Closed Loop Control System Prof. Dr. M. Zahurul Haq http://teacher.buet.ac.bd/zahurul/ Department of Mechanical Engineering Bangladesh University of Engineering & Technology ME 6401: Advanced Mechatronics c Dr. M. Zahurul Haq (BUET) ME 6401 1 / 24 e202.eps Controlled Variable, Process Variable (PV), x Reference Value, Desired Value, Setpoint (SP), w Control Deviation, Error, e Manipulated Variable (MV), y Disturbance, z Controller Output, y R Manipulation Range, y h c Dr. M. Zahurul Haq (BUET) ME 6401 2 / 24 Analog Controller are built from OP-amp. Controller structure and characteristics are largely determined by the design and construction. These are used where there is less requirement for very high accuracy. These have clear advantages in extremely fast control loops. There is very little fuctional difference between digital and analog controllers. e204.eps c Dr. M. Zahurul Haq (BUET) ME 6401 3 / 24 c Dr. M. Zahurul Haq (BUET) ME 6401 4 / 24
Digital Controller The input variables, the process value must initially be digitized before the signal can be processed by the microprocessor. The calculated output signal (manipulated variable) is then converted back to an analog signal using DAC. Increased accuracy of control, depending on the measurement signal and the technology used. High flexibility in the structure and characteristics of the controller. Controller can be midified by modifying the program. Facility for data transfer. Controller paramenters can be optimized automatically. Complex control stratgey can be implemented fairly easily. e205.eps c Dr. M. Zahurul Haq (BUET) ME 6401 5 / 24 Analog & Digital c Dr. M. Zahurul Haq (BUET) ME 6401 6 / 24 Operating Principle a P Controller e208.eps In P mode, linear linearship between Manipulating Varible (MV), y and Error, e exist in Proportional Band (PB), X p : y K p e y o X p 100± K p e203.eps c Dr. M. Zahurul Haq (BUET) ME 6401 7 / 24 Narrower the X p, a small deviation will cause the full manipulating range, i.e. gain increases as X p is reduced. c Dr. M. Zahurul Haq (BUET) ME 6401 8 / 24
Proportional Band Step Response of a P Controller e210.eps MV is only proportional to error over the range 100 150 o C, i.e. for a deviation of 50 o C from SP = 150 o C. Within X p, the controller travels through the full manipulating range, y h, so the K p can be determined as: K y h Maximum manipulating range p X p Proportional Band c Dr. M. Zahurul Haq (BUET) ME 6401 9 / 24 Step Response of a I Controller e209.eps c Dr. M. Zahurul Haq (BUET) ME 6401 10 / 24 Step Response of a D Controller e211.eps c Dr. M. Zahurul Haq (BUET) ME 6401 11 / 24 e214.eps T 1 T d 4 is practical D controller time constant, and its value is specefied by the manufacturer. c Dr. M. Zahurul Haq (BUET) ME 6401 12 / 24
Step Response of a PI Controller Step Response of a PD Controller e212.eps c Dr. M. Zahurul Haq (BUET) ME 6401 13 / 24 Step Response of a PID Controller e213.eps c Dr. M. Zahurul Haq (BUET) ME 6401 14 / 24 Selection of Controller Types e217.eps e215.eps c Dr. M. Zahurul Haq (BUET) ME 6401 15 / 24 c Dr. M. Zahurul Haq (BUET) ME 6401 16 / 24
Recording Step Response The step response of a process, i.e. the PV following a step change in MV can be characterized by two time values: 1 delay time T u 2 response time, T g The ratio T g T u gives information about the character of the process and its controllability: T g T u more than 10: process easy to control T g T u between 10 & 3: process can be controlled T g T u less than 3: process difficult to control e206.eps c Dr. M. Zahurul Haq (BUET) ME 6401 17 / 24 c Dr. M. Zahurul Haq (BUET) ME 6401 18 / 24 Characteristic Values of Processes Controller Quality: Disturbance Change Controller optimation are uaually based on step changes in a disturbance or the setpoint. The overshoot amplitude, X o and the stabiliazation time, T s offer a measure of quality. It is convenient to regard the stabilization after a disturbance as being complete, when the error remains with 1± of the SP. e207.eps e218.eps c Dr. M. Zahurul Haq (BUET) ME 6401 19 / 24 c Dr. M. Zahurul Haq (BUET) ME 6401 20 / 24
Controller Quality: Setpoint Change Unstable Control Loop e219.eps In addition to the X o & T s, the area of control error is also used as a measure of control quality: Linear optimum: A min A 1 A 2 A 3 Magnitude optimum: A min A 1 A 2 A 3 Squared optimum: A min A 2 1 A2 2 A2 3 c Dr. M. Zahurul Haq (BUET) ME 6401 21 / 24 e216.eps c Dr. M. Zahurul Haq (BUET) ME 6401 22 / 24 Oscillation Method of Ziegler & Nichols Control parameters are adjusted until the stability limit is reached, and the control loop is formed by the controller and the process starts to oscillate. The test produces: 1 the critical proportional band, X pc 2 the oscillation time T c of the process variable 1 Reduce any I and D action to their minimum effect. 2 Gradually begin to reduce X p while providing periodic small disturbances to the process. X p is reduced until PV performs undamped oscillations of constant amplitude. This provides the values of X pc and T c. 3 Set the values of the controller constants using the following table: Mode X p T n T d P 2 0X pc N/A N/A PI 2 2X pc T c 1 2 N/A PID 1 7X pc T c 2 0 T c 8 0 c Dr. e220.eps M. Zahurul Haq (BUET) ME 6401 23 / 24 c Dr. M. Zahurul Haq (BUET) ME 6401 24 / 24