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This thesis is concerned with subspace identification and its applications for controller performance assessment and process modeling from closed-loop data. A joint input-output closed-loop subspace identification method is developed which provides consistent estimation of the subspace matrices and the noise covariance matrix required for the LQG benchmark curve estimation. Subspace LQG benchmark is also used for performance assessment of the cascade supervisory-regulatory control systems. Three possible scenarios for LQG control design and performance improvement are discussed for this structure. A closed-loop subspace identification method is also provided for estimation of the subspace matrices necessary for performance assessment. A method of direct step model estimation from closed-loop data is provided using subspace identification. The variance calculation required for this purpose can be performed using the proposed method. The variances are used for weighted averaging on the estimated Markov parameters to attenuate the noise influence on the final step response estimation. / Process Control

In this thesis, black-box models describing the quadcopter system dynamics for attitude control have been estimated using closed-loop data. A quadcopter is a naturally unstable multiple input multiple output (MIMO) system and is therefore an interesting platform to test and evaluate ideas in system identification and control theory on. The estimated attitude models have been shown to explain the output signals well enough during simulations to properly tune a PID controller for outdoor flight purposes. With data collected in closed loop during outdoor flights, knowledge about the controller and IMU measurements, three decoupled models have been estimated for the angles and angular rates in roll, pitch and yaw. The models for roll and pitch have been forced to have the same model structure and orders since this reflects the geometry of the quadcopter. The models have been validated by simulating the closed-loop system where they could explain the output signals well. The estimated models have then been used to design attitude controllers to stabilize the quadcopter around the hovering state. Three PID controllers have been implemented on the quadcopter and evaluated in simulation before being tested during both indoor and outdoor flights. The controllers have been shown to stabilize the quadcopter with good reference tracking. However, the performance of the pitch controller could be improved further as there have been small oscillations present that may indicate a stronger correlation between the roll and pitch channels than assumed.

The actualization of real-time economically optimal process operation requires proper integration of real-time optimization (RTO) and dynamic control. This dissertation addresses the integration problem and provides a formal design technique that properly integrates RTO and model predictive control (MPC) under parametric uncertainties. The task is posed as an adaptive extremum-seeking control (ESC) problem in which the controller is required to steer the system to an unknown setpoint that optimizes a user-specified objective function. The integration task is first solved for linear uncertain systems. Then a method of determining appropriate excitation conditions for nonlinear systems with uncertain reference setpoint is provided. Since the identification of the true cost surface is paramount to the success of the integration scheme, novel parameter estimation techniques with better convergence properties are developed. The estimation routine allows exact reconstruction of the system's unknown parameters in finite-time. The applicability of the identifier to improve upon the performance of existing adaptive controllers is demonstrated. Adaptive nonlinear model predictive controllers are developed for a class of constrained uncertain nonlinear systems. Rather than relying on the inherent robustness of nominal MPC, robustness features are incorporated in the MPC framework to account for the effect of the model uncertainty. The numerical complexity and/or the conservatism of the resulting adaptive controller reduces as more information becomes available and a better uncertainty description is obtained. Finally, the finite-time identification procedure and the adaptive MPC are combined to achieve the integration task. The proposed design solves the economic optimization and control problem at the same frequency. This eliminates the ensuing interval of "no-feedback" that occurs between economic optimization interval, thereby improving disturbance attenuation. / Thesis (Ph.D, Chemical Engineering) -- Queen's University, 2008-08-08 12:30:47.969

In this thesis a quadrotor is studied and a linear model is derived using grey-box estimation, a discipline in system identification where a model structure based on physical relations is used and the parameters are estimated using input-output measurements. From IMU measurements and measured PWM signals to the four motors, a direct approach using the prediction-error method is applied. To investigate the impact of the unknown controller the two-stage method, a closed-loop approach in system identification,  is applied as well. The direct approach was enough for estimating the model parameters. The resulting model manages to simulate the major dynamics for the vertical acceleration and the angular rates well enough  for future control design.

