Controller Tuning Using System Identification

In the industries today, less attention has been put on the development of a unified tuning approach for Proportional-Integral-Derivative (PID) controller of Single Input Single Output (SISO) system and Multiple Input Multiple Output (MIMO) system. The current tuning methods are limited and specific to particular systems. This paper focuses on the development of a unified controller tuning method based on Internal Model Control (IMC) method and system identification using software Matlab Simulink. The controller tuning performance of the proposed method tested on SISO and MIMO systems are being compared with the performance shown by the existing tuning methods; Ziegler-Nichols (ZN) and Simple Internal Model Control (SIMC). The evaluation of performance measurement is done based on Integral Absolute Error (IAE), Integral Square Error (ISE), Integral Time-weighted Absolute Error (ITAE) and Total Input Variation (TV). It is observed that the proposed unified tuning method is effective for tuning on SISO and MIMO systems and gives better performance than ZN and SIMC in terms of IAE, ISE, ITAE and TV in both set point tracking and disturbance rejection

Simulation and control of processes

Process control is required in most of the industries to regulate the output of a specific chemical process. Any improvement in control design results in process optimization, consistent production, hence less waste. In this thesis, process dynamics of first and second order systems was studied in terms of a response to a step input change. A software called LabVIEW from National Instruments was used to simulate a number of processes to observe time response and frequency response to calculate gain, phase margin and Bode plots. This was followed by system stability analysis. Programs in LabVIEW were created to calculate Ziegler Nichols settings for controller tuning and dynamic Relative Gain Array for Multiple-Input Multiple-Output (MIMO) systems. Studies were carried out on the dynamic performance criteria for controller tuning by minimizing Integral Absolute Error (IAE). This was possible since data could be collected and analyzed real time. LabVIEW programs were created to fine tune the controller starting with P, I, D values obtained using Cohen and Coon method. Process parameters required for the calculations were determined from Process Reaction Curve (PRC). Open loop circuit was used to measure the temperature/level to obtain a Process Reaction curve. Control of temperature in a heater was achieved by means of closed loop in which power supplied to the heater by a solid state relay was regulated according to the feedback obtained from the thermocouple. Results showed that PRC method was unsuitable for this process. Temperature controller was tuned using trial and error method and best settings were obtained as P = 2, I = 0.02, D = 0.5. It was desired to use Compact FieldPoint by National Instruments (NI) for liquid level controller tuning. After configuration and testing, it was found, however that output signal from the FieldPoint was in the range of 4-12mA which resulted in opening the control valve to only half of its full capacity. The problem was solved by using traditional Data acquisition device from NI to acquire data. PI controller was tuned from the starting values obtained by Cohen and Coon method using error-integral criteria. The best controller settings were obtained as P = 24, I = 0.35

Adaptive Control For Autonomous Navigation Of Mobile Robots Considering Time Delay And Uncertainty

