CONTROL AND DYNAMIC SYSTEMS: ADVANCES IN THEORY AND APPLICATIONS

By N. CAUNK

CONTENTS INTRODUCTION OF DISTURBANCE OBSERVER TYPES OF DISTURBANCE OBSERVERS INTRODUCTION OBSERVER AND CONTROL SYSTEM DESIGN CONCEPTS FORMAT OF EXAMPLE AND USE OF MATLAB FORMAT OF THE EXAMPLE PROBLEM USING MATLAB/SIMULINK HOW THIS BOOK IS ORGANIZED THE STRUCTURE OF THIS DOCUMENT HOW TO READ THIS BOOK REFERENCES BASICS OF DISTURBANCE OBSERVER WHAT IS DISTURBANCE HOW DISTURBANCE ESTIMATION WORKS DISTURBANCE REJECTION AND ACCELERATION CONTROL SYSTEM CONCEPT OF DISTURBANCE REJECTION AND ACCELERATION DIFFERENT DISTURBANCE OBSERVERS DEPENDING ON HOW THE DISTURBANCE IS CAPTURED BASIC CONTROL SYSTEM DESIGN REACTION FORCE OBSERVER (RFOB) REACTION FORCE OBSERVER DESIGN COMBINED USE OF DOB AND RFOB INTERNAL MODEL AND TWO-DEGREES-OF-FREEDOM CONTROL INTERNAL MODEL PRINCIPLE FEEDFORWARD CONTROL CONTROL SYSTEM WITH DISTURBANCE OBSERVER AND FEEDFORWARD EFFECT OF OBSERVATION NOISE AND MODELING ERROR EFFECT OF OBSERVATION NOISE EFFECT OF MODELING ERROR EFFECT OF VISCOUS FRICTION EFFECT OF VARYING MASS REAL SYSTEM MODELING DC MOTOR TORQUE CONTROL MODEL WITHOUT CURRENT FEEDBACK RELATIONSHIP BETWEEN THE CART MODEL AND ROTARY-TYPE MOTOR IDEA OF ROBUST CONTROL STABILIZED CONTROL AND COPRIME FACTORIZATION COPRIME FACTORIZATION AND DERIVATION OF STABILIZING CONTROLLER DERIVATION OF PARAMETERS FOR COPRIME FACTORIZATION STABILIZING CONTROLLER AND FREE PARAMETERS DOUBLE COPRIME FACTORIZATION INVOLVING Q(S) RELATIONSHIP WITH DISTURBANCE OBSERVER COPRIME FACTORIZATION AND STRUCTURE OF TWO-DEGREES-OF-FREEDOM CONTROL SYSTEM DISTURBANCE OBSERVER IN STATE SPACE IDENTITY INPUT DISTURBANCE OBSERVER HOW TO DESIGN THE IDENTITY INPUT DISTURBANCE OBSERVER IN CONTINUOUS SYSTEM CONTROLLABILITY AND STATE FEEDBACK CONTINUOUS-TIME SERVO SYSTEM WITH IDENTITY DISTURBANCE OBSERVER IDENTITY REACTION FORCE OBSERVER IDENTITY OUTPUT DISTURBANCE OBSERVER IDENTITY HIGHER ORDER DISTURBANCE OBSERVER DESIGN MINIMAL ORDER DISTURBANCE OBSERVER DESIGN OF PERIODIC DISTURBANCE OBSERVER OBSERVABILITY AND NONINPUT/OUTPUT DISTURBANCES MATHEMATICAL MODEL OF A DC MOTOR DC MOTOR OBSERVABLE MATRIX AND RANK OBSERVABILITY OF DISTURBANCE ESTIMATION NONINPUT/OUTPUT DISTURBANCE OBSERVER AND CONTROL DIGITAL DISTURBANCE OBSERVER DESIGN IDENTITY DIGITAL DISTURBANCE OBSERVER DESIGN CONFIRMATION OF SEPARATION THEOREM MINIMAL ORDER DIGITAL DISTURBANCE OBSERVER IDENTITY HIGH-ORDER DIGITAL DISTURBANCE OBSERVER DISTURBANCE OBSERVER OF VIBRATING SYSTEMS MODELING OF THE TWO-INERTIA SYSTEM VIBRATION SUPPRESSION CONTROL IN TRANSFER FUNCTION REPRESENTATION DISTURBANCE OBSERVER AND STABILIZATION FOR TWO-INERTIA SYSTEMS SERVO SYSTEM WITH DOB FOR TWO-INERTIA SYSTEMS COMMUNICATION DISTURBANCE OBSERVER SMITH METHOD OVERVIEW CONTROL WITH COMMUNICATION DOB UNDER DISTURBANCE MULTIRATE DISTURBANCE OBSERVER MULTIRATE SYSTEM MODELING MULTIRATE DISTURBANCE OBSERVER (METHOD 1) DISTURBANCE OBSERVER DESIGN (METHOD 1) CONTROLLER DESIGN USING MULTIRATE OBSERVER (METHOD 1) MULTIRATE DISTURBANCE OBSERVER (METHOD 2) MODEL PREDICTIVE CONTROL WITH DOB MODEL PREDICTIVE CONTROL (MPC) OVERVIEW OF MPC FORMULATION AND OBJECTIVE FUNCTION FOR THE MPC DESIGN CONSTRAINT DESCRIPTIONS TREATMENT OF CONSTRAINTS ON THE CONTROL INPUT Û(K) CONSTRAINTS ON THE CONTROL VARIABLE ?Z(K) CONSTRAINTS ON ?