System identification concerns how to construct mathematical models of dynamic systems based on experimental data. A very important application of system identification is in model-based control design. In such applications it is often possible to externally excite the system during the data collection experiment. The properties of the exciting input signal influence the quality of the identified model, and well-designed input signals can reduce both the experimental time and effort. The objective of this thesis is to develop algorithms and theory for minimum cost experiment design for system identification while guaranteeing that the estimated model results in an acceptable control performance. We will use the framework of application oriented Optimal Input Design (OID). First, we study how to find a convex approximation of the set of models that results in acceptable control performance. The main contribution is analytical methods to determine application sets for controllers with no explicit control law, for instance Model Predictive Control (MPC). The application oriented OID problem is then formulated in time domain to enable the handling of signals constraints, which often comes from the physical limitations on the plant and actuators. The framework is the extended to closed-loopsystems. Here two different cases are considered. The first case assumes that the plant is controlled by a general (either linear or non-linear) but known controller. The main contribution here is a method to design an external stationary signal via graph theory such that the identification requirements and signal constraints are satisfied. In the second case application oriented OID problem is studied for MPC. The proposed approach here is a modification of a results where the experiment design requirements are integrated to the MPC as a constraint. The main idea is to back off from the identification requirements when the control requirements are violating from their acceptable bounds. We evaluate the effectiveness of all the proposed algorithms by several simulation examples. / <p>QC 20150126</p>

Na implementação de controladores MPC, o desenvolvimento e a definição dos modelos do processo é a etapa mais crítica e a que mais consome tempo. Normalmente, os modelos são obtidos através de testes de identificação realizados na planta, onde se observam as respostas em malha aberta das variáveis controladas a perturbações introduzidas individualmente nas variáveis manipuladas. Por este motivo, a aplicação das técnicas de identificação em malha fechada a controladores MPC com restrições nas entradas e/ou saídas é, reconhecidamente, uma área de aplicação de interesse crescente. Neste trabalho é estudada a modificação do controlador MPC convencional através da inclusão de uma nova restrição de excitação em adição às restrições normais do controlador, com a finalidade de perturbar o processo de forma controlada, propiciando a identificação em malha fechada de modelos mais precisos do processo, a partir de modelos aproximados. São desenvolvidas quatro abordagens para implementação desta filosofia e apresentadas simulações para vários casos teóricos, utilizando modelos de dois processos industriais obtidos de artigos recentes relacionados a controle multivariável com incertezas nos modelos. Os resultados das simulações indicam que os dados produzidos permitiram a correta identificação dos modelos tanto no caso nominal (modelo igual à planta) quanto para casos onde a planta era diferente do modelo empregado para as predições do MPC. / In MPC implementation, the process models development and definition is the most critical and time consuming task. Normally, the models are obtained through plant identification tests where perturbations are individually introduced in the manipulated variable while the controlled variable open-loop behavior is observed. For this reason, the application of closed-loop identification techniques to MPC controllers with input or output constraints is a growing interest area. This work studies the traditional MPC controller modification with the inclusion of a new excitation constraint, in addition to input or output constraints, whose function is to perturb the process in a controlled way, permitting the closed-loop identification of more precise models, based on known approximated models. Four implementation methodologies are developed and some simulated theoretical cases are presented using models of two industrial processes extracted from recent papers related to multivariable control with models uncertainty. The simulation results show that the obtained datasets allow the identification of the correct model, both in the nominal case (when the model used by MPC is the true model of the plant) and in the uncertain case, where the model used by MPC is different from the true model.

Dentre os fatores limitantes dos sistemas de controle, o tempo morto está entre os mais críticos e de difícil detecção sem testes intrusivos. O conhecimento do seu valor é essencial para a identificação de modelos e na auditoria de desempenho de sistemas de controle. Em virtude disto, o presente trabalho propõe uma metodologia eficaz para estimá-lo utilizando apenas dados históricos de processo em malha fechada. A principal vantagem frente a técnicas disponíveis na literatura é a não necessidade de testes intrusivos. A metodologia é baseada em um tratamento de sinal para remoção dos efeitos do distúrbio não medido e dos erros de modelo. O tratamento de sinal consiste na minimização das oscilações do sinal erro em malha aberta suavizado como função do tempo morto. Diversas formulações de função objetivo e procedimentos de suavização foram estudados visando facilitar a estimação do parâmetro. A qualidade da metodologia é ilustrada através de simulações em uma série de cenários, os quais simulam processos lineares de diferentes características sob o efeito de distúrbios distintos. A metodologia também é testada frente a estudo de casos com dados reais de processo industrial em malhas de nível e temperatura. Os resultados são comparados com métodos da literatura e demonstram que o método proposto foi eficaz na estimação do tempo morto para a maioria dos casos. / Among the limiting factors of control systems, the pure time delay is one of the most critical and difficult to estimate without an intrusive perturbation. The knowledge of its value is essential for model identification and control loop performance assessment. This work proposes a methodology to determine dead time using ordinary closed loop operating data. The main advantage over available techniques is the non-necessity of intrusive plant tests. The proposed approach is based on a signal processing for removing the effects of the unmeasured disturbances and the model-plant mismatches. The signal processing consists of the minimization of the oscillations of the smoothing open loop error as a function of the pure time delay. Several objective function formulations and smoothing procedures were studied in order to facilitate parameter estimation. The quality of the methodology is illustrated by simulations in a series of scenarios, which simulate linear processes of different characteristics under the effect of different disturbances. The methodology is also tested in case studies with real industrial process data. Results are compared to literature approaches and show the method was effective to estimate the pure time delay for most cases.