Autonomous control of mobile robots has attracted considerable attention of researchers in the areas of robotics and autonomous systems during the past decades. One of the goals in the field of mobile robotics is development of platforms that robustly operate in given, partially unknown, or unpredictable environments and offer desired services to humans. Autonomous mobile robots need to be equipped with effective, robust and/or adaptive, navigation control systems. In spite of enormous reported work on autonomous navigation control systems for mobile robots, achieving the goal above is still an open problem. Robustness and reliability of the controlled system can always be improved. The fundamental issues affecting the stability of the control systems include the undesired nonlinear effects introduced by actuator saturation, time delay in the controlled system, and uncertainty in the model. This research work develops robustly stabilizing control systems by investigating and addressing such nonlinear effects through analytical, simulations, and experiments. The control systems are designed to meet specified transient and steady-state specifications. The systems used for this research are ground (Dr Robot X80SV) and aerial (Parrot AR.Drone 2.0) mobile robots. Firstly, an effective autonomous navigation control system is developed for X80SV using logic control by combining ‘go-to-goal’, ‘avoid-obstacle’, and ‘follow-wall’ controllers. A MATLAB robot simulator is developed to implement this control algorithm and experiments are conducted in a typical office environment. The next stage of the research develops an autonomous position (x, y, and z) and attitude (roll, pitch, and yaw) controllers for a quadrotor, and PD-feedback control is used to achieve stabilization. The quadrotor’s nonlinear dynamics and kinematics are implemented using MATLAB S-function to generate the state output. Secondly, the white-box and black-box approaches are used to obtain a linearized second-order altitude models for the quadrotor, AR.Drone 2.0. Proportional (P), pole placement or proportional plus velocity (PV), linear quadratic regulator (LQR), and model reference adaptive control (MRAC) controllers are designed and validated through simulations using MATLAB/Simulink. Control input saturation and time delay in the controlled systems are also studied. MATLAB graphical user interface (GUI) and Simulink programs are developed to implement the controllers on the drone. Thirdly, the time delay in the drone’s control system is estimated using analytical and experimental methods. In the experimental approach, the transient properties of the experimental altitude responses are compared to those of simulated responses. The analytical approach makes use of the Lambert W function to obtain analytical solutions of scalar first-order delay differential equations (DDEs). A time-delayed P-feedback control system (retarded type) is used in estimating the time delay. Then an improved system performance is obtained by incorporating the estimated time delay in the design of the PV control system (neutral type) and PV-MRAC control system. Furthermore, the stability of a parametric perturbed linear time-invariant (LTI) retarded type system is studied. This is done by analytically calculating the stability radius of the system. Simulation of the control system is conducted to confirm the stability. This robust control design and uncertainty analysis are conducted for first-order and second-order quadrotor models. Lastly, the robustly designed PV and PV-MRAC control systems are used to autonomously track multiple waypoints. Also, the robustness of the PV-MRAC controller is tested against a baseline PV controller using the payload capability of the drone. It is shown that the PV-MRAC offers several benefits over the fixed-gain approach of the PV controller. The adaptive control is found to offer enhanced robustness to the payload fluctuations

Controller Tuning Using System Identification

In the industries today, less attention has been put on the development of a unified tuning approach for Proportional-Integral-Derivative (PID) controller of Single Input Single Output (SISO) system and Multiple Input Multiple Output (MIMO) system. The current tuning methods are limited and specific to particular systems. This paper focuses on the development of a unified controller tuning method based on Internal Model Control (IMC) method and system identification using software Matlab Simulink. The controller tuning performance of the proposed method tested on SISO and MIMO systems are being compared with the performance shown by the existing tuning methods; Ziegler-Nichols (ZN) and Simple Internal Model Control (SIMC). The evaluation of performance measurement is done based on Integral Absolute Error (IAE), Integral Square Error (ISE), Integral Time-weighted Absolute Error (ITAE) and Total Input Variation (TV). It is observed that the proposed unified tuning method is effective for tuning on SISO and MIMO systems and gives better performance than ZN and SIMC in terms of IAE, ISE, ITAE and TV in both set point tracking and disturbance rejection

Fixed-Order Robust Controller Design by Convex Optimization Using Spectral Models

