Introduction to control engineering

Introduction to control engineering Throughout history mankind has tried to control the world in which he lives. From the earliest days he realized that his puny strength was no match for the creatures around him. He could only survive by using his wits and cunning. His major asset over all other life forms on earth was his superior intelligence. Stone Age man devised tools and weapons from flint, stone and bone and discovered that it was possible to train other animals to do his bidding - and so the earliest form of control system was conceived. Before long the horse and ox were deployed to undertake a variety of tasks, including transport. It took a long time before man learned to replace animals with machines. Fundamental to any control system is the ability to measure the output of the system, and to take corrective action if its value deviates from some desired value. This in turn necessitates a sensing device. Man has a number of 'in-built' senses which from the beginning of time he has used to control his own actions, the actions of others, and more recently, the actions of machines. In driving a vehicle for example, the most important sense is sight, but hearing and smell can also contribute to the driver's actions. The first major step in machine design, which in turn heralded the industrial revolution, was the development of the steam engine. A problem that faced engineers at the time was how to control the speed of rotation of the engine without human intervention. Of the various methods attempted, the most successful was the use of a conical pendulum, whose angle of inclination was a function (but not a linear function) of the angular velocity of the shaft. This principle was employed by James Watt in 1769 in his design of a flyball, or centrifugal speed governor. Thus possibly the first system for the automatic control of a machine was born. The principle of operation of the Watt governor is shown in Figure 1.1, where change in shaft speed will result in a different conical angle of the flyballs. This in turn results in linear motion of the sleeve which adjusts the steam mass flow-rate to the engine by means of a valve. Watt was a practical engineer and did not have much time for theoretical analysis. He did, however, observe that under certain conditions the engine appeared to hunt, 2 Advanced Control Engineering Fig. 1.1 TheWatt centrifugal speed governor. where the speed output oscillated about its desired value. The elimination of hunting, or as it is more commonly known, instability, is an important feature in the design of all control systems. In his paper 'On Governors', Maxwell (1868) developed the differential equations for a governor, linearized about an equilibrium point, and demonstrated that stability of the system depended upon the roots of a characteristic equation having negative real parts. The problem of identifying stability criteria for linear systems was studied by Hurwitz (1875) and Routh (1905). This was extended to consider the stability of nonlinear systems by a Russian mathematician Lyapunov (1893). The essential mathematical framework for theoretical analysis was developed by Laplace (1749-1827) and Fourier (1758-1830). Work on feedback amplifier design at Bell Telephone Laboratories in the 1930s was based on the concept of frequency response and backed by the mathematics of complex variables. This was discussed by Nyquist (1932) in his paper 'Regeneration Theory', which described how to determine system stability using frequency domain methods. This was extended by Bode (1945) and Nichols during the next 15 years to give birth to what is still one of the most commonly used control system design methodologies. Another important approach to control system design was developed by Evans (1948). Based on the work of Maxwell and Routh, Evans, in his Root Locus method, designed rules and techniques that allowed the roots of the characteristic equation to be displayed in a graphical manner. Introduction to control engineering The advent of digital computers in the 1950s gave rise to the state-space formulation of differential equations, which, using vector matrix notation, lends itself readily to machine computation. The idea of optimum design was first mooted by Wiener (1949). The method of dynamic programming was developed by Bellman (1957), at about the same time as the maximum principle was discussed by Pontryagin (1962). At the first conference of the International Federation of Automatic Control (IFAC), Kalman (1960) introduced the dual concept of controllability and observability. At the same time Kalman demonstrated that