WHAT IS CONTROL? WHY CONTROL?

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1 The University for business and the professions WHAT IS CONTROL? Control is the process of altering, manually or automatically, the performance of a system to a desired one WHY CONTROL? Because systems by themselves usually do not behave the way we would like them to The University for business and the professions Manual Control Automatic Control system to be controlled automatic controller system to be controlled process operator measured behaviour measured behaviour levers of power process supervisor 1

2 The University for business and the professions MAIN AIMS OF CONTROL SYSTEMS Regulation regulate the output from some process to remain constant to a required value despite disturbances and/or noise Tracking or Servo system make the process output follow a particular changing form Sequential Control make events occur in a particular sequence, either time driven or event driven The University for business and the professions THE THREE ELLEMENTS FOR SUCCESSFUL CONTROL DESIGN a definition of desired behaviour an ability to generate and apply actions a means to select actions or to make modifications that when applied to the system will result in the desired behaviour being obtained 2

3 The University for business and the professions OPEN- versus CLOSED-LOOP CONTROL Open-Loop Control the controller does not use a measure of the system output to be controlled in computing the control action to take Closed-Loop Control the controlled output is measured and fed back for use in the computation of the control action OPEN-LOOP CONTROL input or reference variable Controller Actuator Process plant output or controlled variable Process of which a variable (output) is being controlled Controller determines the action to be taken as a result of the system input Actuator gives an output of some action designed to change the controlled variable 3

4 OPEN-LOOP CONTROL: Some Comments input or reference variable Controller Actuator Process plant output or controlled variable The controller is designed on the basis of previous experience as WE likely PLAY to give GOD the output required. Therefore, the behaviour of the process must be known as accurately as possible OR There is no changing of the control action to WE RELY HEAVILY ON HIM account for any disturbances which may change the output variable CLOSED-LOOP or FEEDBACK CONTROL reference error control variable Controller Actuator disturbance Sensor plant Process noise Main futures: Feedback and Comparison output Sensor measures the system output and feeds it back Comparator computes the difference between the reference signal and the sensor output to give the controller a measure of the system error 4

5 CLOSED-LOOP or FEEDBACK CONTROL Example: Automobile Cruise Control road grade desired speed error control variable Controller throttle actuator Engine process Auto body sensor actual speed Speedometer sensor noise THE EFFECTS OF FEEDBACK Reduce the error between the actual and the desired value Change the stability of the system Change the overall system gain Change the sensitivity of the system gain Change the bandwidth of the system Reduce the effect of external disturbances and noise Reduce the effect of variations of system parameters 5

6 THE DESIGN PROCESS Transform Requirements into a Physical System Control Systems Engineering 4 th Edition, by Norman S Nise 2004, by John Wiley & Sons, Inc THE DESIGN PROCESS Draw a Functional Block Diagram Control Systems Engineering 4 th Edition, by Norman S Nise 2004, by John Wiley & Sons, Inc 6

7 Create a Schematic THE DESIGN PROCESS Control Systems Engineering 4 th Edition, by Norman S Nise 2004, by John Wiley & Sons, Inc THE DESIGN PROCESS Develop a Mathematical Model (Block Diagram) Control Systems Engineering 3 rd Edition, by Norman S Nise 2000, by John Wiley & Sons, Inc 7

8 THE DESIGN PROCESS Reduce the Block Diagram Analyse and Design MATHEMATICAL MODELING WHAT IS A MODEL? The term model, as it is used and understood by control engineers, primarily means a set of differential equations that describe the dynamic behaviour of a system 8

9 MATHEMATICAL MODELING HOW IS A MODEL OBTAINED? Using principles of underlying physics Testing a prototype, measuring the response to specific inputs, and using the data to construct an analytical model MATHEMATICAL MODELING Example: A Simple System; Cruise Control Model x physical system force u bx m free body diagram u Equations of motion: b u bx = mx x+ x = m or ( v= x ) b u v + v= m m u m 9

