Controllers for Marine Engineering Systems - Essay Example

Running Head: PID & Robust and Optimal Controllers for Marine Engineering Systems PID & Robust and Optimal Controllers for Marine Engineering Systems Author's Name Institution's Name Developments in Automatic Control Theory: An Overview Of late there has been much advancement in automatic control theory. It is not easy to provide an fair analysis of an field whilst it is still developing; nevertheless, looking back on the progress of feedback control theory it is by now possible to distinguish some main trends and point out some key advances. The Classical Period of Control Theory In the past, automatic control theory using frequency-domain techniques had come of age, establishing itself as a standard (Kuhn, 1962). Alternatively, a firm mathematical theory for servomechanisms had been recognized, and on the other, engineering design techniques were provided. The era after the Second World War can be called the classical period of control theory. It was characterized by the appearance of the first textbooks (MacColl, 1945; Lauer, Lesnick, & Matdon, 1947; Brown & Campbell, 1948; Chestnut & Mayer, 1951; Truxal, 1955), and by simple design tools that provided great perception and definite solutions to design problems. These tools were employed using hand calculations, or at most slide rules, with graphical techniques. The Space/Computer Age and Modern Control With the dawn of the space era, controls design in the United States prevented from the frequency-domain practices of classical control theory and back to the differential equation techniques of the late 1800's, which were inherent in the time domain. The reasons for this development are as follows. Time-Domain Design For Nonlinear Systems The model of classical control theory was very fitting for controls design problems during and immediately after the World Wars. The frequency-domain approach was suitable for linear time-invariant systems. It is at its best when managing single-input/single-output systems, for the graphical techniques were problematic to use with numerous inputs and outputs. Classical controls design had some successes with nonlinear systems. By employing the noise-rejection properties of frequency-domain techniques, a control system can be designed that is robust to deviations in the system limits, and to measurement errors and external disturbances. Consequently, classical techniques can be applied on a linearized form of a nonlinear system, giving good results at an equilibrium position about which the system performance is more or less linear. Frequency-domain methods can also be applied to systems with simple types of nonlinearities using the describing function approach, which relies on the Nyquist criterion. This method was first used by the Pole J. Groszkowski in radio transmitter design before the Second World War and complied with in 1964 by J. Kudrewicz. Regrettably, it is not possible to design control systems for complex nonlinear multivariable systems, for example those arising in aerospace applications, using the assumption of linearity and treating the single-input/single-output transmission pairs individually. Optimal Control and Estimation Theory In view of the fact that naturally-occurring systems show optimality in their motion, it makes sense to design man-made control systems in a best possible fashion. A major gain is that this design may be realized in the time domain. In the context of modern controls design, it is common to reduce the time of transit, or a quadratic generalized energy functional or performance index, possibly with some constraints on the allowed controls. R. Bellman (1957) employed dynamic programming to the optimal control of discrete-time systems, showing that the normal direction for solving optimal control problems is backwards in time. His modus operandi resulted in closed-loop, usually nonlinear, feedback schemes (Lewis, 1992). PID & Robust and Optimal Controllers for Marine Engineering Systems: An Introduction A Proportional-Integral-Derivative (or PID) Controller is a typical closed-loop control that tries to control one or more reference variable of a plant by identifying the output at a given time and regulating the plant input appropriately. The controller takes a calculated value from a process or other device and compares it with a reference setpoint value. The difference is then used to fine-tune some input to the process so as to bring the process' calculated value back to its desired setpoint. In contrast to simpler controllers, the PID can change process outputs founded on the history and rate of change of the error signal, which gives more correct and stable control. PID controllers do not necessitate complex mathematics to design and can be easily attuned to the desired application, contrasting more complex control algorithms founded on optimal control theory. A PID controller can be used to direct any quantifiable variable which can be influenced by controlling some other process variable. For instance, it can be used to control temperature, pressure, flow rate, chemical composition, speed, or other variables. Automobile cruise control is an example of a process outside of industry which makes use of simple PID control. Some control systems arrange PID controllers in cascades or networks. Specifically, a master control produces signals used by slave controllers. One common state is motor controls: one often wants the motor to have a controlled speed, with the slave controller directly managing the speed