when the system dynamic equations are linear and the performance criterion is quadratic (LQ control), then the mathematical problem has an explicit solution which provides an optimal control law. Also Kalman and Bucy (1961) developed the idea of an optimal filter (Kalman filter) which, when combined with an optimal controller, produced linear-quadraticGaussian (LQG) control. The 1980s saw great advances in control theory for the robust design of systems with uncertainties in their dynamic characteristics. The work of Athans (1971), Safanov (1980), Chiang (1988), Grimble (1988) and others demonstrated how uncertainty can be modelled and the concept of the He~ norm and #-synthesis theory. The 1990s has introduced to the control community the concept of intelligent control systems. An intelligent machine according to Rzevski (1995) is one that is able to achieve a goal or sustained behaviour under conditions of uncertainty. Intelligent control theory owes much of its roots to ideas laid down in the field of Artificial Intelligence (AI). Artificial Neural Networks (ANNs) are composed of many simple computing elements operating in parallel in an attempt to emulate their biological counterparts. The theory is based on work undertaken by Hebb (1949), Rosenblatt (1961), Kohonen (1987), Widrow-Hoff (1960) and others. The concept of fuzzy logic was introduced by Zadeh (1965). This new logic was developed to allow computers to model human vagueness. Fuzzy logic controllers, whilst lacking the formal rigorous design methodology of other techniques, offer robust control without the need to model the dynamic behaviour of the system. Workers in the field include Mamdani (1976), Sugeno (1985) Sutton (1991) and Tong (1978). 1.2.1 Concept of a system Before discussing the structure of a control system it is necessary to define what is meant by a system. Systems mean different things to different people and can include purely physical systems such as the machine table of a Computer Numerically Controlled (CNC) machine tool or alternatively the procedures necessary for the purchase of raw materials together with the control of inventory in a Material Requirements Planning (MRP) system. However, all systems have certain things in common. They all, for example, require inl2uts and outputs to be specified. In the case of the CNC machine tool machine table, the input might be the power to the drive motor, and the outputs might be the position, velocity and acceleration of the table. For the MRP system inputs would include sales orders and sales forecasts (incorporated in a master 3 4 Advanced Control Engineering Inputs Outputs Boundary Fig. 1.2 The concept of a system. production schedule), a bill of materials for component parts and subassemblies, inventory records and information relating to capacity requirements planning. Material requirements planning systems generate various output reports that are used in planning and managing factory operations. These include order releases, inventory status, overdue orders and inventory forecasts. It is necessary to clearly define the boundary of a system, together with the inputs and outputs that cross that boundary. In general, a system may be defined as a collection of matter, parts, components or procedures which are included within some specified boundary as shown in Figure 1.2. A system may have any number of inputs and outputs. In control engineering, the way in which the system outputs respond in changes to the system inputs (i.e. the system response) is very important. The control system design engineer will attempt to evaluate the system response by determining a mathematical model for the system. Knowledge of the system inputs, together with the mathematical model, will allow the system outputs to be calculated. It is conventional to refer to the system being controlled as the plant, and this, as with other elements, is represented by a block diagram. Some inputs, the engineer will have direct control over, and can be used to control the plant outputs. These are known as control inputs. There are other inputs over which the engineer has no control, and these will tend to deflect the plant outputs from their desired values. These are called disturbance inputs. In the case of the ship shown in Figure 1.3, the rudder and engines are the control inputs, whose values can be adjusted to control certain outputs, for example heading and forward velocity. The wind, waves and current are disturbance inputs and will induce errors in the outputs (called controlled variables) of position, heading and forward velocity. In addition, the disturbances will introduce increased ship motion (roll, pitch and heave) which again is not desirable. Rudder Engines Wind Waves Current ,-'~ Position Ship 9 "- w'- Fig. 1.3 A ship as a dynamic system. 