Although it is a simplified model of a helicopter, non-linearity and cross- coupling between subsystems in the model as shown in Figure 4 are still giving significant challenges in extracting the model. The two main subsystems here are the main rotor and tail rotor; the whole system reacts as the impact from these two rotors. In previous study done by Aldebrez et al., the modelling of the system started off with system identification which was said to be the most important stage for getting the model to solve problems . Laws of physics such as electromagnetic and aerodynamics can be found on TRMS, hence the structure of the model can be captured through first principle modelling . Missing parameters are to be found from experimentation and specification table provided by Feedback Instruments. Christensen et al. implemented linearization using Taylor series expansion to convert nonlinear parameters to linear form . Controllers can be designed once the transfer functions of each component are found and linked to form the final model.
Various control approaches were implemented for the control of TwinRotor Multiple Input Multiple Output system . In PID control technique has been proposed for TwinRotorSystem. In, authors defined the coupling effect and dynamic modelling of TRMS and cross coupled PID control was achieved using four PID controllers. InOptimal control technique for TRMS was introduced and in advanced adaptive control technique for twinrotorMIMOsystem was developed. In, the author compared the response of TRMS with PID and LQR controllers. In the present work, dynamic state space model of TRMS has been derived from differential equations. A Linear Quadratic Gaussian (LQG)controller and Linear Quadratic Gaussian controller with integral action(LQGI) have been designed separately. The response(steady state and transient) of the system is analysed for step input.
The twin-rotor multiple-input multiple-output (MIMO) system (TRMS) is a laboratory set-up developed by Feedback Instruments Limited  for control experiments. Its behaviour in certain aspects resembles that of a helicopter. For example, it possesses a strong cross-coupling between the collective (main rotor) and the tail rotor, like a helicopter. A schematic diagram of the TRMS used in this work is shown in Figure 1. It is driven by two DC motors. Its two propellers are perpendicular to each other and joined by a beam pivoted on its base that can rotate freely in the horizontal and vertical planes. The beam can thus be moved by changing the input voltage in order to control the rotational speed of the propellers. The system is equipped with a pendulum counterweight hanging from the beam, which is used for balancing the angular momentum in steady-state or with load.
Constant-gain feedback controllers proposed in early fiftiesfail to provide the better performance for the different operating conditions in high performance aircrafts. Only adaptive controllers that could modify its own behavior through parameter updationdepending on load variablesand variation in the aircraft dynamics are able to offer acceptable performance. Model reference adaptive control (MRAC) technique is attempted  to solve the autopilot design problem for high-performance aircraft.It is considered as an adaptive servo system in which the desired performance is expressed in terms of reference model, which gives the desired response to a command signal.Twin rotor multi input multi output system (TRMS) is considered to be a well-known laboratory prototype with a significant cross coupling and nonlinearitiesfor realisingaero-dynamic behaviour of a helicopter.
In a multi input and output (MIMO) process mathematical modeling of the physical systems has gained importance due to the complexity of interactions within the system. All the parameters used in a model cannot be determined accurately. The major problem in a multivariable process is that loop interaction can arise and cause difficulty in feedback control design. This problem can be solved using centralized or decentralized controllers. One of the centralized techniques is modelpredictivecontrol, which can be measured current to predicted future values of outputs. In this paper, modelpredictivecontrol (MPC) technology for both linear and nonlinearmodel of quadruple tank process is proposed. It consists of four inter connected water tanks and two pumps as shown in figure 1. A general MPC control is presented, and approaches taken for the different aspects of the calculation are described. It is shown that MPC control is more stable, responsive and robust.
RotorSystem (TRS). TRS is a multi input multi output (MIMO) nonlinearsystem. The main objective is to control the angular position of the lever bar of TRS. It is having strong coupling between inputs and outputs. The model is first linearized and then controllers are designed to control the positions of lever bar. Simulations are made in MAT- LAB/SIMULINK. Model parameters are also provided in the end.
Developing efficient control strategies for the control of multivariable system for many areas of engineering is quite challenging due to cost and time consuming on model identification. It is necessary for the controller to have a prototype of the real process to get knowledge about the process it should control. Most of the difficult problems in industries can be preferred to be solved by using ModelPredictive Controller as it has so much impact on industrial control by allowing system restrictions taken into consideration . Liquid Level control for chemical process is a highly remarkable problem in industries. MPC is based on an optimal control algorithm that can yield a good performance under non- linearity and is increasingly significant and successful control approach because of its use of nonlinear multivariable process model and also its ability to handle constraints on inputs, states and outputs. The quadruple tank process in the laboratory is taken into consideration for the analysis by designing and implementation of the predictive controller. Quadruple tank process is a multivariable process which exhibit non-linear behavior . In order to make it easier for deriving the process model that can be carried out to control the lower tanks in the system, its state-space model was developed. The efficiency of the designed MPC controller for constrained and unconstrained situation can be demonstrated by performing simulation studies on the tank system.
