VIEWS: 7 PAGES: 43 POSTED ON: 2/28/2012
1 An overview of signal processing Operator Output Controller D/A converter Process Plant A/D converter Lecture 4, Spring 2006 TMR4240 Marine Control Systems Department of Marine Technology, Norwegian University of Science and Technology, Trondheim, Norway. 3 Feb 2006 Tristan Perez – TMR4240 Spring 2006 2 Why studying signal procesing? To date vessel operations depend on large amounts of information. All this information is mostly processed by computers, and the way these computers communicate and see the outside world is via signals which contain essential information! As we will see, computer systems dedicated to monitoring and control on marine vessels perform many different task to the received signals—this easier done in discrete time. understanding this is essential for implementing control systems. Tristan Perez – TMR4240 Spring 2006 3 Automation system architecture Computer-based control Tristan Perez – TMR4240 Spring 2006 4 Integrated automation system POSITIONING SYSTEM POWER MANAGEMENT VESSEL AUTOMATION ESD FIRE&GAS PROCESS CONTROL CARGO CONTROL Tristan Perez – TMR4240 Spring 2006 5 Positioning control system architecture TAUT-WIRE ARTEMIS GYRO HPR MRU MOORING Thrusters DGPS WIND SYSTEM Thrust Sensor signal allocation processing Wind load feedforward Reference Reference feedforward model Optimal Vessel Model controller model adaption Tristan Perez – TMR4240 Spring 2006 6 Sensor Signal Processing Unit HW Signal Communication already checked Features: • Online Signal Quality Check • Online weighting of sensor signals Signal Processing Unit • Multiple signal voting algorithms • Filtering and smoothing of signals Tristan Perez – TMR4240 Spring 2006 7 Position reference systems SATELLITE NAVIGATION SYSTEM (DGPS / GLONAS) SURFACE REFERENCE SYSTEM HYDROACOUSTIC POSITIONING TAUT SYSTEM WIRE Tristan Perez – TMR4240 Spring 2006 8 Signal Processing - Example Examples of four different signal failures the signal QA module is detecting. 35 High derivative 30 Frozen signal 25 High variance 20 Wild point 15 10 5 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Tristan Perez – TMR4240 Spring 2006 9 Signal quality checking Three level testing: 1. Tests on individual signals – Range check – Variance check – Wild point detection and removal 2. Sensor voting – Detection of sensor drift 3. Sensor weighting – Unbiased minimum variance measurements – Observer test (Innovation/injection term) Tristan Perez – TMR4240 Spring 2006 10 Statistics Consider the sequence of n-1 historical values: Average value: Variance: Tristan Perez – TMR4240 Spring 2006 11 Range check • Most of the signals available have a defined range: – Example: Gyro signal within 0-360 degrees. • Signal outside the range will indicate that the sensor is faulty: signal will be rejected. • Alarm issued to the operator. Tristan Perez – TMR4240 Spring 2006 12 Variance check • The variance of each signal is calculated. High variance limit High variance limit • High variance may indicate sensor failure or inaccurate measurement. Calculated signal variance • Low variance may indicate a frozen signal. Low variance limit • Alarm issued to the operator. Tristan Perez – TMR4240 Spring 2006 13 Wild point check • The signal value is a wild point if it is outside a band around the Wild point Wild point limit estimated signal mean. • The signal value will be rejected Measurement for one sample. • Alarm issued to the operator. Wild point limit Tristan Perez – TMR4240 Spring 2006 14 Sensor voting SATELLITE NAVIGATION SYSTEM (DGPS / GLONAS) • Purpose SURFACE REFERENCE SYSTEM – To detect drift of a sensor or position reference system HYDROACOUSTIC POSITIONING • Actions TAUT SYSTEM – Alert the operator WIRE – If possible, automatically ignore the erroneous sensor • Advantage Value – Improved safety – Better utilization of redundant sensor configurations 1 2 3 Sensor No Tristan Perez – TMR4240 Spring 2006 15 Sensor weighting • Manual weighting 3 sensors: – Operator decide weights wi – Advantages: • intuitive understanding of operation • operator experience and judgement is utilized • Automatic weighting – System calculate unbiased minimum variance measurements – Advantages: • best possible measurements in most situations • automatic operation Tristan Perez – TMR4240 Spring 2006 16 Handling loss of signals • Filtering should not give phase to the measurement. • Tf depends on difference of sensors. Maximum change [m/s] is specified. • A change in average value is inevitable. average Tristan Perez – TMR4240 Spring 2006 17 Enabling of sensors • When enabling sensors, average remains smooth. • No filtering of the sensor signals => no phase added to the measurement. average Tristan Perez – TMR4240 Spring 2006 18 Simplified computer control system The implentation of control systems todate require knowledge of • Vessel dynamics • Signal processing • Digital control • Real-time OS Tristan Perez – TMR4240 Spring 2006 19 Continuous-discrete time domains Operator Output Controller D/A converter Process Plant A/D converter Discrete-time domain Continuous-time domain Tristan Perez – TMR4240 Spring 2006 20 Control design The designer of a control system has two choices: • Design in continuous time and implement a discrete-time approximation of the controller • Obtain a dicretised modelled of the plant and design the controller in Discrete time. Each approach has advantages and disadvantages. Tristan Perez – TMR4240 Spring 2006 21 Continuous time design Discrete time implementation Advantages: • Our world is easy to understand in term of continuous time signals and systems. • Models obtained from first principles of physics are continuous time models. • Tools for control system design are more developed for continuous time--- nonlinear control methods deal almost exclisuvely with continuous-time formulations. Disadvantages: • Controllers are implemented on computers, therefore, we need to implement discrete time approximations of our continuous