Industrirobotar är idag en väsentlig del i tillverkningsindustrin där de bland annat används för att minska kostnader, öka produktivitet och kvalitet och ersätta människor i farliga eller slitsamma uppgifter. Höga krav på noggrannhet och snabbhet hos robotens rörelser innebär också höga krav på de matematiska modeller som ligger till grund för robotens styrsystem. Modellerna används där för att beskriva det komplicerade sambandet mellan robotarmens rörelser och de motorer som orsakar rörelsen. Tillförlitliga modeller är också nödvändiga för exempelvis mekanisk design, simulering av prestanda, diagnos och övervakning. En trend idag är att bygga lättviktsrobotar, vilket innebär att robotens vikt minskas men att den fortfarande kan hantera en lika tung last. Orsaken till detta är främst att minska kostnaden, men också säkerhetsaspekter spelar in. En lättare robotarm ger dock en vekare struktur där elastiska effekter inte längre kan försummas i modellen om man kräver hög prestanda. De elastiska effekterna beskrivs i den matematiska modellen med hjälp av fjädrar och dämpare. Denna avhandling handlar om hur dessa matematiska modeller kan tas fram genom systemidentifiering, vilket är ett viktigt verktyg där mätningar från robotens rörelser används för att bestämma okända parametrar i modellen. Det som mäts är position och moment hos robotens alla motorer. Identifiering av industrirobotar är ett utmanande problem bland annat eftersom robotens beteende varierar beroende på armens position. Den metod som föreslås i avhandlingen innebär att man först identifierar lokala modeller i ett antal positioner. Var och en av dessa beskriver robotens beteende kring en viss arbetspunkt. Sedan anpassas parametrarna i en global modell, som är giltig för alla positioner, så att den så väl som möjligt beskriver det lokala beteendet i de olika positionerna. I avhandlingen analyseras olika metoder för att ta fram lokala modeller. För att få bra resultat krävs att experimenten är omsorgsfullt utformade. För att minska osäkerheten i den globala modellens identifierade parametrar ingår också valet av optimala positioner för experimenten. Olika metoder för att identifiera parametrarna jämförs i avhandlingen och experimentella resultat visar användbarheten av den föreslagna metoden. Den identifierade robotmodellen ger en bra global beskrivning av robotens beteende. Resultatet av forskningen har även gjorts tillgängligt i ett datorverktyg för att noggrant kunna ta fram lokala modeller och identifiera parametrar i dynamiska robotmodeller. / Industrial robots are today essential components in the manufacturing industry where they are used to save costs, increase productivity and quality, and eliminate dangerous and laborious work. High demands on accuracy and speed of the robot motion require that the mathematical models, used in the motion control system, are accurate. The models are used to describe the complicated nonlinear relation between the robot motion and the motors that cause the motion. Accurate dynamic robot models are needed in many areas, such as mechanical design, performance simulation, control, diagnosis, and supervision. A trend in industrial robots is toward lightweight robot structures, where the weight is reduced but with a preserved payload capacity. This is motivated by cost reduction as well as safety issues, but results in a weaker (more compliant) mechanical structure with enhanced elastic effects. For high performance, it is therefore necessary to have models describing these elastic effects. This thesis deals with identification of dynamic robot models, which means that measurements from the robot motion are used to estimate unknown parameters in the models. The measured signals are angular position and torque of the motors. Identifying robot models is a challenging task since an industrial robot is a multivariable, nonlinear, unstable, and resonant system. In this thesis, the unknown parameters (typically spring-damper pairs) in a physically parameterized nonlinear dynamic model are identified, mainly in the frequency domain, using estimates of the nonparametric frequency response function (FRF) in different robot configurations/positions. Each nonparametric FRF then describe the local behavior around an operating point. The nonlinear parametric robot model is linearized in the same operating points and the optimal parameters are obtained by minimizing the discrepancy between the nonparametric FRFs and the parametric FRFs (the FRFs of the linearized parametric robot model). Methods for estimating the nonparametric FRF from experimental data are analyzed with respect to bias, variance, and nonlinearities. In order to accurately estimate the nonparametric FRF, the experiments must be carefully designed. To minimize the uncertainty in the estimated parameters, the selection of optimal robot configurations/positions for the experiments is also part of the design. Different parameter estimators are compared in the thesis and experimental results show the usefulness of the proposed identification procedure. The identified nonlinear robot model gives a good global description of the dynamics in the frequency range of interest. The research work is also implemented and made easily available in a software tool for accurate estimation of nonparametric FRFs as well as parametric robot models.

