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... controller are tuned. In spite of the fact that the MPC algorithm uses for process prediction a simple linear state-space model with only two state variables, the results of laboratory experiments clearly indicate that the MPC algorithm based on such a model works well, i.e. the algorithm is able to effectively stabilise the robot effectively. Fig. 1 shows a heavy, two-wheeled self-balancing robot, similar to Segway products. It has been built from scratch for research purposes. It weights more than 30kg, mostly because of its batteries (two Pb batteries) which power two DC electric motors (200W each). Motors are integrated with a 1:12 gearbox. Custom-made electronic boards take ...
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... objective of model tuning is to tune model's parameters in such a way that the model error is minimised. The square errors of subsequent (and independent) model simulationsˆYsimulationsˆ simulationsˆY The obtained model may be used to calculate the open-loop step-response, which may be next used in MPC. It is depicted in Fig. 11. Obviously, since the process and its state-space model (3) are unstable, a step of the manipulated variable in open-loop leads to an unstable process output ...
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... the next sampling instant, k + 1, the measurement of the process output is updated, the prediction is shifted one step forward and the whole calculation procedure is repeated. Step-response Fig. 11: Step-response of the tuned ...
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... parameters next to the λ coefficient. Eq. (17) shows that it is necessary to keep both horizon values as small as possible to speed-up the control law computations. It is especially important when the algorithm is implemented in an embedded system and requires a controller with high frequency of intervention (with a very short sampling period). Fig. 12 shows how robot comes back to a stable state after strong manual kick-off. It takes some 2-4 seconds for the MPC controller to fully stabilise the process. It is worth mentioning that the trajectory of the manipulated variable calculated by the MPC controller is much smoother than in the case of the PD one, as shown in Fig 3. On the ...
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... and the MPC controller generates more aggressive control action. 2) Sensor fusion and filtering algorithm implemented in robot's Inertial Measurement Unit (IMU) can be a plausible explanation of scaled-down high frequency tilt angle changes. 3) Soft tires with good grip add extra hysteresis to the robot equilibrium point -it can be seen in Fig. 12. The robot stays stable at different tilt angles within range −4° . . . −8°. This effect has been not taken into account by the simplified model (Eq. (3) and (4)) but still the developed MPC algorithm is able to stabilize the robot very effectively. Future research can focus on reducing the gap between the inferred model and the real ...
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Citations
... Another controller that was used to control the TWSBR was the model predictive controller (MPC) controller. It was implemented in ref. [14] for a heavy TWSBR. The results prove the stability of the proposed controller. ...
The two-wheeled self-balancing robot (TWSBR) is based on the axletree and inverted pendulum. Its balancing problem requires a control action. To speed up the response of the robot and minimize the steady state error, in this article, a grey wolf optimizer (GWO) method is proposed for TWSBR control based on state space feedback control technique. The controller stabilizes the balancing robot and minimizes the overshoot value of the system. The dynamic model of the system is derived based on Euler formula and linearized to state space representation to enhance the control technique. Then, the GWO optimizes the state feedback controller parameters. Simulation results show that the system reaches the zero steady-state error with less than 2 ms, which proves the effectiveness of the proposed controller over the classical state feedback controller in terms of fast response, very small overall error, and minimum overshoot.
... Due to the possibility to use modern calculation platforms with high numerical potential, such as microcontrollers [6] and logical arrays [65], it is believed that these algorithms can be applied to the feedback control of fast processes requiring short sampling intervals of tens of milliseconds or even several milliseconds, e.g. robots [49], combustion engines [55] or drones [66]. ...
Model Predictive Control (MPC) algorithms using nonlinear process models are the subject of consideration in this chapter. The applied nonlinear models are in the form of general difference equations or state-space equations. MPC algorithms using directly nonlinear models in the optimization of the trajectory of the manipulated variables are described in the first part of the chapter. This leads to strictly optimal solutions, but is practically restricted to processes with slow dynamics due to difficult, time consuming nonlinear optimization. For the case of state-space models, the original authors’ approach to the modeling of disturbances and state estimation is presented. The most extensive part of the paper is devoted to effective, suboptimal MPC algorithms with successive linearizations, which enables us to replace nonlinear optimization by a quadratic one. Several versions of such algorithms are presented, with different linearization structures. This class of algorithms enables us to apply nonlinear modeling to fast dynamical systems, leading generally to suboptimal results, but usually fully acceptable in engineering practice. This is confirmed by the presented results of simulation studies of two processes. Finally, augmentations of MPC algorithms to incorporate current set-point optimization are described, to increase economic efficiency of the control structures.
... Kim et al. A model predictive control is applied to an unstable heavy self-balancing robot by Okulski et al. (2018). ...
... Kim et al. (2018) present a positiontracking controller using invariant dynamic surface. A model predictive control is applied to an unstable heavy selfbalancing robot by Okulski et al. (2018). Herein, multivariable discrete-time controllers (pole placement and LQR) are developed and they are applied to unidirectional and bidirectional trajectories tracking. ...
In this paper, a model predictive control scheme is developed for networked interval type-2 (IT-2) Takagi–Sugeno (T–S) fuzzy systems. To prevent the excessive use of bandwidth, the controller is designed in an event-trigger manner. However, the event conditions often require the transmission of all system states, imposing a substantial demand on network bandwidth; on the other hand, they are subject to network delay and packet loss. For this reason, in the existing approaches, event-triggered mechanisms primarily deployed in close proximity to the plant, or observer-based structures are used to enhance flexibility for implementing the controller. However, a common limitation in all these solutions is the assumption of network links being ideal, or at the very least, not accounting for all network-related limitations. The occurrence of faults is also an inevitable factor that has been overlooked in most related methods. To resolve this issue, a more comprehensive framework for event-triggered controllers is proposed in this paper in which an adaptive fuzzy observer is embedded, and the effects due to delay and packet loss are included in this observer. In addition, by developing an adaptive fault estimator and the introduction of a compensator term into the observer and controller formulations, a fault-tolerant performance of the event-triggered mechanism along with the controller is provided. Also, the stochastic stability of the closed-loop system is proved. Finally, the proposed control approach is evaluated using numerical and practical examples.