This thesis proposes a new method to design fixed-order controllers in frequency domain using convex optimization. The method is based on the shaping of open-loop transfer function in the Nyquist diagram with infinity norm constraints on weighted closed-loop transfer functions. A parametric model is not required in this method as it directly uses frequency-domain data. Furthermore, systems with multi-model uncertainty as well as systems with frequency-domain uncertainties can be considered. Fixed-order linearly parameterized controllers are designed with the proposed method for single-input single-output (SISO) linear time-invariant plants. The shaping of the open-loop transfer function is performed based on the minimization of the difference with a desired open-loop transfer function under H∞ constraints on the closed-loop sensitivity functions. Since these constraints represent a nonconvex set in the space of the controller parameters, an inner convex approximation of this set is proposed using the desired open-loop transfer function. This approximation makes the problem of robust fixed-order controller design a convex optimization problem. An extension of the method is proposed to design two-degree-of-freedom (2DOF) controllers for SISO plants. The method is also extended to tune fixed-order linearly parameterized multivariable controllers for multiple-input multiple-output (MIMO) linear time-invariant plants where the stability of the closed-loop system is guaranteed using Gershgorin bands. The control problem is solved only using a finite number of frequency-domain samples. However, the stability and performance conditions between frequency samples are also verified if a frequency-domain uncertainty is considered. It is shown that this adds some conservatism to the solution. The proposed frequency-domain method has been tested on many simulation examples. The method has been applied to a flexible transmission benchmark for robust controller design giving extremely good results. Additionally, the method has also been implemented on an experimental high-precision double-axis positioning system. These results show the effectiveness of the proposed methods

Practical Guidelines for Tuning Model-Based Predictive Controllers for Refrigeration Compressor Test Rigs

This paper presents a practical methodology for tuning the parameters of a model predictive control technique for controlling the suction and discharge pressures of refrigeration compressor in test rigs. Typically, in this type of rig, the compressor under test is subjected to similar conditions as the ones found in refrigeration systems, such as refrigerators and freezers. Even though in industrial practice it is common to find proportional-integral (PI) controllers in such rigs, they are multivariable processes with partial coupling between the variables of interest. Model-based predictive control (MPC) is a control technique which uses an explicit process model to predict the future behavior of the system over a horizon, and then calculates a sequence of control actions so that the future outputs of the process track future references. Thus, since MPC is inherently a multivariable control technique, it can be used, for example, to mitigate the coupling between suction and discharge pressures, thus improving the performance of the control of the compressor operating condition and, therefore, the overall test performance. The study presented in this paper is based on a specific test rig used in industry, but the ideas are presented in a general way so that they can be used as general guidelines for tuning MPC for refrigeration compressor test rigs. The rig considered for this paper has two outputs, which are the pressures at the inlet and outlet of the compressor under test, and two manipulated variables, which are two valve openings. The paper begins by showing how to identify the dynamic models that describe the behavior of the compressor pressures and also how to use them to define an expression that relates the static gains of the models identified with the parameters of the predictive controller, with respect to closed loop-performance specifications of the test. In this study, the model predictive control technique known as generalized predictive control was used and, in addition to the tuning methodology, an analysis of the effects of the controller parameters on the closed-loop results is presented. Finally, the performance of the predictive controller tuned according to the proposed methodology is compared to the results obtained by two independent PI controllers, showing the improvement of the responses for both reference tracking and disturbance rejection. The obtained results are promising and show that the proposed methodology can be used as a starting point for the tuning of predictive controllers applied in test rigs. In addition, it is shown that the use of advanced control techniques, such as model-based predictive control, can contribute to increasing the productivity and operational efficiency of compressor tests

Design of Low-Order Controllers using Optimization Techniques

In many applications, especially in the process industry, low-level controllers are the workhorses of the automated production lines. The aim of this study has been to provide simple tuning procedures, either optimization-based methods or tuning rules, for design of low-order controllers. The first part of this thesis deals with PID tuning. Design methods or both SISO and MIMO PID controllers based on convex optimization are presented. The methods consist of solving a nonconvex optimization problem by deriving convex approximations of the original problem and solving these iteratively until convergence. The algorithms are fast because of the convex approximations. The controllers obtained minimize low-frequency sensitivity subject to constraints that ensure robustness to process variations and limitations of control signal effort. The second part of this thesis deals with tuning of feedforward controllers. Tuning rules that minimize the integrated-squared-error arising from measurable step disturbances are derived for a controller that can be interpreted as a filtered and possibly time-delayed PD controller. Using a controller structure that decouples the effects of the feedforward and feedback controllers, the controller is optimal both in open and closed loop settings. To improve the high-frequency noise behavior of the feedforward controller, it is proposed that the optimal controller is augmented with a second-order filter. Several aspects on the tuning of this filter are discussed. For systems with PID controllers, the response to step changes in the reference can be improved by introducing set-point weighting. This can be interpreted as feedforward from the reference signal to the control signal. It is shown how these weights can be found by solving a convex optimization problem. Proportional set-point weight that minimizes the integrated-absolute-error was obtained for a batch of over 130 different processes. From these weights, simple tuning rules were derived and the performance was evaluated on all processes in the batch using five different feedback controller tuning methods. The proposed tuning rules could improve the performance by up to 45% with a modest increase in actuation