Û(K) CHANGE IN THE CONTROL INPUT CONSTRAINTS ON THE CONTROL INPUTS AND QUANTITIES MPC SYSTEM DESIGN DESIGN OF DISTURBANCE OBSERVER-MERGED MPC SYSTEM KALMAN FILTER WITH DISTURBANCE ESTIMATION (KFD) DESIGN OF KALMAN FILTER WITH DISTURBANCE ESTIMATION DESIGN OF STATIONARY KALMAN FILTER WITH DISTURBANCE ESTIMATION (SKFD) DESIGN OF EXTENDED KALMAN FILTER WITH DISTURBANCE ESTIMATION (EKFD) ADAPTIVE DISTURBANCE OBSERVER STRUCTURE OF AN ADAPTIVE OBSERVER DERIVATION OF OBSERVABLE CANONICAL SYSTEM FOR ADAPTIVE DOB CREATING STATE VARIABLE FILTER DESIGN OF KREISSELMEIER-TYPE ADAPTIVE DISTURBANCE OBSERVER METHODS FOR MEASURING AND ESTIMATING VELOCITIES IMPORTANCE OF VELOCITY MEASUREMENT VELOCITY MEASUREMENT AND ESTIMATION METHODS PSEUDO-DERIVATIVE COUNTING AND TIMEKEEPING METHODS M?T METHOD SYNCHRONOUS COUNTING METHOD INSTANTANEOUS VELOCITY OBSERVER INTRODUCTION THIS BOOK INTRODUCES EIGHT TYPES OF DOBS FOR DESIGNING A DOB, AS SHOWN IN TABLE 1 1 KALMAN FILTER IN THE EIGHTH LINE IS NOT AN OBSERVER BUT IS INCLUDED IN 1 EXAMPLES HAVE BEEN PROPOSED SUCH AS REFERRING TO IT AS DISTURBANCE AND VELOCITY ESTIMATION OBSERVER [3, 4] BECAUSE IT ESTIMATES VELOCITY AS WELL OR REACTION FORCE ESTIMATION OBSERVER [5] BECAUSE IT ESTIMATES REACTION FORCE SPECIFICALLY TYPES OF DISTURBANCE OBSERVER DESIGN SYSTEMS DOB DESIGN FORMS OBJECT TO ESTIMATE (1) TRANSFER FUNCTION ONLY DISTURBANCES CONTINUOUS (2) IDENTITY OBSERVER ALL STATE VARIABLES AND DISTURBANCES SYSTEM (3) MINIMAL ORDER OBSERVER ALL STATE VARIABLES EXCEPT OUTPUTS (4) ADAPTIVE OBSERVER PARAMETERS, STATE VARIABLES AND DISTURBANCES (5) TRANSFER FUNCTION ONLY DISTURBANCES DIGITAL (6) IDENTITY OBSERVER ALL STATE VARIABLES AND DISTURBANCES SYSTEM (7) MINIMAL ORDER OBSERVER ALL STATE VARIABLES EXCEPT OUTPUTS (8) KALMAN FILTER ALL STATE VARIABLES AND DISTURBANCES THIS TABLE BECAUSE IT IS DESIGNED FOR ESTIMATING DISTURBANCES THE KALMAN FILTER AND THE ADAPTIVE OBSERVER CAN BE DESIGNED AS BOTH CONTINUOUS AND DIGITAL SYSTEMS, BUT THEY ARE LIMITED TO THE ABOVE MANY REFERENCES USE THE TRANSFER FUNCTION OF THE CONTINUOUS SYSTEM TO REPRE- SENT DOBS, SPECIALIZING ONLY IN ITS ESTIMATION, WHICH CORRESPONDS TO THE FIRST LINE OF TABLE 1 1 THIS MAY BE BECAUSE IT IS SIMPLE AND EASY FOR US TO UNDERSTAND AND IMPLEMENT HOWEVER, WE CAN SIMULTANEOUSLY ESTIMATE THE CONTROL PLANT’S ORIGINAL STATE VARIABLES, SUCH AS VELOCITY AND CURRENT OTHER THAN DISTURBANCES, USING THE GENERAL OBSERVER THEORY THESE CORRESPOND TO LINES 2–4 AND 6–8 OF THE TABLE SUPPOSE THAT READERS WANT TO USE VARIOUS