UNIVERSITÀ DEGLI STUDI DI SALERNO Bachelor Degree in Chemical Engineering Course: Process Instrumentation and Control (Strumentazione e Controllo dei Processi Chimici) FEEDBACK AUTOMATIC CONTROL PERFORMANCE CRITERIA AND TUNING OF PID CONTROLLERS Rev. 2.4 – May 16, 2019

CONTROLLER DESIGN Questions What type of feedback controller should be used to control a given process? Does the controller have to be direct or reverse acting? Which criterion should be used to evaluate the performance and to select the feedback controller when considering both the type of controller and the parameter values? How can we optimize the controller parameters? 11/10/2019 Process Instrumentation and Control - Prof. M. Miccio

CONTROLLER DESIGN Answers What type of feedback controller should be used to control a given process? For the simpler and more common industrial controls (SISO or DISO system) the continuous PID controller is chosen 11/10/2019 Process Instrumentation and Control - Prof. M. Miccio

Process Instrumentation and Control - Prof. M. Miccio RULES OF THUMB When it is possible to use a simple proportional controller A simple proportional controller may be used when: an acceptable offset value with a moderate Kc; the proportional control does not provide offset because of the presence of an integral action in the process; a P-only controller is used for the control of the pressure of gas and liquid. A PI controller is used when a simple proportional controller cannot be adopted: a PI controller should be used when a proportional controller cannot limit adequately to the offset; a PI controller will be used for the control of level and pressure of gas. It is very often used for the control of flowrate. Its dynamic response is quite quick and the dynamic response of the closed-loop system is satisfactory despite the slowdown caused by the integral action. A PID controller is used to increase the velocity of the closed-loop response: a PI controller eliminates the offset but reduces the velocity of the closed-loop response. For a multicapacitive process, for which the response is very slow, the introduction of a PI controller slows down further the response. In this case, the addiction of the derivative action stabilizes this effect allowing the use with a wide range of the gain and with a more proper response without excessive oscillations. The derivative action is recommended for the temperature and composition control. see: §16.4 - Stephanopoulos, “Chemical process control: an Introduction to theory and practice”, Prentice Hall, 1984 11/10/2019 Process Instrumentation and Control - Prof. M. Miccio

CONTROLLER DESIGN Answers Does the controller have to be direct or reverse acting? See the process gain 11/10/2019 Process Instrumentation and Control - Prof. M. Miccio

Process Instrumentation and Control - Prof. M. Miccio What is Process Action ? Process MV PV Process action is how the process variable changes with respect to a change in the controller output (or manipulated variable). Process action is either direct acting or reverse acting. The action of a process is defined by the sign of the process gain. A process with a positive gain is said to be direct acting. A process with a negative gain is said to be reverse acting. adapted from: D. Cooper (2208), "Practical Process Control ", PDF textbook 11/10/2019 Process Instrumentation and Control - Prof. M. Miccio

Process and Controller Action The action of a process is important because it will determine the action of the controller: A direct acting process requires a reverse acting controller. Kc and KP >0 Conversely, a reverse acting process requires a direct acting controller. Kc and KP <0 adapted from: D. Cooper (2208), "Practical Process Control ", PDF textbook 11/10/2019 Process Instrumentation and Control - Prof. M. Miccio

CONTROLLER DESIGN Answers Which criterion should be used to evaluate the performance and to select the feedback controller when considering both the type of controller and the parameter values? Define an appropriate performance criterion and quantify the result using a P or PI or PID controller with a set of values: Kc, tl, tD 11/10/2019 Process Instrumentation and Control - Prof. M. Miccio

SIMPLE PERFORMANCE CRITERIA (CLOSED–LOOP SYSTEMS) The simplest perfomance criteria are based on some desirable characteristic features of a closed-loop system giving an underdamped response. The main criteria refer to: OVERSHOOT DECAY RATIO (e.g. C/A = ¼) FREQUENCY OF OSCILLATION OF THE TRANSIENT RESPONSE RISE TIME SETTLING TIME see: Par. 16.2 in Stephanopoulos, “Chemical process control: an Introduction to theory and practice”, Prentice Hall, 1984 11/10/2019 Process Instrumentation and Control - Prof. M. Miccio