Aerodynamic model of TRMS is shown in Figure-1.1. It consists of two propellers which are perpendicular to each other and joined by a beam pivoted on its base. The system can rotate freely in both vertical and horizontal direction. Both propellers are driven by DC motor and by changing the voltage supplied to beam, rotational speed of propellers can be controlled. For balancing the beam in steady state, counterweight is connected to the system. Both propellers are shielded so that the environmental effects can be minimized. The complete unit is attached to the tower which ensures safe helicopter control experiments. The electrical unit is placed under the tower which is responsible for communication between TRMS and PC. The electrical unit is responsible for transfer of measured signal by sensors to PC and transfer of control signal via I/O card.
Physical model of TRMS is shown in Fig. 1. It consists of two propellers placed on a lever arm at perpendicular planes. They are driven by two DC motors. TRMS can rotate freely around yaw and pitch axes. and are the pitch and yaw thrust forces generated by the propellers. The forces are functions of the input voltages and controlling the pitch and the yaw motions of the system. The rotation of the each propeller also causes cross coupling load torques on the motor shafts that occur at the perpendicular axes in terms of input voltages. and are the distances from pitch and yaw rotors to the pivot point of the system. is the center of mass length along TRMS body from pitch axis. is the force due to gravity acting through the centre of mass.
Sliding mode control is another form of robust control with the added advantage of being applied to nonlinear systems. It also offers the advantage of being able to guarantee robustness over a known operating range and in the face of known bounded disturbances. However in order to ensure perfect tracking using the generic SMC design methodology the system must be square, meaning it must have the same number of inputs as states. The TRMS has only two inputs and six or seven states (depending on the model) making it underactuated. The general solution to this problem is to decouple the system into two single input single output (SISO) systems     .
system dynamics on a neighborhood of the origin is still used to prove Lya- punov stability, but not for attractivity. Although continuity of the system is still assumed in (Meadows et al., 1995), where it is shown that MPC can generate discontinuous state-feedbacks, the Lyapunov stability proof (Theo- rem 2 in (Meadows et al., 1995)) does not use the continuity property. Later on, an exponential stability result is given in (Scokaert et al., 1997) and an asymptotic stability theorem is presented in (Scokaert et al., 1999), where sub-optimal MPC is considered. The theorems of (Scokaert et al., 1997, 1999) explicitly point out that both the system dynamics and the candidate Lyapunov function only need to be continuous at the equilibrium. Stabili- ty of sub-optimal MPC is proven in (Scokaert et al., 1999) under the usual assumptions (existence of class K bounds on the candidate Lyapunov func- tion V and its forward difference) plus the extra requirement that the MPC optimal sequence of controls is upper bounded in norm by a K function of the norm of the state. A recent overview on stability of receding horizon control in discrete-time can be found in (Goodwin et al., 2005). Although continuity of the system dynamics and local continuity of V are assumed in (Goodwin et al., 2005), the stability proof (Theorem 4.3.2 in (Goodwin et al., 2005)) only uses continuity of V at the equilibrium, as done in (Meadows et al., 1995). The interested reader can find a general stability theorem for discrete-time MPC that unifies most of the above results in (Lazar et al., 2007a).
Similarly, we note that the synchronous generator speed deviation (∆ω) is also disturbed by the short-circuit event. Fig. 5 shows the speed deviation response of the generator, where the dotted line indicates the system response with the classical PSS; solid red line indicates case with our BNMPC; whereas solid blue line shows the system behaviour with the linear MPC scheme. In this case too BNMPC ensures good transient stability compared with the PSS and slightly better settling time when compared with the linear MPC.
The main focus of the thesis lies in modelpredictivecontrol (MPC) of nonlin- ear systems. MPC is the favored control technique when an advanced control scheme is implemented (Maciejowski (2002); Camacho and Bordons (2004); Be- quette (2007)). This is highlighted by the application in as various fields as the metal ore industry (Jovanovic and Miljanovic (2015)), the food industry (Kondakci and Zhou (2017)) and the nuclear industry (Eliasi et al. (2012)). The traditional process industry is where it has had its major impact (Qin and Badgwell (2003)) with a growing number of applications since its first imple- mentation in the 1970s. The first software introduced were the IDCOM, but earlier applications were done at Shell Oil utilizing their MPC tool referred to as dynamic matrix control (DMC). Though these techniques were not direct developments from the linear quadratic controllers developed in the 1960s, they have plenty in common. Recurring features include the utilization of a linear model to predict the behavior of the process and that the control performance is obtained based on the optimization of a quadratic objective. However, one of the strengths of MPC, the constraint handling, was not addressed stringently in the early approaches. The constraint handling was rather a part of the second generation setups and software; IDCOM-M, QDMC as well as newcomers with software such as HICON and setups like predictive functional control (PCF) to name a few. One of the major developments in the 1980s was the Shell multi- variable optimizing controller (SMOC), which heralded the use of state-space models into MPC. The state-space model has more or less become the norm in research, while still not totally embraced by the industry (Qin and Badgwell (2003)). This is because most software-based model identification usually relies on response modeling, which will be the model applied the MPC as well. As could be expected the MPC performs best when the time is set aside to do fundamental modeling rather than relying solely on empirical modeling.