time controllers. • A good approximation of a continuous-time controller often requires fast sampling. We may not be able to do this because of limited computer power and speed, and then the discrete-time nature of the implemented controller may affect performance and stability. • If our model is not complete, we may need to use system identification, which often yields models in discrete time. Tristan Perez – TMR4240 Spring 2006 22 Discrete time design Advantages: • Takes advantage of models obtained from system identification • Allows to do things that continuous-time controllers do not allow: dead-beat control. • Current computer power and speed allow the use of on-line optimisation, and this is having a tremendous impact in the idustry. • Some filtering and control problems are more easyly solved in discrete time (Kalman filtering, contrained optimal control). • It is easy to predict stability problems if sampling is not so fast. Disadvantages: • Not so intuitive • Analysis of non-linear control system in discrete-time is more difficult. Tristan Perez – TMR4240 Spring 2006 23 Review continous-time linear models ODE: Solution: (Convolution) State-space: Solution: Tristan Perez – TMR4240 Spring 2006 24 Laplace-transform Domain SISO: The transfer function is the Laplace transform of output divided by the Laplace transform of the Input MIMO: Tristan Perez – TMR4240 Spring 2006 25 Linear systems frequency reponse If the input is Then, due to the linearity of the systemIf the input is where The Transfer Function evaluated at gives the Frequency Reponse of the system . Tristan Perez – TMR4240 Spring 2006 26 Frequency response Tristan Perez – TMR4240 Spring 2006 27 Sampling continuous-time signals When we sample signals to be processed by a computer, we create ambiguity: Discrete time sinusoids whose frequencies are separated by an integer multiple of 2p fs are identical! Tristan Perez – TMR4240 Spring 2006 28 Sampling theorem and Nyquist rate and Frequency The sampling theorem states that for a limited bandwidth (band-limited) signal with maximum frequency fmax, the equally spaced sampling frequency fs must be greater than twice of the maximum frequency fmax, i.e., fs > 2·fmax in order to have the signal be uniquely reconstructed without aliasing. The frequency 2·fmax is called the Nyquist sampling rate. Half of this value, fmax, is sometimes called the Nyquist frequency. Tristan Perez – TMR4240 Spring 2006 29 Spectrum of sampled signal Sampled at greater than the Nyquist rate Tristan Perez – TMR4240 Spring 2006 30 Spectrum of sampled signal Sampled at less than the Nyquist rate Tristan Perez – TMR4240 Spring 2006 31 Disctretising state-space models If we have access to a continuous time LTI model, then there are different methods that we can use to convert it into a discrete-time model: where the index k denotes that the value of the variables is known at the time instant tk = t0 + Ts k, where Ts is the sampling period, and the index takes the values k = 0, 1, 2, ... Tristan Perez – TMR4240 Spring 2006 32 Euler Method A simple method (although not the one with the best numerical properties) is to approximate the derivative in the state equation in a state space model by an increment: which leads to the Euler Method: Tristan Perez – TMR4240 Spring 2006 33 Zero-order hold (ZOH) ZOH Operator Output Controller D/A converter Process Plant A/D converter The control signal is kept constant in the time interval Tristan Perez – TMR4240 Spring 2006 34 Zero-order hold (ZOH) Using the solution of the state-space equation: We obtain the ZOH equivalent: Note that this is not an approximation, and it reverts to the Euler Method if we use a series expansion of the exponential and keep the 1st term only Tristan Perez – TMR4240 Spring 2006 35 Continuous-time filter design Bacause the Transfer Function evaluated at gives the Frequency Reponse of the system . We can then design so we select the frequencies of interest and eliminate the undesired ones: • Low pass filter: reduce high frequencies • High pass filter: reduce low frequencies • Band pass filter: reduces low and high with respect to a desired band • Notch: eliminates a particular band Tristan Perez – TMR4240 Spring 2006 36 Filter specification Tristan Perez – TMR4240 Spring 2006 37 Filter design Filters can be designed in continuous time and implemented with analog electronics, or discretised. Alternatively the can be designed in discrete time directly. Tristan Perez – TMR4240 Spring 2006 38 Butterworth Filter • Very flat pass band • Small transtiotn band requires high order filters, which introduce a significant phase lag. Tristan Perez – TMR4240 Spring 2006 39 Example 4th order Batterworth Tristan Perez – TMR4240 Spring 2006 40 Chevychev Filters • Chebyshev filters have a steeper roll- off and more passband ripple than Butterworth filters. Tristan Perez – TMR4240 Spring 2006 41 Chevychev Filter Example Tristan Perez – TMR4240 Spring 2006 42 Low- High- Band-pass and notch Filters Once we have a low pass filter protetype, we can easy conver it to other type by a transformation. Tristan Perez – TMR4240 Spring 2006 43 Advantages of digital filter design • Digital filter are programmable, i.e. their operation is determined by a program. This means the digital filter can easily be changed without affecting the circuitry (hardware). • Digital filters are easily designed, tested before being implementied. • Analog filter circuits (particularly those containing active components) are subject to drift and are dependent on temperature. • Digital filters can handle low frequency signals accurately. As the speed of DSP technology continues to increase, digital filters are being applied to high frequency signals in the RF (radio frequency) domain, which in the past was the exclusive preserve of analog technology. • Digital filters can be adaptive to changes in the characteristics of the signal. Tristan Perez – TMR4240 Spring 2006
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