Process Instrumentation and Control - Prof. M. Miccio GENERAL PERFORMANCE CRITERIA BASED ON MINIMUM ERROR e(t) (CLOSED–LOOP SYSTEMS) Each integral points out a different aspect of the closed-loop response: ISE and ITSE penalize higher errors more, giving rise to more prompt but more oscillating answers. ITAE and ITSE give more importance to errors in the final part than the initial part of the dynamic response, giving rise to a higher error in the initial part.  the inf. extreme t = 0 identifies the time instant in which the variation is applied on the input variable. see: Ch. 7 in Magnani, Ferretti e Rocco (2007) Par. 16.3 in Stephanopoulos, “Chemical process control: an Introduction to theory and practice”, Prentice Hall, 1984 11/10/2019 Process Instrumentation and Control - Prof. M. Miccio

Process Instrumentation and Control - Prof. M. Miccio CLOSED-LOOP RESPONSE comparison between different general performance criteria see: par. 16.3 - Stephanopoulos, “Chemical process control: an Introduction to theory and practice”, Prentice Hall 11/10/2019 Process Instrumentation and Control - Prof. M. Miccio

CONTROLLER DESIGN Answers How can we optimize the controller parameters? Use the tuning methods: OPEN LOOP TUNING Self-Regulating Systems Non Self-Regulating Systems CLOSED LOOP TUNING 11/10/2019 Process Instrumentation and Control - Prof. M. Miccio

OPEN LOOP TUNING for Self Regulating Systems

OPEN LOOP TUNING see: §16.5 - Stephanopoulos Cohen e Coon (1953) proposed the Process Reaction Curve method for the open loop process: CO(t) t Make a step-wise variation of amplitude A in the input variable Record the dynamic response ym (t) until the stationary state B is asymptotized. Adapt a FOPDT model to the ym (t) response and determine its parameters: Calculate the optimal parameters of the PID controller from the parameters of the FOPDT model. 11/10/2019 Process Instrumentation and Control - Prof. M. Miccio

Process Instrumentation and Control - Prof. M. Miccio BLOCK DIAGRAM (in the time domain) manual mode of the controller  Open Loop operation Final control element PROCESS SENSOR PID Controller ySP(t) ε(t) o(t) m(t) d(t) ym(t) y(t) + - 11/10/2019 Process Instrumentation and Control - Prof. M. Miccio

First Order Plus Dead Time (FOPDT) MODEL Complex or unknown process f(t) y(t) First order process Dead time f(t) y(t) y(t-td) L[y(t-td)] 11/10/2019 Process Instrumentation and Control - Prof. M. Miccio

COHEN and COON FORMULAS The performance criteria of the controller consist of obtaining a closed-loop response with: decay ratio = ¼, minimum offset, minimum ISE  Really good for first-order processes K≡Kp ≡p PB=100/Kc see: §16.5 - Stephanopoulos, “Chemical process control: an Introduction to theory and practice”, Prentice Hall 11/10/2019 Process Instrumentation and Control - Prof. M. Miccio

1st ZIEGLER–NICHOLS METHOD Tuning table NOTE: in Magnani, Ferretti e Rocco (2007), respect to Stephanopoulos (1984): t  td T  t NOTE: the table was obtained by a simulation on a really first-order plus dead time system changing the ratio /T in order to have underdamped dynamic response with  = 0.21  It can be used only for controllability ratio: see: Ch. 7 in Magnani, Ferretti e Rocco (2007) 11/10/2019 Process Instrumentation and Control - Prof. M. Miccio

Internal Model Control (IMC) FORMULAS θP≡td LOOP-PRO software uses IMC formulas adapted from: D. Cooper (2208), "Practical Process Control ", PDF textbook 11/10/2019 Process Instrumentation and Control - Prof. M. Miccio

