certain level where further increase in the gain parameter causes the system output to oscillate [3]. Unfortunately, it fails to eliminate the steady state error and it is observed to amplify the process noise in the system. The PI controller solves the P controller’s drawback as it eliminates the steady state error and the oscillations as a result of the high proportional gain constant. Unfortunately, this controller is observed to have a poor performance when it comes to the speed of response and the overall stability of the system. Further, it is unable to decrease the rise time. The PD controller increases the system stability while improving the controlling nature of the system with the aim of predicting future error of the system response.

The PID controller combines all the benefits of the other controllers such as the elimination of steady state error and oscillations in the output, ensures system stability while controlling the process plant, as well as decreasing the rise time. The controller can be used with single energy systems or the commonly known first order systems as well as with higher order systems.

It is perceived that, when the step response of the system is obtained, the output response is given as,

  • Increasing the proportional constant reduces the steady state error.
  • Increasing the proportional constant after a given value may cause an overshoot.
  • Increasing the proportional constant may reduce the rise time.
  • The integral control eliminates the steady state error.
  • The limit increases the integral constant and increases the overshoot.
  • Slightly increasing the integral constant reduces the rise time by a small value.
  • Increasing the derivative constant decreases the overshoot.
  • Increasing the derivative constant reduces the settling time.

A feedback loop may undergo tuning so as to ensure that all the control strictures are implemented to their optimum principles so as to obtain the preferred control response. Controller tuning requires that one chooses a good initial set of controller parameter values to avoid leading the system to instability or cause it to have a deterioration of performance of the closed loop system.

Tuning seeks to find the optimum settings of the PID parameters such as the proportional constant, integral constant, and the derivative constant through experimentation or following specific tuning methods. The process of tuning can be done for both open loop and closed loop systems. The output is expected to be steady and it should not waver at any condition of the set point or disturbance. The bounded oscillation condition for a marginal stability is accepted. The process is expected to meet the regulation and command breaking requirements as set by the controller designer. To meet the command breaking requirements, the designer focused on the rise time and settling time attributes of a system response. The system controller in section 5 discusses the methods used in tuning a control loop.

  • To determine the system design using MATLAB software
  • To design the mixer system with a PID controller and Cohen-coon tuning method.

Proportional-Integral-Derivative Controller

The water flow rate in the pipe is given as 2 liters per second. The pipe has a cross sectional area of 5 cm2. The regulating value is a first order system with a time constant of 0.2 second and a steady-state gain of 0.6mLs-1mV-1. The mixing process is modeled as first order with a steady state gain of 0.8 ppm s mL-1. The dye concentration is expected to obtain a response in 99.3% in 20 seconds. The magic photo-detector is extremely fast, and the response is linear over a large concentration range. The optical sensor is installed at 2 meters from the dye injection. 

The transforms are given such as the process transfer function, the control valve transfer function and the transport lag















The disturbance transfer function is implemented after the output of the plant is obtained before the output signal is feedback to the error summer or computer. The disturbance can be analyzed in both open loop and closed loop systems. The disturbance is given as,The open loop step response is the process reaction curve function given as,

Control Variables

  • Steady state error

The feedback control is used to reduce the steady state error  [4]. These errors are caused as a result of the instrumentation of measurement errors, system nonlinearity during saturation, forms of input signal, forms of the system transfer function and the external disturbances acting on the system. It is denoted as

The steady state error varies with the step, ramp, and sinusoidal input used as the reference input. It is the variance between a prescribed input and the output. It is perceived that the control system has a steady state that does not align to the input and the steady state error is considered to be the physical control variable. Unfortunately, it suffers as a result of the input type at the reference input point.

  • Rise time

The time response of the dynamic and linear time-invariant systems is observed to have two components namely the transient response and the steady state response [5].

The peak time is that required for the response to reach the first peak of the overshoot.

  • Overshoot

It is possible to get an overshoot in the response.

The system is conveyed as a transfer function and through the transfer function, the stability of the system can be determined. The time domain and the frequency domain features of the system and the retort of the system are easily obtained for a given input. The system can have absolute and relative stability. The roots of the denominator polynomial in the transfer function gives values referred to as poles while the numerator polynomial give zeros. When the poles or denominator roots are negative or placed on the left of the root locus plot to determine system stability.

Different types of controllers and their applications

When the poles lie on the right hand side of the s-plane, the system is considered to be unstable and when they lie on the imaginary axis, the system is said to marginally stable.

The PID tuning rules adopted need to be well-motivated and should be model-based and analytically derived. They are simple and easy to implement and they ought to be applicable over a wide range of processes. The PID controller is a weighted blend of the proportional, integral, and derivative terms. The controller is the most suitable controller in a myriad of industrial applications.