PHYSICAL ESTIMATES EFFECTIVELY IN DESIGNING THE CONTROL SYSTEM IN THAT CASE, THEY CAN DESIGN THE DOB USING THE IDENTITY OBSERVER DESIGNING METHOD HOWEVER, IF THEY EMPHASIZE THAT THEY DO NOT NEED TO ESTIMATE THE OBSERVED OUTPUT, THEY CAN USE THE MINIMAL ORDER OBSERVER DESIGN METHOD AS AN EXCELLENT CHOICE THEORETICALLY, DOBS EXPRESSED IN TRANSFER FUNCTIONS ARE EQUIVALENT TO THOSE DERIVED FROM THE DESIGN PROCESS FOR MINIMAL ORDER OBSERVERS, AS SHOWN IN ROWS 3 AND 7 MANY STUDIES USE THE FORM OF THE TRANSFER FUNCTION FROM THE BEGINNING BECAUSE ONLY THE DISTURBANCE ESTIMATION FUNCTION IS EXTRACTED AND REEXPRESSED IN THE FORM OF A TRANSFER FUNCTION IN THE DESIGN PROCESS THE DIFFERENCE BETWEEN A CONTINUOUS AND A DIGITAL SYSTEM IS WHETHER THE DESIGN IS BASED ON CONTINUOUS CONTROL THEORY OR DIGITAL CONTROL THEORY 2 IF THERE IS NO NEED TO CONSIDER THE EFFECT OF THE LENGTH OR SHORTNESS OF THE CONTROL PERIOD, IT IS BETTER TO DESIGN A CONTINUOUS SYSTEM WHERE THE PHYSICAL MEANING IS EASY TO GRASP HOW- EVER, IT IS MORE DESIRABLE TO DESIGN IT AS A DIGITAL SYSTEM IF THE CONTROL CYCLE AND THE 2 NOTE THAT THIS BOOK DOES NOT DISTINGUISH BETWEEN THE WORDS DISCRETE SYSTEMS AND DIGITAL SYSTEMS 1 1 TYPES OF DISTURBANCE OBSERVERS BASIC STRUCTURE OF THE CONTROL SYSTEM BASED ON ACCELERATION CONTROL 3 IF THE DISTURBANCE IS INPUT AS A NEGATIVE COMPONENT, POSITIVE FEEDBACK IS USED TO CANCEL IT OUT (POSITIVE FEEDBACK), AND NEGATIVE FEEDBACK IS USED TO DEFINE IT WITH A POSITIVE SIGN (NEGATIVE FEEDBACK) HOWEVER, FEEDBACK IS NOT ALWAYS A MUST 4 IN THIS BOOK, M DENOTES THE MASS OF THE CONTROL PLANT GENERALLY HOWEVER, ONLY WHEN WE WANT TO EMPHASIZE THAT IT IS A NOMINAL VALUE THIS BOOK USES M0 FORMAT OF THE EXAMPLE PROBLEM MOST STUDIES DEALING WITH DOBS ARE EXAMPLES OF ROTATING SYSTEMS BASED ON MOTOR CONTROL HOWEVER, TO UNDERSTAND THE ESSENTIAL THEORY, THIS BOOK INTRODUCES SINGLE-INPUT SINGLE-OUTPUT (SISO) SYSTEM EXAMPLES WITH A CART AS AN INSTANCE OF A LINEAR MECHATRONICS SYSTEM BECAUSE WE BELIEVE THAT IT IS SIMPLE AND EASY TO UNDERSTAND 6 THE READER WHO NEEDS TO DESIGN A ROTATING SYSTEM COULD CONVERT THE LINEAR MODEL TO A ROTATING MODEL CONSIDER A SIMPLE SPRING-MASS DAMPER SYSTEM USING THE POSITION X, VELOCITY ??, FORCE F, EXTERNAL FORCE FEX, COEFFICIENT OF VISCOUS FRICTION C [N/(M/S)], AND COEF- FICIENT OF ELASTICITY K [N/M], THE FOLLOWING EQUATIONS CAN BE OBTAINED: M ???(T) + C??(T) + KX(T) = F(T) ?FEX(T) (1 1) 5 THE CONCEPT OF ACCELERATION CONTROL IS TO CONTAIN THE PROBLEMS OF THE DYNAMIC SYSTEM INSIDE AFTER THAT, IT IS TO CONSIDER THE KINEMATIC MODEL AS THE CONTROL PLANT HOWEVER, THIS DOES NOT MEAN THAT FRICTION AND THE LIKE HAVE DISAPPEARED THEREFORE, CARE MUST BE TAKEN NOT TO OVERLOOK THE ESSENTIAL ASPECTS OF MECHATRONICS SYSTEM STRUCTURE AND DYNAMICS 6 SOME MAY ARGUE THAT WE ARE ONLY DEALING WITH LOW-DIMENSIONAL OBJECTS, BUT WE PRIORITIZE EASE OF UNDERSTANDING 1 3 HOW THIS BOOK IS ORGANIZED