Feedback Control System Controller Controlled variable Error + Control function Set value Process Actuator - Measurement * Error = Set value - Measured value Control function gives the signal to the actuator which is feeding energy to the process. Only input for control function is the error. The controlled value is measured and compared to the set value. The basic idea of the closed loop control is to get error signal so small as possible, (zero).

Heating process Energy W = ∫ P dt Thermal energy Heat capasity = Heater Output power = losses Energy W = ∫ P dt Tout Thermal energy Q = c m dT Input power 2 1 3 Heat capasity = c [ kJ/kg K ] 230 V

CAPACITY Many common processes can store the energy. The phenomenon is named for capacity Because of the capacity the state of the process can not been altered very fast. It is needed time to alter the state of the process. This is the time delay of the process. EXAMPLES: If solid mass is heated by certain power, the temperature of this mass is warming slowly. The capacity affects the delay of the process. Correspondingly we need time to move the mass on the ground and increase the velocity. So the moving body is storing energy. Rotating mass is similar process, but mass is changed to mass of inertia. In electrical circuits capacitors can store voltage energy and inductors have current energy. .

ON-OFF CONTROLLER Output of the control function block has normally only two states: on or off. Output is on, if the set point is bigger then measured value (error > 0). Output is off, if the set point is smaller than measured value (error < 0). Often the turn-on and turn-off points are deliberately made to differ by a small amount, known as the hysteresis. This moderates the switching frequency. Typical for on-off controller is the simple construction and the actuator is type: open/closed. On-off system is also oscillating all the time ! .

TEST FUNCTIONS Impulse function Ramp function Step function Test functions are profitable, if we need more knowledge of unknown dynamic process. Process input is the test signal and output is the response. The response gives us very useful data for tuning the system and making decisions. . Impulse function Ramp function t t Step function Sine function t t

P-CONTROL Control block is the amplifier, which has constant gain. The error signal is multiplied by constant = Kp = P-control gain We can say that P-block is “exaggerating” the error. Drawback is that P-control is normally not able to do the job without error ! Bigger gain Kp gives smaller error. If the gain is too large the feedback system starts to oscillate. If P-controller could have: Set point = controlled value. It gives the error = 0 and output of the controller is also zero. This means: there are no power to the process (in most cases impossible to support). Advantage is rapid function. There are no delay between controller input and output. Any changes in the control system gives fast response.

I-CONTROL Control block is integrator, KI = 1/TI = I- gain , TI = integration time Output is integral of the error. If error is positive, output signal is increasing. Bigger error gives faster increasing output. If error is negative, output signal is decreasing. If error is zero, output keep constant (“memory”). Integrator is able to eliminate control error. Drawbacks are rather slow response and saturation. Very often P- and I-control are used together.

D-CONTROL Control block differentiates error signal. Kd = D-gain. If the error signal increases fast, the output signal has big positive value. If the error signal decreases fast, the output signal has big negative value. D- block is able to accelerate or put the break to process (forecast). Processes with large dead time or noise cannot utilize D- block. D block is not used alone.

Cascade control SET VALUE CONTROLLED VARIABLE Control block 1 + Control block 2 PROCESS PROCESS + - - fast loop Main feedback (slow loop) Cascade Control uses the output of the primary controller to manipulate the setpoint of the secondary controller as if it were the final control element.

Reasons for cascade control Allow faster secondary controller to handle disturbances in the secondary loop. Allow secondary controller to handle non-linear valve and other final control element problems. Allow operator to directly control secondary loop during certain modes of operation (such as startup).

Requirements for cascade control Secondary loop process dynamics must be at least four times as fast as primary loop process dynamics. Secondary loop must have influence over the primary loop. Secondary loop must be measured and controllable.