10 Example: A Simple System; Cruise Control Model b u Apply Laplace transform to v + v= with zero initial conditions m m 1 m V() s = U() s = G() s U(), s s C s+ b m Transfer Function input U(s) G(s) output Y(s)=V(s) Y(s)=G(s)U(s) INPUT/OUTPUT DESCRIPTION FREQUENCY DOMAIN (s=jω) FREQUENCY RESPONSE Example: A Simple System; Cruise Control Model Introduce two variables (states) x1 = x, x2 = x Then x x1 0 = + u x 0 bm x 1 m 2 2 y v [ 0 1] x 1 = = x 2 inputs u(t) outputs y(t) x = Ax+ Bu y = Cx+ Du states x(t) STATE SPACE or INTERNAL DESCRIPTION 10

11 BASIC PERFORMANCE CRITERIA Stability Time response shape Frequency response shape BASIC PERFORMANCE CRITERIA Input/Output Stability Bounded-Input Bounded-Output (BIBO) Stability For every bounded input the output of the system is bounded as well input u(t) output y(t) BIBO stable BIBO unstable 11

12 BASIC PERFORMANCE CRITERIA Internal Stability Asymptotic Stability All states tend to zero as time tends to infinity for every initial condition inputs u(t) outputs y(t) states x(t) x 1 (t) x 1 (t) x 2 (t) Asymptotically stable x 2 (t) Asymptotically unstable BASIC PERFORMANCE CRITERIA Time Response Shape 1 input u(t) output c(t) steady-state error 1 Control Systems Engineering 4 th Edition, by Norman S Nise 2004, by John Wiley & Sons, Inc 12

13 BASIC PERFORMANCE CRITERIA Frequency Response Shape WHAT IS FREQUENCY RESPONSE? G( jω) = M( ω) φ( ω) Control Systems Engineering 4 th Edition, by Norman S Nise 2004, by John Wiley & Sons, Inc BASIC PERFORMANCE CRITERIA Frequency Response Shape -3db 20logM (db) bandwidth Control Systems Engineering 4 th Edition, by Norman S Nise 2004, by John Wiley & Sons, Inc 13

14 BASIC PERFORMANCE CRITERIA Frequency Response Shape Crossover frequency Control Systems Engineering 4 th Edition, by Norman S Nise 2004, by John Wiley & Sons, Inc THE CONTROL DESIGN TRADE OFF D(s) R(s) E(s) Y(s) Controller G 1 (s) Process G 2 (s) N(s) GG G GG = + + = Y Yr Yd Yn R D N 1+ GG GG GG 1 2 If G1 >>> { Yr R, Yd 0 and Yn N} Y R N If G <<< { Y 0, Y G D and Y 0} Y G D 1 r d 2 n 2 14

15 THE CONTROL DESIGN TRADE OFF If G1 >>> { Yr R, Yd 0 and Yn N} Y R N If G <<< { Y 0, Y G D and Y 0} Y G D 1 r d 2 n 2 Make the controller gain G 1 large at low frequencies so that the closed loop system follows its reference input and rejects the external disturbances Make the controller gain G 1 small at high frequencies so that the closed loop system rejects the measurement noise Ensure reasonable gain and phase margins at crossover frequency for stability purposes Example: Primitive Pitch Control of the RPV XRAE-1 Open Loop XRAE-1 (Flight Controller Off) elevator XRAE-1 pitch angle 6 Open loop response to a step in the elevator of XRAE Pitch angle (rads) Time (secs) 15

16 6 Open loop response to a step in the elevator of XRAE Pitch angle (rads) Time (secs) Example: Primitive Pitch Control of the RPV XRAE-1 Closed Loop XRAE-1 (Flight Controller On) pitch angle demand Flight controller K elevator XRAE-1 actual pitch angle 1.4 Closed loop step response of XRAE Pitch angle (rads) Ti ( ) 16

17 1.4 Closed loop step response of XRAE Pitch angle (rads) Time (secs) R(s) PID: A Commonly Used Controller D(s) E(s) Controller G 1 (s) Process G 2 (s) Y(s) Proportional action N(s) K p error signal Ki d Kd dt Derivative action control signal Integral action 17