rooted in a proportional input. This slave input is fed by the master controllers' output, which is controlling based upon an interconnected variable. Robust Control Defined Chandraseken defines Robust Control as "the control of unknown plants with unknown dynamics subject to unknown disturbances". Evidently, the significant concern with robust control systems is improbability and how the control system can handle this problem. There is uncertainty in the model of the plant. There are disturbances that take place in the plant system. In addition there is noise which is read on the sensor inputs. Each of these uncertainties can have an additive or multiplicative aspect. Robust control methods aim to allot the uncertainty rather than articulate it in the form of a distribution. Given a bound on the uncertainty, the control can deliver results that meet the control system requirements in all cases. Hence robust control theory might be stated as a worst-case analysis method rather than a conventional case method. It must be acknowledged that some performance may be omitted so as to ensure that the system meets definite requirements. Nevertheless, this appears to be a common issue when coping with safety critical embedded systems Optimal Controllers Defined It is an extension of the calculus of variations for dynamic systems with one independent variable, generally time, in which control (input) variables are established to increase or decrease some measure of the performance (output) of a system at the same time as satisfying specific constraints. Optimal Control Theory is divided into two parts: optimal programming, where the control variables are established as functions of time for a specified initial state of the system, and optimal feedback control, where the control variables are established as functions of the existing state of the system. Examples of optimal control problems are: (1) determining paths of vehicles between two points to reduce fuel or time, and (2) determining feedback control logic for vehicles or industrial processes to keep them near a desired operating point in the presence of disturbances with adequate control magnitudes. The controller used for the Marine Engineering Systems can be designed in different ways. The normally considered control approaches are Proportional-Integral-Derivative Control (PID), Gain-scheduling Control, and Linear Quadratic Gaussian (LQG) Control, Adaptive Control, H-Infinity Control H, Fuzzy Logic approaches and Neural Network Methods (Craven et al, 1998). The following is the summary of each of these methods. PID-control The PID controller has been put into service for a long time with different results; see for example Lots et al (2001). It is extremely dependent of a precise linearized model of the vehicle. When the system operates far from the operating point used for the linearization the performance of the PID controller decreases drastically. The ability to adjust the PID controller also controls how well it may function. Gain-scheduling & Adaptive Control Gain-scheduling is a method which makes the controller less exposed to errors as a result of operation far away from the operating point. Using this approach several linearizations are made about different operating points. A scheduler is then used to establish which linearization best describes the system at any given time, and uses a set of gains related with that linearization. A problem with this method is designing the scheduler in a way that prevents the controller outputs from exhibiting "jumps" when the scheduler switches from one set of gains to another. This is a method generally used in tandem with other control methods, such as PID and LQG. The use of adaptive control is another way to justify the vehicle operating under different circumstances. As with gain-scheduling, the gains are changed to regulate the controller to the new operating point. This is performed by using a gain adjusting algorithm to recalculate the gains at every step. Designing this algorithm without causing the system to become unstable at any point can be very complicated (See Sarkar et al (1999) for an example of adaptive control). LQG (Linear Quadratic Gaussian) Control Robust control design using LQG control theory creates an optimized controller. The control strategy entails a linearized representation of the plant. A swapping between reducing the input signals to the plant and the outputs from the plant is set by hand. This situation should be based on the type of application where the controller is put into service. The LQG technique then derives the optimal gains for the operating point used in the linearization. When applying to Unmanned underwater vehicles (UUV) which are an extremely nonlinear and coupled system, the success of a LQG controller, also known as a LQR (Linear Quadratic Regulator) depends greatly on the choice of operating point and the capacity to derive a linearization of the plant with high precision. Naeem et al (2003) effectively used a LQR though they only tried it on a single input single output (SISO) system. H-control The H based control is another method for designing a robust controller able to handle the differences between the physical plant and the model of the plant used for controller design. Designing the weighting matrices involves prudent thought for optimal performance. Common problems involve controller demanded inputs that are higher than what is possible as a result of saturation. Fuzzy Logic Control Fuzzy Logic based controllers is designed to imitate the