9 Forward Velocity Heading 9 Ship Motion (roll, pitch, heave) Introduction to control engineering Disturbance Input Control Input m Controlled Variable I~ or Output Plant Summing Point Fig. 1.4 Plantinputs and outputs. Generally, the relationship between control input, disturbance input, plant and controlled variable is shown in Figure 1.4. 1.2.2 Open-loop systems Figure 1.4 represents an open-loop control system and is used for very simple applications. The main problem with open-loop control is that the controlled variable is sensitive to changes in disturbance inputs. So, for example, if a gas fire is switched on in a room, and the temperature climbs to 20 ~ it will remain at that value unless there is a disturbance. This could be caused by leaving a door to the room open, for example. Or alternatively by a change in outside temperature. In either case, the internal room temperature will change. For the room temperature to remain constant, a mechanism is required to vary the energy output from the gas fire. 1.2.3 Closed-loop systems For a room temperature control system, the first requirement is to detect or sense changes in room temperature. The second requirement is to control or vary the energy output from the gas fire, if the sensed room temperature is different from the desired room temperature. In general, a system that is designed to control the output of a plant must contain at least one sensor and controller as shown in Figure 1.5. Forward Path Summing Point Error I ~ @ Signal Desired Value l 1 Measured Value Controller Control, Signal..I "1 Plant I I Sensor Feedback Path Fig. 1.5 Closed-loopcontrol system. Output Value r 5 6 Advanced Control Engineering Figure 1.5 shows the generalized schematic block-diagram for a closed-loop, or feedback control system. The controller and plant lie along the forward path, and the sensor in the feedback path. The measured value of the plant output is compared at the summing point with the desired value. The difference, or error is fed to the controller which generates a control signal to drive the plant until its output equals the desired value. Such an arrangement is sometimes called an error-actuated system. 1.3.1 Room temperature control system The physical realization of a system to control room temperature is shown in Figure 1.6. Here the output signal from a temperature sensing device such as a thermocouple or a resistance thermometer is compared with the desired temperature. Any difference or error causes the controller to send a control signal to the gas solenoid valve which produces a linear movement of the valve stem, thus adjusting the flow of gas to the burner of the gas fire. The desired temperature is usually obtained from manual adjustment of a potentiometer. Insulation Desired Temperature..I Potentio- Control ,Signal Gas Solenoid ~ Controller "1meter ~ Measured Temperature " ' Valve !1 Gas _ _ ~ Flow-rate illl I Outside Temperature l Gas Fire ~1 Actual Room Temperature Heat ~put c ------~Heat ---~Loss J I ~---~Thermometer Fig. 1.6 Roomtemperature control system. Outside Tempirature Error Desired Signal TemperatureI Potentio-I +..-..<~)1 "- meter ~ C o n t r o l l e r ~ (oc) "7 '(v)'l' I (v) Gas Heat I InsulaControl Flow-rateLoss I tion Actual Signal (m/s) (W) " ~ . I Temperature IIvll Gas Gas ] ~' ~' _ Room ~_~C) Solenoid ~ Burner I I Valve I+ Heat Input (w) Thermometer Fig. 1.7 Blockdiagram of room temperature control system. Introduction to control engineering A detailed block diagram is shown in Figure 1.7. The physical values of the signals around the control loop are shown in brackets. Steady conditions will exist when the actual and desired temperatures are the same, and the heat input exactly balances the heat loss through the walls of the building. The system can operate in two modes: (a) Proportional control: Here the linear movement of the valve stem is proportional to the error. This provides a continuous modulation of the heat input to the room producing very precise temperature control. This is used for applications where temperature control, of say better than 1 ~ is required (i.e. hospital operating theatres, industrial standards rooms, etc.) where accuracy is more important than cost. (b) On-off control: Also called thermostatic or bang-bang control, the gas valve is either fully open or fully closed, i.e. the heater is either on or off. This form of control produces an oscillation of about 2 or 3 ~ of the actual temperature about the desired temperature, but is cheap to implement and is used for low-cost applications (i.e. domestic heating systems). 