An open loop controller has no sensing while the feedback control is implemented in the closed loop system. It experiences sense error and determines the control response. In the closed loop, there is feed forward control which encounters the sense disturbance, predict resulting error and it responds to the predicted error before it happens. The model predictive control, on the other hand, plans the system trajectory to reach the goal.

Manual tuning Method

It is achieved by arranging the parameters that are as per the system response. This is more of a trial and error method that seeks to determine the desired system response by changing the controller parameters observing the system behavior. The method is quite simple but it requires to be carried out by a very experienced person and a lot of time is consumed.

Ziegler-Nichols method

The Ziegler-Nichols method defines standards for a l the PID controller parameters such that,The controller parameters are defined as,

The integral and derivative controller parameters are disabled and the controller is rendered a pure proportional controller. A step alteration is made to the set plug. The controller gain is adjusted until the stable oscillation is attained. The final section achieves the ultimate improvement and the ultimate period.  It is denoted as the ¼ wave decay alongside the Pessen with little or no overshoot. The Ziegler-Nichols continuous cycling method is a trial and error method conducted while a control loop is in an automatic mode for the closed loop systems [6]. The Ziegler-Nichols step method uses the reactive curve to perform calculations and the manual mode of the method uses the stable open loop systems.

The PID controller is faster and does not produce oscillations though it tends to have unstable conditions when slight changes are introduced at the reference input or when the external disturbances are experienced in the system plant. The method is considered to be very efficient in increasing the usage of the PID controllers. The tuning method is obtained such that.

Tuning methods for PID controller

The tuning method is quite easy to implement as only the proportional controller is adjusted. The method includes the dynamic of the whole process and gives a more accurate perspective of the system behavior. Unfortunately, the method may be quite time consuming and the system is bound to encounter instability when testing for the value of the proportional controller. The outcome of the system is that it may go out of control. As a result, it might result in aggressive gain and overshoot.

Cohen-Coon Method

There are several of methods used to adjust a PID loop. One of the most operative methods that bring about the process model is based on the dynamic model strictures. The most effective methods are involved in making the process models and the individual components operate based on the dynamic model constraints. Some methods allow for the feedback loop to be taken down for tuning without affecting the performance of the system while others require it to be integrated to the system. The most preferred methods allow for offline tuning and these methods may issue the system to a step change in input. The output is measured as a function of time and the response is used to regulate the control parameters. This method was discovered shortly after the Ziegler-Nichols. The method requires up to three parameters as obtained from the system reaction curve.

The Cohen coon method is placed in the system manually and the changes made are observed in the controller output and the process variable is obtained as a new value. The process gain is given as The time constant is obtained as the difference between the connection at the end of the dead time and the process variables are given such that 63 percent of the system is given as the percentage of the total change.

The Cohen coon method is used in this analysis as it can be applied as a first order system controller while the Ziegler-Nichols method is only applicable to higher order systems. It is more flexible for the first order systems as it has a dead time equivalent to 0.5 less the actual time constant. The value of the Cohen coon output is tolerable until 75 percent of the output value.


Industrial automation is quite crucial in the industries. Organizations are trying to reduce as much human interaction as possible especially where the actions are quite redundant. Some of the applications are such as the dye injection which is a redundant process that requires mixing of the dyes and concentration.


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  • Manesis, S. A. and Grammaticos A. J. Small expert systems as intelligent modules of programmable logic controllers. Intelligent Control, IEEE International Symposium, ISBN: 0-7803-0546-9, 11–13 Aug 2002, pp. 526–530.
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  • Su, S., Anderson, B. and Brinsmead, T. Constant disturbance rejection and zero steady state tracking error for non-linear system design, in ACCSC, Datta, B., ed. Kluwer, 2001, pp. 1–30.
  • Karasakal, O., Yesil, E., Guzelkaya, M. and Eksla I. The implementation and comparison of different type self-tuning algorithms of fuzzy pid controllers on PLC. Automation Congress, Proceedings World,, Vol. 17, ISBN: 1-889335-21-5, June 28 2004 - July 1 2004, pp. 489–494.
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  • Samin, R. E., Jie, L. M. and Zawawi, M.A. PID implementation of heating tankin mini automation plant using Programmable Logic Controller (PLC). Electrical, Control and Computer Engineering (INECCE), International Conference, ISBN: 978-1-61284-229-5, 21–22 June 2011, pp. 515–519.
  • Balaji, M. and Porkumaran, K. A Mamdani-type fuzzy gain adapter for PID controller on a thermal system using PLC. India Conference (INDICON), ISBN: 978-1-4673-2270-6, 7-9 Dec. 2012, pp.-670–675.
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