OPEN LOOP TUNING for Non-Self Regulating Systems

Process Instrumentation and Control - Prof. M. Miccio BLOCK DIAGRAM (in the time domain) manual mode of the controller  Open Loop operation Final control element PROCESS SENSOR PID Controller ySP(t) ε(t) o(t) m(t) d(t) ym(t) y(t) + - 11/10/2019 Process Instrumentation and Control - Prof. M. Miccio

FOPDT model integrating  In this case we cannot use the common procedure for the FOPDT model because the dynamic response does not reach a new steady state value.  Adopt a FOPDT model integrating 11/10/2019 Process Instrumentation and Control - Prof. M. Miccio

PROCESS REACTION CURVE for Non-Self Regulating Processes The dynamic response to a step input change is a straight line (either increasing or decreasing). The slope of the response line is Kp*. The time interval before the answer starts is just td. Example: dynamic response to a step input change for a pumped tank tYstart tUstep 11/10/2019 Process Instrumentation and Control - Prof. M. Miccio

Internal Model Control (IMC) FORMULAS for Non-Self Regulating Processes Standard Tuning: Conservative Tuning: p  td LOOP-PRO software uses IMC relations adapted from: D. Cooper (2008), "Practical Process Control ", PDF textbook 11/10/2019 Process Instrumentation and Control - Prof. M. Miccio

CLOSED LOOP TUNING

BLOCK DIAGRAM FOR THE FEEDBACK CONTROL CONTROLLER FINAL CONTROL ELEMENT PROCESS MEASURING DEVICE ySP(t) ε(t) o(t) m(t) d(t) ym(t) y(t) + - 11/10/2019 Process Instrumentation and Control - Prof. M. Miccio

2nd ZIEGLER – NICHOLS METHOD ySP t P controller FINAL CONTROL ELEMENT PROCESS MEASURING DEVICE SET POINT ε(t) o(t) MANIP. VAR. LOAD CONTR. VAR. MEASURED VAR. Kc CLOSED LOOP METHODS are popular for two reasons: it is sufficient to determine only a parameter (the natural oscillation period T) many works are reported in literature, in particular for the electric application Note: the process is brought to the limit of stability (marginal stability). What risks can it entail? 11/10/2019 Process Instrumentation and Control - Prof. M. Miccio

2nd ZIEGLER – NICHOLS METHOD The method acts on the proportional controller with a fixed P.B. The integral and derivative actions are deactivated. The procedure starts from a steady state of the process. A step input change is forced on the set-point and the dynamic response y(t) is monitored. The P.B is reduced until a stable cycle (constant amplitude oscillation of y(t)) is reached (with the final controlling element not close to saturation) The specific value Ku of Kc is recorded, for which the stable oscillation (with the closed-loop) of y(t) occurs The distance between two consecutive peaks is measured (natural period of oscillation t0 or Pu or T) The natural frequency of oscillation is f0=1/t0 The crossover frequency is ωco =2π/t0 by trial and error 11/10/2019 Process Instrumentation and Control - Prof. M. Miccio

Process Instrumentation and Control - Prof. M. Miccio CLOSED-LOOP METHODS ySP t y(t) SET POINT ySP  Subsequently to a step input change of the set-point, the dynamic response of the closed loop reaches a continuous oscillating condition Kc=Ku Kc<Ku Kc>Ku 11/10/2019 Process Instrumentation and Control - Prof. M. Miccio

2nd ZIEGLER–NICHOLS METHOD Tuning table Only 2 parameters ―> They were obtained by assuming a closed-loop underdamped response  = 0.25  Validity range: 2 < KuKp < 20 NOTE: the actual plant is brought to the stability limit. What are the risks? see: §18.3 - Stephanopoulos, “Chemical process control: an Introduction to theory and practice”, Prentice Hall see: Ch. 7 in Magnani, Ferretti e Rocco (2007) 11/10/2019 Process Instrumentation and Control - Prof. M. Miccio