The scope of the thesis is to estimate the parameters of continuous-time models used within control and communication from sampled data with high accuracy and in a computationally efficient way.In the thesis, continuous-time models of systems controlled in a networked environment, errors-in-variables systems, stochastic closed-loop systems, and wireless channels are considered. The parameters of a transfer function based model for the process in a networked control system are estimated by a covariance function based approach relying upon the second order statistical properties of input and output signals. Some other approaches for estimating the parameters of continuous-time models for processes in networked environments are also considered. The multiple input multiple output errors-in-variables problem is solved by means of a covariance matching algorithm. An analysis of a covariance matching method for single input single output errors-in-variables system identification is also presented. The parameters of continuous-time autoregressive exogenous models are estimated from closed-loop filtered data, where the controllers in the closed-loop are of proportional and proportional integral type, and where the closed-loop also contains a time-delay. A stochastic differential equation is derived for Jakes's wireless channel model, describing the dynamics of a scattered electric field with the moving receiver incorporating a Doppler shift. / <p>The thesis consists of five main parts, where the first part is an introduction- Parts II-IV are based on the following articles:</p><p><strong>Part II</strong> - Networked Control Systems</p><p>1. Y. Irshad, M. Mossberg and T. Söderström. <em>System identification in a networkedenvironment using second order statistical properties</em>.</p><p>A versionwithout all appendices is published as Y. Irshad, M. Mossberg and T. Söderström. <em>System identification in a networked environment using second order statistical properties</em>. Automatica, 49(2), pages 652–659, 2013.</p><p>Some preliminary results are also published as M. Mossberg, Y. Irshad and T. Söderström. <em>A covariance function based approachto networked system identification.</em> In Proc. 2nd IFAC Workshop on Distributed Estimation and Control in Networked Systems, pages 127–132, Annecy,France, September 13–14, 2010</p><p>2. Y. Irshad and M. Mossberg. <em>Some parameters estimation methods applied tonetworked control systems</em>.A journal submission is made. Some preliminary results are published as Y. Irshad and M. Mossberg.<em> A comparison of estimation concepts applied to networked control systems</em>. In Proc. 19th Int. Conf. on Systems, Signals andImage Processing, pages 120–123, Vienna, Austria, April 11–13, 2012.</p><p><strong>Part III</strong> - Errors-in-variables Identification</p><p>3. Y. Irshad and M. Mossberg. <em>Continuous-time covariance matching for MIMOEIV system identification</em>. A journal submission is made.</p><p>4. T. Söderström, Y. Irshad, M. Mossberg and W. X. Zheng. <em>On the accuracy of acovariance matching method for continuous-time EIV identification. </em>Provisionally accepted for publication in Automatica.</p><p>Some preliminary results are published as T. Söderström, Y. Irshad, M. Mossberg, and W. X. Zheng. <em>Accuracy analysis of a covariance matching method for continuous-time errors-in-variables system identification</em>. In Proc. 16th IFAC Symp. System Identification, pages 1383–1388, Brussels, Belgium, July 11–13, 2012.</p><p><strong>Part IV</strong> - Wireless Channel Modeling</p><p>5. Y. Irshad and M. Mossberg.<em> Wireless channel modeling based on stochasticdifferential equations .</em>Some results are published as M. Mossberg and Y. Irshad.<em> A stochastic differential equation forwireless channelsbased on Jakes’s model with time-varying phases,</em> In Proc. 13th IEEEDigitalSignal Processing Workshop, pages 602–605, Marco Island, FL, January4–7, 2009.</p><p><strong>Part V</strong> - Closed-loop Identification</p><p>6. Y. Irshad and M. Mossberg. Closed-loop identification of P- and PI-controlledtime-delayed stochastic systems.Some results are published as M. Mossberg and Y. Irshad. <em>Closed-loop identific ation of stochastic models from filtered data</em>, In Proc. IEEE Multi-conference on Systems and Control,San Antonio, TX, September 3–5, 2008</p>