In comparison with a fixed time delay, results are already a lot better. The system stays stable everywhere and only at the third step (of 9°C) the system still oscillates when the setpoint changes again. Taking into account the variability of the time delay, is a big improvement for our model. It becomes a lot more realistic. Predictivecontrol heavily relies on the quality of the model at hand. With an improved model the output prediction is better, leading to a more accurate determination of the optimal input. This allows setpoints to be followed in a wider range around the equilibrium point ∗ .
Modelpredictivecontrol (MPC), on the other hand, is a model based advanced control technique that have been proved to be very sussefull in controlling highly complex dynamic systems. It naturally supports design for MIMO and time-delayed systems as well as state/input/output constiants. MPC is generally based on online optimiza- tion but in the case of unconstrianed linear plants, closed form solutions can be derived analytically. MPC usally requires a high computaional power; however, since chemical processes are typically of slow dynamics, they have been designed and implemented on various chemi- cal plnat with great success. Therefore, MPC seems to be good candicate for controlling MMA polymerization based on physical (first-principle) modeling.
The contribution of the proposed solution is that it permits to solve the formation control problem for a wide class of vehicles which satisfy a set of requirements typically possessed by unmanned vehicles. The proposed solution takes into account saturation constraints for the control actions, together with collision avoidance constraints. Moreover it is fully decentralized, thus each control agent must solve only a reduced optimization problem. Finally stability is granted by adding an auxiliary vector which imposes an upper bound to the system states. The authors are currently working to modify the proposed approach in order to deal with asynchronous communication and packet loss, by allowing a limited variable delay for each packet and introducing a fault tolerant policy whenever the delay exceeds the chosen thresholds. Both these aspects, together with a practical implementation of the proposed algorithm on a real system, are actually under investigation.
A nonlinearmodelpredictive controller has been developed to maintain normoglycemia in subjects with type 1 diabetes during fasting conditions such as during overnight fast. The controller employs a compartment model, which represents the glucoregulatory system and includes submodels representing absorption of subcutaneously administered short-acting insulin Lispro and gut absorption. The controller uses Bayesian parameter estimation to determine time-varying model parameters. Moving target trajectory facilitates slow, controlled normalization of elevated glucose levels and faster normalization of low glucose values. The predictive capabilities of the model have been evaluated using data from 15 clinical experiments in subjects with type 1 diabetes. The experiments employed intravenous glucose sampling (every 15 min) and subcutaneous infusion of insulin Lispro by insulin pump (modified also every 15 min). The model gave glucose predictions with a mean square error proportionally related to the prediction horizon with the value of 0.2 mmol L −1 per 15 min. The assessment of clinical utility of model-based glucose predictions using Clarke error grid analysis gave 95% of values in zone A and the remaining 5% of values in zone B for glucose predictions up to 60 min (n = 1674). In conclusion, adaptive nonlinearmodelpredictivecontrol is
economy is being exposed to shocks in credit spread. In particular, our model incorporates investment as one of endogenous constraints. By using a nonlinearmodelpredictivecontrol approach, we have examined how finan- cial instability is created endogenously. The model established in this paper can be used to capture the core of the financial instability hypothesis and demonstrate financial endogenous instability. Our theoretical model im- plies that unfavorable credit spreads and high leverage ratios play an important role for the recession of the in- vestment and financial instability. In the presence of large credit spreads and high leveraging, increasing lever- aging can induce instabilities and the meltdown of investment. In terms of policy implications, our results strongly suggest that excessive leverage is one of the important reasons leading to declining investment at pre- sent in China, and so deleveraging can be currently a wise strategy in China. For future research, one may con- duct empirical test to verify the theory developed in this paper.
Rockwell Automation MPC technology uses hybrid modeling capabilities that enable each model to incorporate all available knowledge about the process to deliver the most accurate, highest fidelity models possible. Rockwell Automation uniquely provides a single solution that can handle both nonlinear and linear processes simultaneously, providing consistent results across a wide range of process technologies.