Through the overall analysis of the three-degree-of-freedom helicopter model experiment system, the idea of multi-model switching is introduced and a multi-model LQR controller is established. Aiming at the multi-model LQR controller, the mathematical model is set up by taking altitude angle and pitch angle as variables. The simulation experiment of the controller is carried out by using MATLAB. The tracking accuracy, rapidity and overshoot of the helicopter altitude angle, pitch angle and rotation angle are measured directly. The control effect of the controller is good or bad. The multi-model LQR controller with the best control effect is applied to the helicopter physical model. Real-time workspace (RTW) in MATLAB and Wincon, the special control software of Quanser Company, are used to realize the real-time control of the helicopter physical model. The control effect is good. In the late 1970s, we began to study helicopters. We introduced mature helicopter models such as Black Eagle and Apache from developed countries which are leading in the world in helicopter research, such as the United States and France. However, for a long time, our efforts only stop at how to imitate others, and at most make some modifications on the basis of others. We have not really succeeded in the core areas of helicopter technology.
For example, the core control system of helicopter flight has made few achievements, which puts forward higher requirements for later scholars and researchers. It urges us to further explore [1]. In domestic colleges and universities, Liu Xin of Northeast University designed the PID controller for the helicopter first, then designed the fuzzy controller for the helicopter system, and finally combined the two together to design a control method combining fuzzy control and PID control, which achieved good results; Ge Jinlai of Shandong University, he not only designed the PID controller for the helicopter system, but also designed the fuzzy controller for the helicopter system. The PID and LQR controllers are designed, and the experiment of whether the helicopter model has the disturbance of Active Disturbance System (ADS) is carried out. Finally, the performance-guaranteed control of the helicopter model is studied [13]. Foreign controllers, such as Jonas Witt, are designed by using the nonlinear approximate model predictive control; Ali T. Kutay has completed the design of the controller.
Self-adaptive output feedback control; Konstantin K. Starkov designed a sliding mode controller for the control of non-linear system; Mitsuaki Ishitobi also used parameter identification method to carry out a series of closed-loop control on the basis of predecessors. The above control methods do not model the helicopter model system, but use the theoretical analysis method of the non-linear system to design the controller. However, the non-linear theory itself is not a perfect theory, so there are inevitably some approximation or neglect of secondary factors in the design of controllers, leading to real-time control in accuracy is not satisfactory, most of them are still in the simulation stage, but the requirements are not very strict. The system still has great reference and guidance value. In this paper, a three-degree-of-freedom helicopter model developed and manufactured by Canadian Quanser Company is used as an experimental platform. Based on the real-time Workshop (RTW) physical simulation control system of the system, the dual-rotor three-degree-of-freedom helicopter model is thoroughly studied in this development environment, and a new type of control is designed by using the theoretical results. The controller can control the position and flight speed of helicopter model. As a simulation platform for the study of tandem twin-rotor helicopter, the experimental system is mainly composed of hardware system and software system. The hardware system includes mechanical control system and electrical control system. The control process can be simply described as follows. The helicopter flight attitude is transmitted to the computer through the data acquisition card. The computer processes all variables in real time. Then the control command is transmitted to the power module through the motion control card to control the power supply voltage of the helicopter drive motor, so as to adjust the flight attitude of the model. The whole experimental system can be clearly shown by the block diagram shown in Fig. 1. The hardware system of Quanser’s three-degree-of-freedom helicopter model experiment system is composed of helicopter body, power module, data transmission line, data acquisition card and a computer.
The helicopter body belongs to the mechanical control part of the hardware system, and the data transmission line, the data acquisition card, the power module and the computer belong to the electrical control part of the hardware. The software system used in the helicopter model experiment system in this paper is completely installed in a special computer for experiment, including Wincon [2], a control software based on Simulink software package in MATLAB and TCP/IP technology developed by Quanser Company, and RTW real-time workspace generated and optimized from Simulink. Establishing multi-model controllers by weighting: The method needs to apply the segmentation theorem in mathematical theory. According to the weight proportion of each independent model, the final controller can be obtained by using probability weighting method. According to a switching strategy, multi-model controllers are established: ensuring the stability of controller switching is the primary premise of this method. Because this method is more direct than the first method and is not difficult to design, various research results emerge in endlessly [5,6]. In the process of this study, the second multi-model research method introduced above, namely the control strategy of model switching, is used. Around the three-degree-of-freedom helicopter model experiment system, according to the actual changing characteristics of the model, several models are established to form a reasonable multi-model set, which can approximate the real dynamic performance of the helicopter system in flight as much as possible. Based on this multi-model set, a set of multi-model controllers is designed. Finally, based on the real flight, a set of multi-model controllers is designed. In order to achieve more effective control of complex systems, different models of line state are selected to approximate the current state, and the corresponding controller is the most suitable for the current helicopter state to implement the control strategy. Therefore, according to the actual situation of helicopter model flight, the model parameters suitable for the current system are established by using the idea of model switching instead of the model weighting theory. At the same time, several groups of LQR controllers are designed. Each group of controllers sets the sum matrices corresponding to the current situation respectively.