1.3.2 Aircraft elevator control In the early days of flight, control surfaces of aircraft were operated by cables connected between the control column and the elevators and ailerons. Modern high-speed aircraft require power-assisted devices, or servomechanisms to provide the large forces necessary to operate the control surfaces. Figure 1.8 shows an elevator control system for a high-speed jet. Movement of the control column produces a signal from the input angular sensor which is compared with the measured elevator angle by the controller which generates a control signal proportional to the error. This is fed to an electrohydraulic servovalve which generates a spool-valve movement that is proportional to the control signal, e;i, reO ~ ! ,evator CO?ut rmOln Contro~na, (/ I'. I ~ Sensor ' Controller~ ~ )/ //-II .I ~ - E] ~-~. I & Meas~176176176i /r~ . \ \ Hydraulic Cylinder Fig. 1.8 Elevatorcontrolsystemfor ahigh-speedjet. . Electrohydraulic Servovalve Actual Angle 7 8 Advanced Control Engineering Fluid Desired Error Control Flow-rate Hydraulic Actual Angle Signal Signal m3/s) Force Angle (deg) (deg) ] Input ] ~ ~ ] ~ Servo-Hydraulic ~ Angular Controller valve ~ Cylinder Elevator G Sensor (v) Output Angular Sensor I-, r Fig. 1.9 Blockdiagramof elevatorcontrol system. thus allowing high-pressure fluid to enter the hydraulic cylinder. The pressure difference across the piston provides the actuating force to operate the elevator. Hydraulic servomechanisms have a good power/weight ratio, and are ideal for applications that require large forces to be produced by small and light devices. In practice, a 'feel simulator' is attached to the control column to allow the pilot to sense the magnitude of the aerodynamic forces acting on the control surfaces, thus preventing excess loading of the wings and tail-plane. The block diagram for the elevator control system is shown in Figure 1.9. 1.3.3 Computer Numerically Controlled (CNC) machine tool Many systems operate under computer control, and Figure 1.10 shows an example of a CNC machine tool control system. Information relating to the shape of the work-piece and hence the motion of the machine table is stored in a computer program. This is relayed in digital format, in a sequential form to the controller and is compared with a digital feedback signal from the shaft encoder to generate a digital error signal. This is converted to an analogue Computer Controller MachineTable Movement v Computer Program 9 ooo ///// ~,. DC-Servomotor / / / / / ~l ~[ Digital Controller I ooo Encoder Pl ~ II LXJ Bearing" a l.t t-l-i-i-t ...... 4.-i-.i-.t.-t-.b.t.~ ...... l- [-li>L// I, JLead-Screw Power IIII1~1 mplifier I Digital PositionalFeedback | I AnalogueVelocity Feedback Fig. 1.10 Computernumericallycontrolledmachinetool. IX] N._ / I chogenerator | Introduction to control engineering Digital Desired Position Actual Control Actual Torque Digital Signal Velocity Position (m/s)........ Error (Nm) Computer~ Digital ~ Power DC Machine I IIntegrat~ Program i :~:y ,-i Controlleri ,-T_,-I Amplifier Serve motor a9 ,e l i ] I Anal~ I Tacho- I.,, ~ V e l o c i t y Feedback I generator I" I Digital Positional Shaft I., Feedback EncoderF Fig. 1.11 Blockdiagramof CNCmachine-tool control system. control signal which, when amplified, drives a d.c. servomotor. Connected to the output shaft of the servomotor (in some cases through a gearbox) is a lead-screw to which is attached the machine table, the shaft encoder and a tachogenerator. The purpose of this latter device, which produces an analogue signal proportional to velocity, is to form an inner, or minor control loop in order to dampen, or stabilize the response of the system. The block diagram for the CNC machine tool control system is shown in Figure 1.11. 1.3.4 Ship autopilot control system A ship autopilot is designed to maintain a vessel on a set heading while being subjected to a series of disturbances such as wind, waves and current as shown in Figure 1.3. This method of control is referred to as course-keeping. The autopilot can also be used to change course to a new heading, called course-changing. The main elements of the autopilot system are shown in Figure 1.12. The actual heading is measured by a gyro-compass (or magnetic compass in a smaller vessel), and compared with the desired heading, dialled into the autopilot by the ship's master. The autopilot, or controller, computes the demanded rudder angle and sends a control signal to the steering gear. The actual rudder angle is monitored by a rudder angle sensor and compared with the demanded rudder angle, to form a control loop not dissimilar to the elevator control system shown in Figure 1.8. The rudder provides a control moment on the hull to drive the actual heading towards the desired heading while the wind, waves and current produce moments that may help or hinder this action. The block diagram of the system is shown in Figure 1.13. Desired.Heading "" /ErrorL - Actual rudder-angle ". . . . . . ~ ~ (n~::l~, ~ " Auto-pilot . . .