Process Dynamics & Control KM32104/4 PDF 2024/2025

KMJ32104/4 Process Dynamics & Control Dynamic behaviour of closed- loop control system o Block diagrams and transfer functions o Dynamic behaviour of several simple close-loop systems. Dr. Norzilah binti Abdul Halif...

KMJ32104/4 Process Dynamics & Control Dynamic behaviour of closed- loop control system o Block diagrams and transfer functions o Dynamic behaviour of several simple close-loop systems. Dr. Norzilah binti Abdul Halif MBM 5, Materials Department, Taman Muhibbah KMJ32104/4|PDC|NAH|2024/2025 [email protected] 1 Block Diagram KMJ32104/4|PDC|NAH|2024/2025 2 Block Diagram Description o Fig. 11.1 shows the blending tank with the flow rate of pure component A, w2, as the MV. o The CO is to regulate the tank composition, x, by adjusting the mass flow rate w2. o The primary DV is assumed to be inlet composition x1. o The tank composition is measured by a sensor/transmitter whose output signal xm is sent to an electronic controller. o Because a pneumatic control valve is used, the controller output (an electrical signal in the range of 4 to 20 mA) must be converted to an equivalent pneumatic signal pt (3 to 15 psig) by a current-to-pressure transducer. o The transducer output signal is then used to adjust the valve. KMJ32104/4|PDC|NAH|2024/2025 3  Block Diagram: The Process Process: Blending Dynamic model of a stirred-tank blending system in s-domain: KMJ32104/4|PDC|NAH|2024/2025 4 Block Diagram: The Measuring Element Measuring element: Composition Sensor-Transmitter o 1st order transfer function. o Instrument has negligible dynamics when  ≫ m o A useful approximation is to set m = 0. o The steady-state gain Km depends on the input & output ranges of the composition sensor-transmitter combination. KMJ32104/4|PDC|NAH|2024/2025 5  Block Diagram: The Controller Controller: P, PI, PD, PID comparator KMJ32104/4|PDC|NAH|2024/2025 6  Block Diagram: The Current-to-Pressure (I/P) Transducer o Linear characteristics o Negligible (fast) dynamics Example: The output from the controller is an electronic current signal ranging from 4 to 20 mA. The signal that the control valve requires is a pneumatic signal of 3 to 15 psig. KIP = KMJ32104/4|PDC|NAH|2024/2025 7  Block Diagram: The Control valve Final control element: Control valve o 1st order transfer function o has negligible dynamics when  ≫ v Example: The flow of A through the valve varies linearly from 0 to 2 cfm as the valve-top pressure varies from 3 to 15 psig. KMJ32104/4|PDC|NAH|2024/2025 8 Block Diagram: Entire process control system KMJ32104/4|PDC|NAH|2024/2025 9  Closed loop transfer function / Overall transfer function The transfer function that used to predict the system's response to various inputs, such as step inputs or sinusoidal inputs. Block Diagram Reduction X 3 = X 2  G3 = X 2G3 X 2 = X 1  G2 = X 1G2 X 1 = U  G1 = UG1 KMJ32104/4|PDC|NAH|2024/2025 10 Closed loop transfer function / Overall transfer function KMJ32104/4|PDC|NAH|2024/2025 11 Closed loop transfer function / Overall transfer function Find: Y (a) D2 Y (b) D1 Y (c) E1 Y (d) Ysp KMJ32104/4|PDC|NAH|2024/2025 12 Closed-loop responses of simple control systems Case I: Proportional Control & Set-Point Changes Case 2: Proportional Control & Disturbance Changes Case 3: PI Control & Disturbance Changes Case 4: PI Control of an Integrating Process KMJ32104/4|PDC|NAH|2024/2025 13 Closed-loop responses of simple control systems Understand the CO, CV, MV & DV Identify the transfer functions for each of element STEPS: Develop the closed-loop block diagram Construct an overall transfer function over SP change or load change Identify the type of input. Introduce the input to the control system. Determine the response in s-domain or t-domain. Sketch or plot the behaviour (t-domain). Evaluate or interpret the responses. KMJ32104/4|PDC|NAH|2024/2025 14  Closed-loop responses of simple control systems Identify the type of input o Refer to different types of inputs: Sinusoidal, step, ramp & impulse. o Identify also their expression in s-domain Introduce the input o Identify the value of the input and multiply by the type of the input. Determine the response in o Response = Input (s-domain) x Overall transfer function (closed loop transfer s-domain or t-domain. function) Sketch or plot the behaviour o Using inverse Laplace transformation and then plot the CV vs time. (t-domain) o Sketch the response (if second order response, use the values of overshoot, decay ratio and damping ratio). o Determine the initial and final values of CV using Final Value Theorem (FVT) and Initial Value Theorem (IVT). Evaluate or interpret the o Discuss the behaviour (if second order system, based on damping ratio can estimate responses whether the system is underdamped, overdamped or critically damped). o Determine the offset. (Offset = SP – SS value). KMJ32104/4|PDC|NAH|2024/2025 15  Closed-loop responses of simple control systems The liquid level is measured and the level transmitter (LT) output is sent to a feedback controller (LC) that controls liquid level h by adjusting volumetric flow rate q2. A second inlet flow rate, q1, is the disturbance variable. Assumptions: o The liquid density ρ and the cross-sectional area A of the tank are constant. o The flow-head relation is linear, q3 = h/R. o The level transmitter, I/P transducer, and pneumatic control valve have negligible dynamics. o An electronic controller with input and output in % is used (full scale = 100%). Unsteady-state mass balance for the tank contents: Kp = R & τ = RA. The Gp(s) and Gd(s) transfer are identical, because q1 and q2 functions: are both inlet flow rates and thus have the same effect on h. 16 KMJ32104/4|PDC|NAH|2024/2025 Closed-loop responses of simple control systems KMJ32104/4|PDC|NAH|2024/2025 17  Closed-loop responses of simple control systems Case 1:Proportional Control and Set-Point Changes Gc(s) = Kc The closed-loop response to a unit step change of magnitude M in set point: Rearranged in the standard form for a 1st order transfer function: Open-loop gain KOL KMJ32104/4|PDC|NAH|2024/2025 18 Closed-loop responses of simple control systems KMJ32104/4|PDC|NAH|2024/2025 19 Closed-loop responses of simple control systems Case 2: Proportional Control & Disturbance Changes KMJ32104/4|PDC|NAH|2024/2025 20