The most direct and effective control quantity is obtained, which makes the helicopter track the given signal quickly and accurately. The block diagram of the control method is shown in Fig. 2. In the process of realizing the multi-model control theory, the first problem is how to establish a clear mathematical model for the control process. In the actual research process, only the input and output of the system can be taken as the entry point, and some common identification methods, such as the non-linear autoregressive moving average model, can be used.
The multi-model control strategy that decomposes and synthesizes first can solve this problem to a certain extent. Some object systems with complex structure can not get the model that can contain the whole control domain. Therefore, the piecewise method is used to establish the appropriate model for each piecewise region, and then these piecewise models are processed mathematically, whether it is the case or not. Weighting or switching are feasible means. This method mainly includes two aspects: one is to decompose the problem; the other is to use appropriate methods to synthesize. The ultimate goal is to select an appropriate method to effectively combine the previously decomposed piecewise model with the controller to get the final result. Through consulting a large number of related literatures, we know that in the field of multi-model method to build model sets, linearization of non-linear systems [7], T-S Type Fuzzy Multi-model [8-10], neuron network multi-model [11], instant learning algorithm [12-16] are widely used and the effect is obvious. In view of the structural characteristics of Quanser’s three-degree-of-freedom helicopter model experiment system, based on the original mathematical modeling, the physical characteristics of the experimental system are further analyzed, and the previous approximation and linearization are reconsidered to establish a more accurate mathematical model. The helicopter altitude angle and pitch angle are taken as the entry points for the establishment of multi-model sets, and the multi-model sets of multi-model LQR controllers are obtained, thermostatic element as shown in Table 1. Finally, through the control software Wincon based on Simulink software package in MATLAB and TCP/IP technology developed by Quanser Company, the compiled control statements are applied to the three-degree-of-freedom helicopter body connected to the data acquisition card and power module through the encoder and data transmission line to achieve the final control of the helicopter model object. Objective. The control effects of single model LQR controller and multi-model LQR controller are compared and analyzed in Simulink simulation and subsequent physical platform. Firstly, a single model LQR controller is used to simulate the helicopter model in Matlab. In the initial stage of simulation, a relatively simple function curve is used as a given signal. A sinusoidal signal with a period of 100 seconds and an amplitude of 20 is used as a given signal of the height axis. The tracking effect of a single model LQR controller is shown in Figure 3 below. Similarly, the sinusoidal signal with the same period of 100 seconds and the amplitude of 20 is used as a given signal, and the multi-model LQR controller is designed for the flight tracking control of the altitude axis. The results are shown in Fig. 4.
Through the comparison of figs. 3 and 4 above, it can be clearly found that the single model LQR controller has large overshoot and long adjustment time in the process of tracking sinusoidal function curve. It can achieve better tracking effect only when the simulation time reaches 200 seconds in two cycles, and the performance of multi-model LQR controller is much better. In a single model LQR controller, not only the change of given signal can be well tracked in about 50 seconds, but also the overshoot is much smaller than that of a single model LQR controller.
After completing the preliminary simulation experiments of the two controllers, more complex experiments will be carried out. The most effective and reasonable way is to change the given function signal into stepped square wave. Because the stepped square wave is a group of constantly changing signals, the actual requirement of helicopter changing flight attitude during flight is simulated very well. At the same time, the stepped square wave can keep stable for a period of time, which coincides with the fact that the aircraft flies smoothly for a long period of time. Therefore, stepped square wave is a good tracking signal source which can perfectly simulate the real flight condition of helicopter. In the physical simulation, the stepped square wave, which is the most simulation and practical significance for the actual flight of helicopter, is used as the given signal. The tracking effects of the altitude axis and the rotation axis are shown in Fig. 5 and 6, respectively. From the physical curve, we can see that the performance of multi-model LQR controller in helicopter is still satisfactory, which shows that the controller we designed is quite successful. Firstly, this paper introduces the structure of Quanser’s three-degree-of-freedom helicopter model experiment platform, and introduces the hardware system and software system respectively. Through the study of multi-model control, the design of multi-model LQR controller focuses on the realization of multi-model control through model switching. Secondly, aiming at the requirement of multi-model set for multi-model control, the mathematical model of helicopter model was optimized, and the angle factors which were neglected before were restored in the differential equation. The multi-model set was designed for the angle variables of altitude angle and rotation angle. At the same time, LQR control was designed for each model.
A set of LQR controllers is obtained to complete the design of multi-model LQR controllers. By comparing the simulation results, the advantages of the multi-model controller are brought into full play, and the control effect is obviously better than that of the single-model LQR controller. In the subsequent physical control of helicopter, the performance of multi-model LQR controller is still very good.