Multivariable System Controller Tuning Techniques Based on Sensitivity Measures

A controller tuning technique using sensitivity functions of the controller parameters is proposed which does not require a detailed model of the plant either based on physical principles or through system identification. Only simple signal processing is required in the tuning process. The sensitivity information is used by an adjustment algorithm involving a least squares type of criterion function. The generation of the sensitivity functions which are of central importance in this approach is described in this thesis, involving use of a signal convolution approach and a two-stage method both in the time-domain and frequency-domain. Three different forms of input signal, which involve the step input, the impulse input and the extended pseudorandom binary sequence (PRBS) input signal are selected in the calculation of the sensitivity functions. The two-stage approach to generating the sensitivity functions of the controller parameters in systems with unknown plants has been investigated for the first time in this research work. The advantage of this novel approach is that there is no limitation on the form of the test input signal. The sensitivity functions can be obtained from measurements directly without any calculations. No problems of implementation arise with the sensitivity filters required. In the controller tuning process, the least squared approach is used to provide the figure of merit for each projected system response. The changes of the controller parameters are altered to minimise the difference between the response of the actual system and the desired response. The details of an application of the tuning procedure using the signal convolution approach for generating the sensitivity functions for a two-tank system with two inputs two outputs both in the time-domain and the frequency-domain are given. Special consideration is given to the accurate modelling of the two-tank system upon which this work is based. Questions of plant nonlinearity and measurement noise and their effects on the tuning process are given careful consideration but no significant problems were encountered. In order to prove that the technique is suitable for more complex problems, the technique has also been applied successfully to helicopter flight control system design optimisation. This is of potential interest as a means of reducing the period of time for test flying and design modification for practical helicopter flight control systems. The tuning process is a very "visible" one and likely to be attractive for applications of this kind. From the results of these two applications of the tuning technique it can be seen that the tuning process is very effective although the initial responses of the system may be far from the desired responses. In fact, the adjustment procedure provides fast is convergence in the cases considered. Significant progress is made at each adjustment without any oscillations in parameter values. The number of experiments needed to generate the sensitivity information needed for controller tuning is, in general, significantly smaller than that required for a traditional parameter perturbation method for sensitivity function generation

Model Predictive Control Using Orthonormal Basis Filter

Proportional Integral Derivative (PID) controller is the most common controller that acts as standard tool in a process control industry. However, when interacting with Multiple Input and Multiple Output (MIMO) process, the interaction is difficult to be controlled by PID controller. Therefore, this project will focus on Model Predictive Control (MPC) that is one of optimization strategy that can control MIMO interaction by predicting the effect of potential control action. In this project, a mathematical model of Orthonormal Basis Filter (OBF) will be developed on the distillation column based on Wood-Berry model with a feedback control (a closed loop system). A simulation of MPC is done by using MATLAB coding while PID is simulated using SIMULINK. Based on the simulation, the performance of MPC and PID controller are evaluated by using the Integral Error Criteria: Integral Absolute Error (IAE), Integral of the Squared Error (ISE) and Integral of the time-weighted absolute error (ITAE) and also with total input variation. Lower integral error criteria and total input variation value indicate a better model accuracy and efficiency of controller for MIMO system