~_~4-n~=n ..... D --'-Ot i Steeringgear ,J :;:;" . . . . . . . . . . . . . '. . . . . . -" I II II 13 -Demandedrt]dder_angle Measured rudder-angle Fig. 1.12 Shipautopilot control system. ~ "] Sensor.J ....... "" / J ' 9 10 AdvancedControl Engineering Actual Disturbance Rudder Moment Angle (Nm) Actual ,(deg) I Rudder ~ Heading SteeringL_~ICharactI (deg) Hull - ~eristics I Gear Demanded Rudder Angle Desired Course Error Heading Autopilot ~ (deg) ~ 1 Potentio- _ ~ meter (V)j / (Controller) II'l I Angle RudderI~ I Sensor ~ Measured Heading (V) Rudder Moment (Nm) Gyro- I.,, Compass I" Fig. 1.13 Blockdiagramof ship autopilot control system. In order to design and implement a control system the following essential generic elements are required: 9 Knowledge of the desired value: It is necessary to know what it is you are trying to control, to what accuracy, and over what range of values. This must be expressed in the form of a performance specification. In the physical system this information must be converted into a form suitable for the controller to understand (analogue or digital signal). 9 Knowledge of the output or actual value: This must be measured by a feedback sensor, again in a form suitable for the controller to understand. In addition, the sensor must have the necessary resolution and dynamic response so that the measured value has the accuracy required from the performance specification. 9 Knowledge of the controlling device: The controller must be able to accept measurements of desired and actual values and compute a control signal in a suitable form to drive an actuating element. Controllers can be a range of devices, including mechanical levers, pneumatic elements, analogue or digital circuits or microcomputers. 9 Knowledge of the actuating device: This unit amplifies the control signal and provides the 'effort' to move the output of the plant towards its desired value. In the case of the room temperature control system the actuator is the gas solenoid valve and burner, the 'effort' being heat input (W). For the ship autopilot system the actuator is the steering gear and rudder, the 'effort' being turning moment (Nm). 9 Knowledge of the plant: Most control strategies require some knowledge of the static and dynamic characteristics of the plant. These can be obtained from measurements or from the application of fundamental physical laws, or a combination of both. 1.4.1 Control system design ~ ~ ~ . . . . With all of this knowledge and information available to the control system designer, all that is left is to design the system. The first problem to be encountered is that the Introduction to control engineering Define System Performance Specification Identify System Components L Model Behaviour of Plant and System Components Is Component Response Acceptable? r Select Alternative Components No Yes Define Control Strategy I. [ Simulate System Response Does Simulated Response Meet Performance Specification? No Modify Control Strategy T Yes Implement Physical System Measure System Response No Does System Response Meet Performance Specification? Fig. 1.14 Stepsin the design of a control system. Modify Control Strategy 11 12 AdvancedControl Engineering knowledge of the system will be uncertain and incomplete. In particular, the dynamic characteristics of the system may change with time (time-variant) and so a fixed control strategy will not work. Due to fuel consumption for example, the mass of an airliner can be almost half that of its take-off value at the end of a long haul flight. Measurements of the controlled variables will be contaminated with electrical noise and disturbance effects. Some sensors will provide accurate and reliable data, others, because of difficulties in measuring the output variable may produce highly random and almost irrelevant information. However, there is a standard methodology that can be applied to the design of most control systems. The steps in this methodology are shown in Figure 1.14. The design of a control system.is a mixture of technique and experience. This book explains some tried and tested, and some more recent approaches, techniques and methods available to the control system designer. Experience, however, only comes with time.