way humans control multifaceted nonlinear systems. The range of all input variables is broken into states and then rules are instituted for every combination of these states. An output signal is then allocated to each rule and these outputs are evaluated together to produce the output signal from the controller. Fuzzy logic provides a controller which is compatible to manage nonlinear, time dependent and complex systems. This type of controller provides a highly robust controller. The ability to design rules and allocate outputs limits how well this controller functions. The fuzzy approach is compatible for pitch control of UUVs normal GNC (see DeBitetto, 1995). PID & Robust and Optimal Controllers: An Analysis Following is the analysis of the different controllers vis--vis PID. PID Controller It is the most common form of process controller used industrially which combines three forms of the error variable namely: i) a proportional component ii) the derivative of the error, and iii) the integral of the error. PID control has been effectively applied to many processes and machines; however it has its drawbacks. a) It is difficult to control nonlinear systems in which the gains need to change. For instance, some positioning servos perform much better using error squared control. Here, the control signal is proportional to the error squared, and therefore the gain is higher when the error is large. When the error is small, the gain decreases, so stability for final approach to the desired position is better. If the inertia of a motor shaft changes when the load changes, then a PID controller with fixed gains may go into uneven oscillations. b) If the dynamics of the process are more multifaceted, then a PID controller may not provide a suitable stable response. For instance, if a motor drives a load on a long shaft which can rotate by a considerable amount, the simple model may not be precise. A more complex model of the dynamic behaviour will be required, and a more complex controller may be needed to control the torsional vibrations of the load on the long, compliant shaft. Highly developed control techniques are available to design such a controller. These include: - Cascade controllers, where extra feedback loops are used to steady parts of the system, making the whole system easier to control and - Adaptive controllers which repeatedly adjust themselves to changing dynamics PID vs. Fuzzy Logic in Temperature Control The general view is that temperature control is an established and mostly fixed area of technology. There are still industrial applications, which need not only specific temperature control, but also a quicker heat up time and faster reaction to disturbances with least overshoot and undershoot when the setpoint changes. Long-established proportional-integral-derivative (PID) control techniques cannot meet these additional tests. In essence two directions are present for designing highly advanced temperature controllers. One solution is based on adding special features not found in established PID controllers and the other solution is based on using fuzzy logic control. Fuzzy control becomes appealing particularly for the smallest microcontrollers, since this method involves less computational power and lays emphasis on less operational memory than usual PID compensation (Galan, 2004). PID versus Self Tuning & Adaptive Controllers To control some processes, there is a need to adjust the gains of a simple PID controller to keep the response stable and remove unnecessary errors. A number of techniques have been developed to do this automatically. Many companies offer self-tuning & Adaptive controllers which regulate their gains automatically in response to varying conditions. References Bellman, R 1957, Dynamic Programming, New Jersey: Princeton Univ. Press. Brown, GS & Campbell, DP 1948, Principles of Servomechanisms, New York: Wiley. Chandrasekharan, PC 1996, Robust Control of Linear Dynamical Systems, Academic Press. Chestnut, H & Mayer, RW 1955, Servomechanisms and Regulating System Design, vol. 1, 1951, vol. 2, Wiley. Craven, P, Sutton, R and Burns, R 1998, Control Strategies for Unmanned Underwater Vehicles. DeBitetto, P 1995, Fuzzy Logic for Depth Control of Unmanned Undersea Vehicles, IEEE Journal of Oceanic Engineering, Vol. 20, No. 3, July. Galan, P 2004, Temperature control: PID vs. Fuzzy Logic, Control Engineering, January 1, 2004. Kuhn, TS 1962, The Structure of Scientific Revolutions, Chicago: Univ. of Chicago Press. Lane, JD, Trucco, E & Chaumette, F 2001, A 2-D visual Servoing for Underwater Station Keeping, Proceedings of the 2001 IEEE International Conference on Robotics & Automation Seoul, Korea - May 21-26. Lauer, H, Lesnick, RN & Matdon, LE 1947, Servomechanism Fundamentals, New York: McGraw-Hill. Lewis, FL 1992, Introduction to Modern Control Theory, in: F.L. Applied Optimal Control and Estimation, Prentice-Hall. MacColl, LA 1945, Fundamental Theory of Servomechanisms, New York: Van Nostrand. MacFarlane, AGJ, & Postlethwaite, I 1977, The Generalized Nyquist Stability Criterion and Multivariable Root Loci, Int. J. Contr., vol. 25, pp. 81-127. Naeem, W, Sutton, R & Ahmad, S 2003, LQG/LTR Control of an Autonomous Underwater Vehicle Using a Hybrid Control Law. Sarkar, N, Yuh, J., & Podder, T 1999, Adaptive Control of Underwater Vehicle-Manipulator Systems Subject to Joint Limits, Proceedings of the 1999 IEEE/RSJ International Conference on Intelligent Robots and Systems. Truxal, JG. 1955, Automatic Feedback Control System Synthesis, New York: McGraw-Hill. Read More